In a sentence that will surprise no one, I absolutely love Dark Souls. It is my most played game of...ever. On PC alone, I have put in 120 hours, after putting in nearly 200 on XBox. I know that doesn’t sound like a lot compared to people who really like games like Civ 5 or Skyrim, but for me, that is some serious dedication. So basically, I know a thing or two about the game, and hold it near and dear. With that, I wanted to talk about the preorder bonuses that everyone has been ranting and raving about, and why they don’t matter. At all.
1. The Game Isn’t About Your Gear
This isn't my accomplishment. I am not that masochistic
There are a lot of ways that you can prove this point to yourself. Consider level one runs where the character doesn’t have the stats to wield anything too strong, yet they can still beat the game. I know I have imposed many a challenge run on myself for the game, including using only a whip, only a fist, uppercutting bosses to death, only using a crossbow to kill bosses, and outside of that I have used a vast majority of the weapons during a normal playthrough. The only weapon I don’t think would be relatively easy to beat the game with is the broken sword. After the first sword you pick up, anything can take you from T to G. Taurus….to Gwyn….it sounded cooler in my head, OK? The reason for this is because Dark Souls isn’t about how good your character is, its about how good your player is. Everything is about how you play.
Think about what made Blighttown hard on your first playthrough. Assholes with poisoned clubs. Assholes with poison darts. Assholes that jump on to you. Assholes that shoot fire at you. A single asshole with tentacles. Also, the fact that you don’t know where you are going, and a single misstep can send you back twenty minutes of progress. And at the bottom of Blighttown, what do you find? Some asshole poisoned the entire bloody swamp, and you have to crawl through it. So now you have to wander by assholes with teeth, assholes with rocks, assholes with clubs, while on a timer, searching for a bonfire (assuming you thought it was there...you could just try and rush the boss). So what does your super awesome weapon do? Let you stab the swamp? Slash the poison out of your system? Just like you will slash the boulder trap in Sen’s? All in all, the design, the placement, and the war of attrition will bring down an idiot with a good sword in no time flat.
Finally, the bosses. I spent a run just trying to build the highest damage I could. The strongest weapon, crystal magic weapon, and power within. There was a lot of sequence breaking and grinding to get that going. And yeah, it helps a lot to have a weapon that can do 900 damage in a single hit to a boss. But do you know what I knew? Every single bosses animation, the relative timing to swing my weapon, and how long I have before they will counter. The strength would do me nothing fighting against a tough boss. A lesson I learned my tenth time fighting Kalameet.
2. Weapons Are (kind of) Balanced
Quick, name the best weapon in Dark Souls! Is it the low durability lightning katana? The long animation Avelyn? Slow as balls Dragon Tooth? The ‘30 seconds is all I need’ Ricard’s Rapier? As I mentioned above, every weapon is viable. In order for this to be possible, they all have to be within the same power curve, offering the same DPS, plus or minus a few. Why do I say ‘kind of’ above? Novelty weapons. The whip sucks something fierce. The shotel is cute. The bleed on the LIfehunt Scythe is symmetrical.
3. Invaders Will Always be Dicks
I saw a lot of people say things along the lines of ‘but then people who pre ordered will have better gear to invade people with’. Have you never played Dark Souls online? So many times I would make it to the Parish to be invaded by a player in full dragon form with a +5 lightning weapon. The only time where this is a valid argument is if you played the game on the midnight release for the first four hours. After that, you are going to have low level players with high level gear griefing those who know less about the game. The speculation is that the pre order weapons will have less scalability into the mid game, which means that you should replace them after maybe four or five hours. The good weapons will probably be maybe twelve hours in before someone figures it out? After a week, there will be a guide on how to rush to the most overpowered weapon at level one, just to invade people at the start of the game. There will be videos. There will be indictments. There will be Dark Souls.
4.Accessibility Doesn’t Suck and There is Some Custom Difficulty
I’ll go ahead and say it. I believe it. The first Dark Souls could have used some improvement. Especially to make it more accessible. You can’t play at the highest level until you understand equipment burdens, poise, and stability. It could have stood to teach you more about kindling and reinforcing weapons. Trying to beat the gargoyles with a +0 halberd and 5 estus was not fun for me. The game was torture. But it was pretty, and it was different, so I wanted to keep going with it. If items like the pre order ones let people get a little bit further in than they would otherwise, if it lets them get hooked into the game, then so much the better. On top of that, this in no way affects how you get to play the game. If you want to start with a slightly worse weapon and impose some more strict guidelines, you have that ability! I have been doing it since about playthrough 3, because otherwise the game is too easy, and too much the same. Or you could go Diablo on it and beat the ‘too easy’ version and go straight to NG+. Or run and get yourself cursed early. Turn off the HUD. The game doesn’t hurt for challenge if you look for it.
Yeah, I'm starting a blog with Fiddler on the Roof. Don't like it? There's the door.
A lot of my previous chart ons have focused on mechanics found inside of games, but today, I decided to go into something else behind the scenes in games, but not directly used in the game while playing: Matchmaking. There are actually a lot of different ways to match players of similar skill together, and man, do they ever get complicated. I’m not going to say that the subject matter is over my head, but the way it is presented anywhere else is what I call “pumpernickel”: it is very dry, and very dense. There’s a lot of greek, and just mathematical grossness. And when its me saying that? You know its bad. But with that, I wanted to talk about 3 methods.
This isn't relevant to anything here. Or anywhere. This is garbled math of use to no one, from one of the sources I was looking at. Scary stuff.
I just came to say "Elo"
The first method is the Elo method, often pronounced “E. L. O”, and not to be confused with the guys who sang Mr Blue Sky. Can we talk about music instead? No? Math? Balls. So Elo ranking comes from a guy who really, really liked chess with the last name of Elo. The system has you starting with an arbitrary amount of pointsl. When you play against someone else, the difference between your scores is the system’s prediction of who will win.
Getting a bit more complicated with this, each player’s skill level is on a bell curve, which is you have been reading these for a while means you know where this is going. The reason why you are on a bell curve is because the ranking isn’t completely precise: You are expected to perform at your skill, but maybe that day you are just on fire, or possibly hung over. And no, I don’t care to elaborate if that condition is supposed to aid or impede your performance. Basically, there can be exceptions to your skill, otherwise, there would never be upsets.
So sick of googling "bell Curve" for these
When talking specifically about Chess and the system that Mr. Blue Skies set up, the bell curve that was used was very specific. The intention was that if two players were separated by 200 points of skill, that the more advanced player should win 76% of the time. In my research I read 76% and found that to be quite odd...it doesn’t say if they figured out the math first and backed into 76, or started with ¾ and backed into the curve, but either way isn’t clean, as it returns a standard deviation of 283 units. How does it do this? Any normal curve shares some characteristics, which can be solved forwards to get the cumulative distribution for a given “X”, or backwards, to get an X value for a given percentage. This is what a z table actually provides, but fortunately I had Excel to back into my number! This 283 tells us that at a difference of 0 in skill, the game should end up in a draw, at 283 the better player is favored by 34%, at 566 the odds increase (or decrease depending on which side of a one sided ass beating you are on) to 47.7, and at 849 your fate is sealed at 49.7. Now, if you were curious how to figure this out yourself, you just need to create an imaginary bell curve, and place yourself at the mean, or center. Then, find your opponent's skill and draw a line straight up from that point on the curve. Any area under the curve to the right is your odds of winning, and any area under the left is your opponent’s chance of winning. In this example, a 50 point difference represents about a 7% chance for a player to win, so it is probably a close game. 25 would obviously be better, but you would be looking for people in a similar population.
The last piece of this puzzle is how your rank changes as you win or lose. The system that ELO uses is called a “K Factor”, and it is important to note that this number is debated to absolute death by people who are bad at the sport. Hah! Burn! But seriously, there are many ways to come up with a K Factor, but they all revolve around some key ideas. The first is that there is a floor and a ceiling to how many points you can gain or lose. For instance, chess sets this value to 24 per game. The next important step is how to distribute these points, and this is generally accepted (in my research) as your chance of winning minus the outcome, multiplied by the K Factor. The outcome is binary, so 0 is a loss and 1 is a win. If you are favored 10% and win, you get 10 percent of the K. If you are a supreme underdog (or not properly rated) you can get the full value. Some other systems have the K factor change as you play on. For instance, chess has a larger K factor for newer players, but as you play more games, the K factor decreases.
This system is also used by League of Legends, incidentally, and does also use games played as an adjustment for the K Factor, although I couldn’t find the explicit formula. What are the advantages or disadvantages? Well in theory new players will find their skill bracket quicker, for better or worse. Many people feel it is unfair at the early stage because it is more random, so pushing you into a lower bracket doesn’t really represent your skill. These people are also sore losers. Another concern is “ELO Hell” or being in “The Trench”. This effect is where you are ranked, and the system is confident, so you cannot escape your rank because each game doesn’t contribute enough points to get you out of your rank. That being said, the system is what it is, and has been good for chess for quite some time, with minimal in fighting.
I wanted to take a little bit of time to talk about Magic The Gathering, as it also used an ELO system in the past, with a K Factor of 8, if memory serves. However, the designers felt that the system was putting too many constraints on the players and wanted to change it. The main problems they wanted to solve were 1. players would sit idly at high ELO rankings to avoid losing precious points, 2. players would become nervous while playing, which would cause them to spend less money on cardboard crack, and finally 3. geographical concerns. If I play Magic every week against the same people, I don’t have an opportunity to change my bracket significantly. As a quick aside, League does solve for #1 by having an ELO decay, forcing you to play a certain amount of matches or else you lose your ranking. Surely, no one would sit idly just to get a 10 game winning streak though, right? Right?
Back to Magic, they actually switched over to Planeswalker Points, their proprietary system. How do those work? If you lose you get 0 points. Tie, you get 1. Win, you get 3. And that’s it.
This, in my opinion, is a terrible system for anything more than ego stroking. Let me explain: First of all, this assumes that games played equals an increase in skill which is completely incorrect. One of my DOTA loving co workers has a friend who refuses to learn from his defeats. He refuses to update his skill builds. He doesn’t counter pick. He doesn’t learn. His playing skill has capped out, and his learning skill refuses to grow. If he nurtured those while playing, his skill might increase, but as it is, he has been complaining about being stuck in “The Trenches” for a while. Anecdotally, I have played 80 games and found myself playing with people who have played anywhere from 150 to 400 to 1200 games. The biggest problem with this system is that a newcomer doesn’t get accurately ranked. You could be a strategic mastermind, but unless you play harder than people who have been playing their whole lives, your ranking will never ever reflect this, which goes against the idea of matchmaking entirely. It does breed a friendlier format, and also encourage people to play more (thus, spending more and more money on 100 dollar Planeswalkers).
By far, the most interesting thing I found in my research though was TrueSkill. Have you heard of True Skill? It is a matchmaking system designed in 2006 by Microsoft, specifically for XBox Live. Usually when people compare the PS3 to the 360 it is price against the stability against the community, but I think it really says something about Microsoft where they researched a new system for their matchmaking. I thought it was pretty cool. The XB1 has also seen some improvements of the online area, which they really brought up in marketing, so it is clear that they care about this kind of stuff. And just so I don’t lose people who hate Microsoft, this system is also used (in some ways) by DOTA.
So how does this system work? It still has the same bell curve system for your skill, but it adjusts the bell curve’s standard deviation by another factor: certainty. If you are a new player, you are assigned a rating of say 25, and an uncertainty of 8.3. Why 8.3? It assumes your skill is anywhere between your skill +/- the uncertainty times 3. So your skill is between 0 and 50. (Note: remember how the difference in ELO was 200? A significant difference here is actually 6, judging by one of my sources. Like I said, it varies a lot). There is a super fancy term for this uncertainty called Bayesian_analysis. As you play more games, the certainty factor changes. So if you are an 80/20 to win, and you win, your ranking goes up and the system is more confident in your skill, and vice versa (losing decreases certainty and ranking). There are some interesting interactions with all of this. The first is that if you play against a game with 7 other people at your same rank and certainty and you come out in first, the system figures increases the amount it distrusts your skill level. Why? You haven’t met your match yet! You never hit your skill ceiling this game. Unfortunately, that also applies to whoever was unlucky enough to get the biggest beatdown that game. The people who are in the middle are the people whose certainty moves the least.
The other thing that separates this system from the ELO ranking is that it can compare more than 2 teams. From what I have gathered, in ELO two teams of five are grouped together into a single ranking which is used to determine points allotted after the match. TrueSkill compares each player and each team against each other to determine how many points they should receive. Kind of neat that way. This also means that when you place you are ranked against each other player. In an 8 player game, your rating actually changes 7 times to its final results, depending on who you outperformed and underperformed against. In this way, the rating is much more a result of your actions in the game as opposed to the teams action, and your individual contributions to the result can be taken into consideration for your overall ranking. Sadly, I don’t have any hard math on this, because I honestly don’t follow a lot of the numbers because I am doing this at home with the comforts of Reptilia and Laphroaig. So sue me.
The drink of all statisticians
There were a few things specific to XBox that were rather interesting in there as well. If a game only has 2 players, it adjusts to a system similar to ELO. If there are outside factors, such as lag, it can update your skill based on partial results. That one had a URL labeled “math paper” behind it so I was not touching that bad boy. I clicked on it and saw “Bernoulli” and “Gaussian” and just about crapped my pants. OH GOD. I FOUND THE CALCULUS. No. Thanks. Finally, just because everyone loves a circlejerk, this same method is applied to Bing to figure out how best to deliver ads to people.
Last Note on Matchmaking
Now here is something that is really rather curious: in both Chess and Magic the rating isn’t as important as in TF2, DOTA, LoL, and Halo. Why? Geography. The best players in the world rarely get a chance to test their skills against the other best players, with rare exceptions of large tournaments. Because of this, ratings aren’t as important in the actual matchmaking process. But when you connect people to the internet? Both systems can search for matches they they feel are close. Matches where either side has a chance to win. On the DOTA side of things, they often try to even out teams across 500 points (the K factor is something like 32, if that helps you visualize how much 500 is). In addition, the matchmaking tries to match stacks of players (preformed teams) in an even way, as communication is often critical in games like these.
Below is further research if you are interested. And as a warning, you aren’t. This stuff is not written in a friendly format, except maybe the last one, but that links out to the real math. There are integrals, and sigmas, and I think I even saw some calculus hanging out there. I did my best to sum up.
I was going to ask a friend of mine if he thought that today’s topic would be interesting, then I remembered that interesting is highly subjective. Many people couldn’t care less about how and why a game works than if a game is fun or not. I am not one of those people. Once I get hooked into a game, I want to get an understanding of each of the systems behind it, and today I decided to indulge that curiosity as it applies to Psuedo Random Distribution, or PRD for short.
So what is PRD? If you are diagnosed with PRD, how can you still behave like a normal human being? Many times in games, the game will make a check on whether an attack hits, an effect ‘procs’ (activates or happens...get with the lingo!), you dodge, all sorts of neat stuff. Now if you were playing a pen and paper game, this would be done with an evenly weighted die, and would be subject to random chance. If you observed 100 coin flips 100 times, you would see that you expect to have 50 heads and 50 tails, but some of those trials would be 60/40 in either direction. Given enough observations, you could see it being 30 heads out of 100. Now consider the effect of this on a highly competitive game - if you have an ability with a 10 percent chance of activating, it can happen 10 times in a row, or it can not happen 29 times in a row. Why 29 specifically? Because I have the numbers, of course! The odds of missing a 10 percent chance 29 times in a row with random distribution are about 5%. Ouch. Obviously, either example is going to produce a bad time for someone, and isn’t refined for a competitive environment.
So what can be done? Remove random chance? That’s one avenue. The other is to introduce PRD into your game! So what exactly is it? It is any system that replaces a random event with a new system that works similarly to a random event, but has controls build around it, preventing it from being truly random. Instead it is kind of random. Semi random. The diet coke of random. Not quite random enough.
In DOTA (of course) the PRD system has a ‘seed’ value for the odds. That value is what gets used the first time you attack. The second time you attack, the seed is added to your current odds. If the seed was 5%, by 20 attacks, you would be guaranteed to see the ability happen. So lets get some concrete examples of what the system would do. If you wanted to emulate a 10 percent chance using this PRD method, you would need a seed of ~1.48%. By the 68th attack, you are guaranteed to activate the ability - although we will later see that you expect it to happen by the 23rd attack. Here’s how the math works (I think)....
Your first attack has a 1.48% chance of hitting. Your second attack has a 2.96% chance of hitting, but that only is relevant 98.52 percent of the time - when you miss the first attack. Taking the 1.48 plus the 2.96 x 98.52 gives your cumulative odds of the attack procing by that point. Using the 2.96 x 95.52 x 2 (the second observation) gives what I’m calling the EV for the observation. When you do this across 68 records, you finally reach a 100% chance to proc, given cumulative percentage of 100% and an EV of 10 - which is what we want for a 1 in 10 chance. Using this same logic for the random distribution means that we start with 10% instead of 1.28, but do not tick it up each observation, and also we never ever stop. If you were truly unlucky, you could miss 1,000 times in a row. But thats in ‘killed by a feral gerbil while being struck by lightning on the way to claim your winning lotto ticket’ territory. Theoretically possible. When you take the total EV for the random numbers, you get close to 10 as well, meaning the two systems are just about equal. Neat, huh? So what are the major differences? Lets look at our first chart:
This chart is showing the odds of the ability activating on the Nth hit. So the random attack has a 10 percent chance to happen on hit one, then a 9 percent chance to be on hit number two - you miss ninety percent of the first hits, then you have a ten percent chance. If I were to show the chart all the way out, the random distribution would never actually hit zero. It has an asymptote! (Ok, you got me, that word is just fun to say). Because we are messing with the percentages for the PRD, it actually forms a curve instead of just declining. This curve actually does reach zero by the 68th point, but as I mentioned before, it is practically zero after 36, so I cut off the scale there.
So now that we know what the chart means, what is it telling us? There are 2 places where the lines intersect, so lets talk about what that means. Before the first intersection at the 5th observation, Random has a significantly higher chance to proc over PRD. You are giving up 8% odds on the first attack, which is pretty crazy, actually. After the 5th observation though, PRD is significantly more likely to proc, up until the 20th attack. After that, random is more likely to activate - however, that is actually not desirable in this case, as you don’t want your 1 in 10 chance ability to hit on the 70th attack. So basically, the PRD set up makes it so that your attack is more likely to activate between the 5th and 20th attack than it would randomly. This is enough of a range where it still feels random, but is less likely to happen repeatedly. Imagine a randomized stun hitting three times in a row!
Now for a different view on the same data:
This chart shows the cumulative chance to proc by the Nth attack (instead of on the Nth attack), and is mostly included because I thought it looked cool. Here the inflection point is at about the 12th observation. Up until that point, your odds are actually better of procing the ability with random distribution, but after that, the PRD is better.
Now with all the numbers out of the way, it all becomes a question of philosophy. From the perspective of a designer, I think it is a really cool idea that makes it so that chance has less to do with the game than it would otherwise. As a player though? I don’t think I like it anymore. It feels like it negates the effect until the item has ‘warmed up’ a bit. After I see the ability, I know I have a much longer wait than I should to see it again, even though it is for the intention of being fair.
Finally, this is just one method of creating a psuedo random distribution. The numbers can be changed in pretty much any way that you want to as long as you create a system that has the same EV score. For instance, 100% of activating on the10th attack would produce the same results, but is obviously less desirable in a competitive scene, as you can prime it with 9 previous attacks. You could even weight it so it is more likely to happen between attacks 1 through 5, then through attacks 15-20 if you really wanted to. Is that a good idea? No. But its the same outcome, and that’s what really matters. So what are your thoughts? Totally lost? Intrigued? Angry? Suspiciously aroused?
Today is an incredibly exciting day. Do you know why? Today, we get to unravel the secrets of the gaming world by looking at through a lens of analysis instead of baseless conjecture. I have actually been very excited for quite a long time to be able to provide this information to you all, and to unravel its deepest secrets. As an aside, I work with statistics and data, in a very real way. I have several systems at my work with hundreds of thousands of records that I can use to try and mine out information from the data. My boss told me when I first started that one of the larger failings of courses in statistics is that analyzing the data is the last 5% of the project; the real bulk of the work is in collecting the information. So today, I get to that juicy five percent and get to find out information! What information? How long have I been collecting? Well...I have been collecting information starting on November 6th and ending December 30th. Every day I had it in my bookmarks to copy the results from Valve’s top 100 games by the current player count, which you can view
HERE (but don’t click just yet, it will be fun to see some stuff in the blog, I promise!)
And if you want to see the data I collected, it is available HERE
So, already, we have to talk about some of the flaws in this method. I am using current players at my time of sampling to determine a game’s rank. That is to say, 1 is the most popular game for the day, and 100 is the ‘least’ popular game (least being a very relative term considering the 1000’s of games for sale though). However, current players could wax and wane much more than peak players, so I am using peak players for some volume trending, which we will see later. Now, I tried to capture this data as soon as I checked my bookmarks on my computer, which for most Monday through Fridays would have been at about 5 PM. I think that the data may be a 48 hour period, but that timeframe should always be consistent. Weekends I tend to forget to check at the same time, and we also had 2 major holidays making my checks slightly inconsistent. There were even a few days that it slipped my mind completely! In addition, the holidays and the Steam sales will skew these stats in a horrible way, but they will provide some interesting details later, so I think the timing is just fine. It can also be neat to see how much a good sale affects a game! (protip...a lot) However, I still believe that the data is representative enough for what I want to show, so we will say that it is probably good enough. If it wasn't so bothersome to collect and analyze the data, I would be very curious to keep going with it, as there are some games I would love to see more on (Rust and Revengeance come to mind).
Also, one last side note before I get started: Anything that isn't Excel sucks. This makes me very sad. I tried to use Google Docs to analyze the data, but because it is cloud based it runs very slowly. In addition to that, the way that it creates charts is flat out terrible. It was unworkable. I would have done it on my work computer with Excel, but unfortunately, Docs are blocked as a site, so I couldn't move the data over. I ended up using OpenOffice, which is an open source office like product, meaning it is free. It has similar tools to Excel, but it just feels clunky...one of the biggest things I miss was being able to drag a range for a chart up and down the data set to change what the chart was showing, as that would let me see what the charts would look like for all 200 some games. I hate to say it, but when it comes to this kind of stuff, you really can't beat Excel. Who knew? Anyway....
WHAT IS A POPULAR GAME
So obviously, the most important thing it what the top five games played are. Going into this, I could have made a few guesses for one or two, but I don’t think I would ever nail the top five. In the number five slot, taken as an average of rank by the entire timeframe:
#5. Football Manager 2014.
Hah. Wait. What? With an average peak of 58,000 players, those crafty Eurpoeans with their sissy ‘no padding’ ball game managed to crack the top 5. It is worth noting that other iterations of the series are all over the top 100, making bald eagles everywhere cry.
#4. Civ 5
Boasting a lowly 48,000 average players, yet getting an advantage over football manager 2014 by abusing my numbers, the strategy game managed to work its way into the top 5. I actually don’t know much about Civ 5, but I am going to have to learn, clearly…
This game has been around in some form or another for at least a decade, and apparently shows no sign of slowing with 67,000 average peak players each day. Online, refined, strategic, and incredibly tense, its no small wonder that people still love this game today.
This doesn’t surprise me in the least. At 66,000 average peak players, it consistently ranks in the number 2 slot every day. Going free to play may have revitalized this game, or it could have always been this popular, but apparently, headware sells.
No, I can't write a blog NOT about DOTA. Its in my contract
Turns out, DOTA isn’t just ‘popular’ it is incredibly popular. How popular, you ask? Whereas the average rank for TF2 was 3.22, DOTA was uncontested in the number one slot. An average rank of 1. The best, and highest. So how many people play? Take a guess. In terms of TF2, how much more popular is DOTA?
Would five times be insane?
Try eight and a half. With a whopping 567,000 average peak players per day, DOTA is king of Steam.
INDICATORS OF SUCCESS
Successmanship 101 right here
Now, obviously, success is not just having people play your game, but in this instance lets define it as such. The more people playing, the more people bought the game if it was sold for a price, otherwise, the more chance you have to sell people microtransactions.
So let’s talk about these results a bit, while diving deeper into the top 25 games. Out of the top 25 games, 21 are online capable, with many focusing entirely on an online only, PvP or MMO style. Again, out of the top 25, 5 are free to play games, with a few more as the list goes on. So what can we learn from this? Well, if you are an executive in a suit looking at these games, it is almost impossible to argue against multiplayer. Successful (in our definition, remember) single player games are only 20% of the market. Naturally, there is a bunch of crap that isn’t on the top 100 with multiplayer - say, Homefront - but the fact remains that multiplayer PvP action is incredibly popular. Next, we see that the F2P model is wildly successful, with the top 2 most played games being completely free (and also super well made). Are these systems abused? At times. But are they successful? No one can argue.
As an aside, the wild success of DOTA really proves a point for the MOBA trend...it literally is as popular as the next 15 games combined. Out of the total of the 200 games on the top 100, DOTA makes up 31% of the total peak volume, and 7% of all players on Steam, assuming 7 million concurrent users. Any business man will tell you that is worth trying to crack into. Yet, we see Awesomenauts, another MOBA, sitting down in 148th...maybe not fantastic, but still in the top 100 at times.
Sorry, but I do have to soapbox just a little bit here, as well...out of the 200 some games that appeared in the top 100 games in a given day, Call of Duty shows up in 11 of those slots. Ghosts was in rank 18 for multiplayer with nearly 20,000 users (and 78th for single player). These games are actually really popular, and many iterations are still being played today. Despite the imbalance, despite the not updated engine, and all of its flaws, the games are still really fun and popular. Its sort of strange to affirm that with numbers, but there ya go….why Ghosts was made, and why we will see another one this year.
IS IT REALLY SUCCESSFUL?
So, what does the bottom of the top 100 look like? It should come as no surprise when good games do incredibly, but how many games are really in rotation at one time? It reminds me of a concept known as the monkeysphere, where we only consider a good 50 people as humans, and the rest as just filler space. The bottom of the top 100 has games like Poker Night 2. Mass Effect (the first one). Half Life 2. Serious Sam 3. Portal.
If someone asked me to name 100 games that over 2 months would have been more popular than the original Portal, I would have chuckled and rambled off any game made in the past 2 years. And yet...There really aren’t that many games out there. I don’t really know what I’m trying to say here, but it seems so odd to me that Half Life 2 is still one of the most popular games played on Steam, with 1,000 concurrent users at a time. It just seems like there should be more games to bump it off the top 100. And more recent! But maybe games just fall off.
Speaking of falling off..
BEING AHEAD OF THE CURVE
Arguably, the most interesting part of all of this is looking at what happens to games over the course of two months. How fast do we latch on, and how quickly do we forget? So to start, let's look at Path of Exile.
The game was released to the public in late October, meaning it was basically brand spanking new at the first data point. And after two months, we see that the number has fallen to about 15,000 players, down from its peak of 30,000. So in about 2 months, half of the player base dropped off completely. Now obviously, there is a good reason for this with any game: people have beaten the game. Once you complete the game once, you have less reason to go back to it. In the case of PoE, the game has a large multiplayer base, along with several different builds, so the 50% drop off doesn't seem too harsh. Another thing that I really like about this chart, and many of the others, is that you can clearly tell when the date is a weekend. When dealing with daily data, it can often resemble a ECG machine - or whatever those are called...I am on a long list of people you shouldn't ask for medical advice. In this case, we see the weekend volume get a small bump up, then decline when it is back to the weekday. Weekend gamers are really a thing.
So lets look at something else!
Haha! My dumb sampling time with the holidays pays off yet again, as Call of Duty was released just at the start of the window as well! As a note, all Call of Duty games have separate games for single player and multiplayer as far as Steam cares, so this is only looking at single player, for now. Remember the 50% drop rate for PoE? Well, Call of Duty actually drops off the top 100 within the same time period, meaning it has a horrid drop off, but one could argue it levels out at about 2000 (still, 14% is nothing to be proud of). Also, the time it takes to get there is significantly shorter than PoE. Then again, the campaign is much shorter, and is less robust as far as multiple playthroughs. However, as mentioned above, the game was still pretty successful, at least from a 'broke the top 100' perspective. But no one plays for single player, right! So lets look at the multiplayer:
For Ghosts, the playerbase ends at about where the single player begins, which definitely passes the sense check. No one really buys the games for campaign. Again, that dropoff of pretty horrendous. After what looks to be only a week, the game suffers a 15,000 player drop, with spikes for each weekend, as expected. However, we see that all of the multiplayers for COD are still well represented in the top 100, and are in fact pretty reliable. Apparently, people still have fun with these! Combining every non-Ghost game gives an average of about 30,000 players putting its combined count in the top 10 most played. Really, not a bad showing for a game that people shout about so often. Also, props to Modern Warfare 2 for staying relevant 4 years after release. A small community, sure, but still bigger than many others! Another amusing tidbit, is that I believe the popularity is more or less in order of year released. Now I know I'm being preachy here, but these are online focused games, and after years they still have a large player base. PvP keeps a game alive, folks!
On the topic of picking up momentum, staying relevant, and multiplayer, how about a game that was released 3 years ago (2010), and was recently given life by the modding community?
Chart is for multiplayer only
Wow! Talk about some good press! Pretty much out of nowhere, the game skyrocketed out to 10,000 players. Various avenues covered the mod, and word of mouth really helped the game's popularity rise up out of complete obscurity....for a little while at any rate. I think this shows a really interesting example in what good a little press does. There were several examples of games that went on sale and had similar trends, but this one was particularly awesome.
And finally, just because I thought it was funny, here is what Portal 2 was doing:
I just....what....how does it? What does it mean? It looks like there were 3 different sales in the 60 day window, but that doesn't make much sense. What is that middle hump? Was there an LP somewhere that revitalized the Portal 2 community? I missed it. Sometimes with data, you get your Portal 2's: somewhere out there is the rhyme and reason for what is happening, and if you aren't tuned into it, the data is just meaningless.
If you want to see the charts for any games, let me know, and I can pull them up and post what the chart is. Otherwise, what do you think? Is there anything on here that doesn't match up to what you would expect?
I decided to merge together 3 different things that I like, and make them into a blog today! They are a love of math, a love of video games, and a burning desire to use my video capturing software! So I decided to mix things up and talk over some video instead of typing out walls of text explaining some basic mechanics.
This chart on was heavily inspired by my playthrough of EDF. The game gives you an incredibly varied selections of guns, with new guns unlocking constantly as you play. So to a normal player, this is the opportunity to play around, see what each gun feels like, and determine the best one by feel, right? Well for a mad statistician, this is the perfect opportunity to talk more about numbers! My entire playthrough was based on the best weapon for each tier, as determined by its DPS: Damage Per Second. The formulas required weren't that hard to come up with, and it was actually very interesting to see how different some of the weapons would be.If for whatever reason you want to see the spreadsheet I used for EDF, you can view it here. As you can tell (or if you didn't click the link), the spread of DPS is actually pretty crazy...anywhere between 2,000 to 4,000 damage were represented in the second highest tier of weapons! Where it got really fun for me was, of course, the insecticide rifle, boasting an insane 100,000 dps! Thats with its incredibly slow reload animation included! And that doesn't even take into account burst damage, which was the main reason for using the Boham Bay grenade launcher as my primary weapon the highest difficulty. It also has a massive AOE explosion that was pretty critical when clearing out large waves of ants.
Naturally, this applies to any game that has a system where you deal damage over a period of time, so it is pretty flexible, but the math ins't all that difficult. So want to know all the secrets and listen to my soothing Midwestern baritone? Then watch this:
Ive got a few other episodes in the works, but I am starting to run out of questions as I shift deeper and deeper into my backlog away from RPGs and more into a territory of a sandbox, so if you have any suggestions for future topics, I would love to hear them!
Whoo! It has been quite a year hasn’t it? For me, it has been an INSANE year. I wound up buying my first house, my second car, paid off two student loans, built my own computer, received a hefty bonus, and gotten two promotions! I have beaten Dark Souls to death on variouschallengeruns, started a YouTube channel, started a community series, made the front page, watched all of Fist of the North Star, and gotten crazy, wicked, pass out drunk more than a few times.
The first of many asides - if you like to drink, make friends with a bartender. Just be kind, tip well, and keep your first few drinks in order so they remember you. Don’t be a pain. Why? One place has gotten to know me pretty well, and they usually ‘forget’ that I order a drink or two, which I pass on to the bartender as a tip. Its a system. Anyway. One guy knew that I liked scotch, so asked if I wanted a pour of this bottle he had taken down, so I said sure. He gave it to me, told me what it was, then told me the price. Laphroag. 30 year. 50 dollars a pour. Delicious.
However that isn’t what I wanted to talk about! I wanted to talk about my Steam Backlog! See, after building a PC I indulged in many a sale, then immediately realized the task at hand. To date, I own 169 games. I play with the games in grid view, and when I finish one, I “X” it out so I don’t have to worry about it. Plus, it feels really gratifying to change that image. So I wanted to list and recap and note all the games. With that, in almost chronological order, and an asterisk next to my favorites …
Magic the Gathering: Duels of the Planeswalkers - nowhere close to real magic!
Home - this is one of the most artsy fartsy smells its own farts head up its ass indie games I have ever played. To me, it is a showcase of literally every thing that the indie scene does wrong. Retro for the sake of retro, telling an interactive story instead of being a game, and a super vague up to your interpretation ending.
Jamestown - A fantastic shooter, made even better by the historically accurate alternate dialog option. Seriously, this game is great on several levels and I am super glad I picked it up.
Magic the Gathering: Duels of the Planeswalkers 2012 - Now with MORE CARDS
Spec Ops: The Line* - I shouldn’t even have to mention that I love this game with all my heart and soul. This was also the first game to technically benchmark my new computer, so a lot of my love for it goes to how well my rig actually run. That being said, this is easily on the top games of the year that I have played, and you owe it to yourself to play the game. Not watch. Not read about. Play. Do it.
Dark Souls* - 114 hours and going strong. Technically my first modding experience!
The Walking Dead - Not the most demanding technically, but this was probably the best story of the year...although it is reallllly close with To the Moon. I think Walking Dead was a better experience 100 times over, but it didn’t tug at my heartstrings nearly as hard as To the Moon.
Homefront - here’s an odd recommendation. Play this game after playing Spec Ops. It does everything Spec Ops does, but completely straight faced. It should come with a bald eagle feather in the case. Team America should play in the background constantly while playing it. That said, it controls incredibly well, and is a solid shooter if you can overlook all the plot.
Bionnic Commando Rearmed - if this were released as an original game instead of an NES remake, the world would have never known. The fresh paint job on this game was fantastic, and the mechanics were actually had a really good feel and a lot of depth to them. Worth playing, even, or maybe especially, if you never played the original.
Borderlands - grind, loot, shoot. Yay!
Spoice Mahrine* - Space Marine is probably one of the best games ever created. It has almost a Saints Row dedication to fun, but with way more gore and action. You regenerate health in this shooter by being in melee range of your enemies and killing them with your bare hands. You get a jetpack and a sledgehammer. It reminds me of the military quote “they have us surrounded? Those poor bastards”. Play this game!
Hotline Miami - lets make a stealth game with unpredictable AI, so the same movement results in a different reaction! One hit kills! Twitch reflexes! Fun! I actually didn’t beat it, but I rage quit at the 2nd to last level, and frankly, I’m amazed I made it that far. The game is cool, has a great atmosphere, but the gameplay is ultimately too much for me to handle...coming from a guy who loves Dark Souls. At least Dark Souls was fair, and you knew why you died.
Ys Origin* - This is another sleeper hit for me. The gameplay feels really good, it has a meaty amount of challenge to it, and it has a plot that actually gets really touching at a few points. It was a game that made me incredibly sad at the end because I only wanted more. It didn’t overstay its welcome, and left me craving, and if a game does that, hell, I have to recommend it.
Binary Domain - I can’t tell you why anymore, but I had a blast with this game. Don’t use voice controls with it, but everything about it just has some weird charm.
Antichamber - Fantastically immersive puzzle game that bends the rules of physics. Yep.
Bioshock Infinite - I really liked the combat in Infinite. I saw it more like a Fallout or Skyrim where you try to find a way to build around a certain weapon or vigor, which was a lot of fun. If you just tried to find the most OP gun it wasn’t nearly as entertaining. I am sadly missing a single audio log, and I have no idea where. This also has one of the best opening scenes in a game released in recent memory. It all goes to shit so fast!
Tomb Raider - Fun gameplay, great hair. Another game that is hard to put into words why I liked it, but every part about it was solid enough to make a great overall experience.
Far Cry 3: Blood Dragon - We need more like this. Every series. I want an Assassins Creed game like this.
Darksiders - it didn’t age well.
Proteus - Remember Home above? Its like that, but worse. Hate this game with a fiery passion.
Bastion - Really solid gameplay, a fantastic story, cool art, and that steampunk guitar music thats been in vogue lately. Kind of overstayed its welcome. I stuck with only a few weapons though, so I feel like I missed a lot.
Capsized - This game has a lot of annoying design to it, and I never finished it, and never want to.
Dear Esther - I hate indie games so much...usually. This game has its head up its ass, but its heart is in the right place. It tells a good story, left me wanting to research some possible endings, and was very brief in presentation. Even using a modded half life engine (I believe), it delivered some amazing scenery. Almost any screenshot could be a desktop picture. Its actually really good. In price and content, justify it as a movie more than a game.
Borderlands 2* - My 3rd most played game this and last year (beat by Dark Souls and DOTA)
Battlefield 3 (Origin!) - It sure did check all the boxes!
Darksiders II - I did not see this game coming. It is actually incredible, with a decently deep combat system, good RPG elements, a compelling enough story, and some cool bosses. You can skip the first for this one, but it actually is something I unironically liked a lot.
EDF: IA - Just wanted to see the BIGGEST boom. And I did. Awesome.
Magic 2014 - the computer cheats so hard, but it does make it fun to be challenged. Even still, the AI is nothing compared to a human, so it is still disappointingly hollow.
Hitman Absolution - This was my first Hitman game, and I really liked it. It was like a puzzle game more than a stealth game. It lasted a few more missions than I would have liked, but I could see revisiting it to find all the things that I missed the first few times. It has a lot of life in it if you are into that sort of thing.
Sniper Elite Nazi Zombie Army - Boom headshot.
Sniper Elite Nazi Zombie Army 2 - BOOM HEADSHOT. Worse than 1, but still a good amount of fun. They made some good decisions, and some really really bad ones as far as enemies and level design.
DMC - I liked it, but I can see where people are coming from. I thought Dante came off as being a teen rather well...cocky, headsure, and swears for no reason. It fit well enough into the story where I didn’t mind him ‘not being Dante’. But I have only played DMC 4. Still need to get to 1, 2, and 3….someday. The combat was really fun, and the trigger based weapon switching felt really, really good. Plus, Limbo had some fun designs at some points, like the Nightclub.
Papa y Yo - This game shits whimsy. Everywhere. But beats you over the head with its thinly veiled message. Endearing enough to finish, but didn’t leave a lasting impact. I thought it would hit a lot harder when I started up, because I have been known to hit the sauce, and I do know I have some anger like issues, so I was hoping not to stare too deeply back at myself, but I just never saw it.
To the Moon* - This thing. Yeah. Needlessly 8 bit, frustrating at times, inconsistent in tone...but also unbelievably amazing. The tone issue is taken care of by the characters created, really, and they go through a crazy arc. The game drags on for 3 hours for a half hour payoff, but it hits like a ton of bricks. This is up there with NieR as far as ‘games that have made me feel the saddest thing ever’. Be patient with it. Play it. Love it.
Little Inferno - Its a game about waiting! That's the whole mechanic! Wait….then burn things….so you can wait...for more things! I played this off and on for what felt like 6 months, and hated the mechanics every time I started it up. I’m sure there’s some message. I guess the end was different. But man….I did not care for this one either. I whipped out a guide just to be able to say I beat it because I wanted to see what it had to offer at the end. Ech.
Mark of the Ninja - Yeah. This was a game. Not bad. Not fantastic. I did get to sick carnivorous insects on a guy in front of his two friends, and while they gnawed through his bones, another guard panicked and shot his friend in the face. So there’s that.
Saints Row 2 - I had already completed 2 and 3 on the Xbox, but switched to PC for Saints Row 4. I collected 2 and 3 on PC because they were cheap, and decided to revisit 2. It has aged poorly. The graphics are underwhelming, you have to mod in controller support, and the control scheme is nothing short of archaic. But the story that it tells is oddly compelling and often revolting, so still wound up being a fun experience, with only a few cheats enabled.
Then there are the games that you can never really beat, so these are the ongoing games:
DOTA* - I’m afflicted, you’re addicted.
Path of Exile* - See above. Year of the FTP model. So many hours wasted between these two guys, at a cost of zero dollars. You should at least try these games if you are remotely interested as there is no cost to do so. Beaten on 2/3 difficulties with 1 character, with another rolled.
Binding of Isaac - Roguelikes never die. This has been beaten, at least!
FTL -see above, but not beaten.
Rogue Legacy - this one does die, but its a small filesize, so it can stay. Not yet beaten, but getting ever closer!
Skullgirls - after getting the Beta codes from this wonderful site, I got addicted pretty hard into this game. I was incredibly sad when the beta was over, so I waited until the game went on sale then pounced on it. This is one of my favorites fighters in a long time!
Howdy everyone! Hope you all enjoyed the holidays! Mine were, in a word, interesting. First of all, you have to know that I live in Iowa, which is about six hours away from my original home back in Illinois, so I had quite a commute to go. In addition, I wanted to see one friend who had some intense personal drama, had to deal with families, manage poor weather, and keep my sanity with my family for the week that I took off of work...meaning there’s going to be plenty when I get back. So I thought, knowing my own Christmas list and plans for the week, that I would break out the ol’ Wii U for the trip, and get some more mileage out of the system.
I was actually a day 1 buyer of the Wii U, a decision which I don’t really regret because I have disposable income. However, since I built my gaming PC in January (see above: disposable income) I was in no rush to play pretty much any console games. Not to be elitist, but most multi platform games that exist will run better and be cheaper on PC. Long story short, I played NSMB U, Rayman, and half played a few other games on the console, so I was actually interested in giving it a fair shake, especially with some of the stellar titles coming out this holiday. I know I had asked for the new Mario and the Wind Waker remake, among other things, so I figured I would have some time. I needed something before the actual holiday, though, so I decided to pick up a game that I had previously played, hated, demoed, hated, and generally knew I didn’t care for: Monster Hunter 3.
Let me tell you about Quropeco. Let me tell you:
You have limited item slots, and limited recovery items. As you fight monsters in MH3, you are facing the depleting of about 5 different gauges: your health, your stamina, your weapon sharpness, time, and the monster’s health. You have 50 minutes to kill the monster, or you can die after you have used up every single steak (stamina recovery) and potion (hp recovery). Against most monsters, this is just a matter of evading attacks, and counter attacking - something I am intimately familiar with given my history in Dark Souls. The thing that is different between these two games is that in Dark Souls, bosses are confined to a room, and have a visible health bar. In Monster Hunter, you don’t know how much damage you have done to the monster, how close you are to victory, so it is hard to grasp which moments are clutch and which are not. After fighting a monster for twenty minutes (yes, seriously, this is common) you can see the monster begin to limp, meaning your victory is close! In a last act of desperation, the monster runs away from you into a new zone. For most monsters, they either leave through an exit for the zone, or through a gate that clearly telegraphs their path. And, if you have some foresight, you can tag them with a paintball that tells you where they are. Then there’s Quropeco. The flamboyant bastard bird. Quropeco has a call that summons another monster to fight, sometimes a boss monster. Sometimes THE boss monster. He has another call that heals him. And oh yeah he flies. As in he can run to any area on the map whenever he feels like it. There, he can eat fish to recover health, or just sing to recover health. So after twenty minutes, five whetstones, ten potions, and three paintballs, you can have no idea where he is, and no idea how much health he has left. Plus, he has thick armor that makes your weapon rebound off his skin, lights you on fire, and is a general jackass. I quit this game on the Wii because of that ass, and I have no regrets. He is absolutely infuriating. But Gamestop had a sale. And I’ll be damned if I pass up a good sale. So I got MH3 yet again. After trying the demo and remembering why I hated it. After remembering the terrorizing memories of that flying Mardi Gras float. And its pretty fun!
So I packed my bags to make the treacherous journey across the mighty Miss. My dad who recently retired came out to pick me up, which was very nice of him, so I didn’t have to stress about the trip. However, he has a nasty habit of waking up at around 5, so we were off about two hours earlier than I had anticipated. In my hurried packing, I forgot to bring the charger for the Wii U Gamepad (Okama Gameshpere!), which was going to be a problem. Its not a huge deal, but it is a sizeable complaint that despite the fact that every other technology uses 2-3 different methods (USB, the smaller USB, or batteries), the gamepad has a charge hole that is more or less unique. Not a problem! Surely, GameStop carries a charger! And for all I know they do, but the staff working there that day didn’t. Se we tried Best Buy the next day and found a Nyko charger that said it fit the gamepad! I took it home, and...well...Nyko lied. Pretty hard. The product that they clearly state should fit didn’t. I wouldn’t normally care, and would just visit with family for a week, but I was sick of reddit after a few hours, so I went back to Best Buy, returned the open product (props to them for doing that, by the way), and got an Energizer stand/charger which actually worked. Hooray! I could finally game!
No seriously, I hate Nyko right now
So lets talk about the Gamepad, good and bad. Bad? Short battery life. About 3-4 hours. And when I get to 2 bars I worry about death in the middle of a long encounter, so I was at about 2 hour sessions, and then 1 hour of charging before I got sick of my family again. Not ideal. What was really nice about it though was that I was playing in the living room where my folks were watching TV, and was able to play entirely on the gamepad. I didn’t have to lock myself away in a room, secluded during the holidays (as much as I would have liked to at some points), but instead I could carry half conversations! The screen is a little bit too small to get some of the finer details visible, like your location on the minimap in MH3U, but the game was clearly designed to be played with gamepad only - there is a ‘zoom in’ feature for the minimap! The controller is very conducive to ‘the claw’. I often forgot where my fingers were resting moments before, but then remembered that the claw is simply the best way to play almost any 3d game. Embrace the claw. Love the claw. Overall, I was very happy with how the off screen play worked in general. Specific to MH3U and Wind Waker, it needs to be better communicated. the Minus button in Wind Waker switches between gamepad and tv, and in MH3U, it is buried deep within the options. Not impossible, but not intuitive. Easier with the help of a full screen, a luxury that I didn’t have.
Then I went to my super Danish Christmas Eve celebration, which I will explain here because diversity and holidays. We have some odd traditions, and odder family members. For starters, the Christmas tree is decorated in red and white heart baskets made out of paper. There are many patterns, and they range from a simple checkered style to some amazingly intricate designs. It isn’t uncommon that my grandfather puts up a string of Danish flags going around the tree similar to how the lights are set up. Dinner is more or less American style with the exception of dessert. We have a dish called ‘citronfromage’ (citron from osh ah is how I hear it pronounced). It is kind of like an orange flavored pudding, but a little firmer and lighter. Whoever makes it hides a single almond in the dish while it sets, which is then the ‘object’ of the dessert: whoever finds the nut wins a prize! And just to be cruel, you hide the nut when you find it to make everyone stuff their already bloated selves trying to find it. The traditional prize in our family is a marzipan pig. After digestion and coffee, we then sing songs while dancing around the Christmas tree, ending with “Jingle Bells” because of reasons. I really have no idea why...then gifts, and finally returning back home to feed the dogs - and play more video games!
We use a really far removed recipe for the citronfromage, so it doesn't look much like this, but this is what google gave, so hey. There it is.
Even after receiving more games for the Wii U, I found myself drawn to Monster Hunter. Mario was fun, Zelda was good as always, and Rayman is still a treat to play, but Monster Hunter was just...the best. It is like a condensed Dark Souls. Find the rare stuff, find the boss, kill the boss for a long, long time. The game is rarely cheap - each move has a tell, and larger monsters only have a few moves. All of your actions have to be deliberate as attacks have a very small area that they hit, and every single thing has an insane animation window. Want to sharpen your sword? You have to unequip it, find a whetstone in your inventory, then sharpen for what feels like 2 seconds (without getting hit), then wait a second while you admire your work (getting hit is annoying, but not end of the world). It rewards caution and patience very well, basically, and isn’t something that many other games offer. Granted, I am only at the 4 star quests now, so maybe it becomes a dick later, but I spent 17 hours over the course of a week playing it, and hell, that isn’t half bad.
I finally hooked up my Wii U to my normal TV today to see how it holds up on a larger screen. First off, I had an issue with my HDMI cable, in that the Wii U and TV refused to talk to each other. After trying to change every setting on both, I finally resorted to the stupidest idea that came to mind and switched which end was plugged into what device, and voila! it was fixed. By the way, googling support on this problem is infuriating. It seems to be fairly common, but most people just ask questions like ‘is your tv HD? Is it plugged in? Are you sure its plugged in?’ People on gamefaqs forums aren’t 80, alright, internet? C’mon. After addressing that issue, I really like the way that everything looks. I’m used to equating jaggies and Nintendo so much that how good MH3 looks in 62” HD glory made me smile. And HD Wind Waker? Yum! Now I associate Nintendo with Jaggis! Hah. Monster Hunter humor. The gamepad features on those two games are also wonderful in my experience so far. Being able to check the map while sailing without pausing, switching items on the fly, and navigating a pouch full of items all on a touch device absolutely nail the simple possibilities that the gamepad offers, and maybe what smartglass or whatever the hell XBox/PS4 are doing these days.
So basically, what I’m driving at here, is that I think that the Wii U is pretty cool. It works as advertised on the ‘not hogging the tv’ front, and is pretty comfortable to use. While not a graphical powerhouse, I think that the HD looks plenty good enough to justify it. The always excellent Nintendo exclusives, and some of the possibilities with control schemes (gamepad menus, wiimote for RTS likegames) are pretty dang cool. Overall, after this holiday, I’m really happy to own a Wii U, and I’m hoping to see it shine.
Besides people who don't get this reference, of course
I hate people who post ‘gamer logic’ pictures. Quite a bit. “Hey, did you know the police will give up on chasing you after 50 feet? Lol, not like real life at all” “Falls into hay off Empire State Building. Survives”. Shut up. No one cares. Games are about fun, not realism. Any game that sacrifices fun for being realistic has failed as entertainment, in my mind. Take for instance, Receiver: a first person shooter where you have to reload in a real fashion. As a thought experiment, it is really fun. PvP in the game would be a wonderful fustercluck. The novelty is interesting, but the actual gameplay is less entertaining, than say, pressing R then continuing to shoot stuff. I think FarCry handled it very well, but on the fly, brutal self surgeries, but still keeping pace.
Whoa dude, you are soooooo right! I can never play Mario the same way again! But seriously, headbutt a bullet.
So why do I bring all this up? Well, I have one complaint that actually does drive me crazy about videogames. It’s like some weird kind of fear. And that is that I am almost never standing on solid ground. Ever. I am playing a game in a papercraft diorama of what a real world situation might look like.
For anyone who has played Dark Souls on PC, you may be familiar with the DSFix mod. One aspect is that you can unlock the frame rate which comes with the ominous message that you ‘may’ fall through the floor on occasion. And that is genuinely what happens. Instead of sliding down a ladder and having your feet touch ground, your slide shreds the paper flood beneath you as you descend into the dark void.
Thanks to the Game Grumps I now know how flimsy the world of Skyrim is. Everything in the game is paper thin. The floors. The walls. Mountains. Stairs. Other humans. There are no guts...no brains...just a shell with facial muscles, eyes, and teeth. Some kind of walking talking flesh heap. But even worse, these systems allow the player to abuse these systems by the use of a bowl...you can literally use a bowl to walk through walls, falling through the abyss and seeing the darkness of the world outside of your doll house. It’s just...creepy.
Almost every game where you are playing in a 3D environment has the same situation. You can often tell this just by moving the camera so that it clips through the one dimensional layer. Behind every brick is just another flat surface. No dirt. No minerals. No fossils. Just...nothing. Its like walking on ice.
Oh yeah, thats the good stuff.
So this explains why it is so comforting to me when the games let me know what is around me. Minecraft is a fantastic example. Every single structure is actually made up of blocks. You start on grass, but you can see the feet of dirt, stone, and eventually bedrock beneath you, and even if you find a gap in the bedrock, you just fall into the core of the earth and die. It almost makes sense in that regard. Terraria uses the same system, so it is also nice to see that other people share my odd phobia. As far as the people, there have been some fairly good advances in this as well! Most zombie games at least recognize that humans are made up of 4 limbs, a torso, and a head with a brain. Sniper Elite even goes a step further and fills in the remaining organs and bones, and even shows how people die as your bullets rip through their organs. The entry and exit wounds leave something to be desired, but remember what I was saying above about reality? Bloody gaping wounds followed by muffled screaming? Not fun. There are also the new Mortal Kombat games which used the XRay system to show the damage that was done. Was it exclusive to a QTE? Sure. But it helped to...flesh out the world.
I was musing on this a bit, and I realized that only modern games have this problem. See, back in the good old days of the NES and SNES, a few bricks were reserved for the ground. Mario had a brick and a half beneath his feet. Even if, for some reason, he jumped super hard, he would still have a lot of brick to go through. Even Simon Belmont had a good block beneath his feet most of the time.
I know I’m crazy, but does anybody else share this kind of paranoia?
When was the last time that you snap bought a game, sight unseen. Sure, some people buy games day 1 after tons of press release, or after enjoying the previous game in the series, but a game that just sort of stumbles out there, well...odd things can happen. Sometimes, they are beautiful, and sometimes they are hideous decisions. Being a PC gamer, I can resist the temptation of almost any game on the basis that I know it will be for sale in the near future, and I have an incredible backlog to play through. That did not stop me when I saw “Sniper Elite Nazi Zombie Army”. I had played Sniper Elite V2, and found it….lacking, to say the least. But seeing a combination of Nazis AND Zombies used so blatantly, with pentagrams, and a B movie horror flair behind it? That was a game that I had to pick up. Knowing nothing of what I was getting into, I put the money down on that game. It turned out to be a Sharknado/Snakes on a Plane experience...you pretty much pay to say the name for the next month or so, but it is enjoyable while it lasts. Delivers what it promises. Not to get too far off topic, the first game was actually incredible, in my opinion. It took the mechanics of the first game and refined them in every single way, almost to a comical fault. The joy of playing a sniper is being able to shoot people’s heads, and what better target than one that can barely walk towards you? SEV2 (acronyms, begin!) gave you tools to set traps, but you had to have the foresight of knowing where to place them. SENZA gave you an improv situation - you could guess what will and will not be critical. Secondary weapons had purpose! Running like an idiot and wasting your breath was important! It was really, genuinely, fun. From a mindless face exploding simulator point of view, it was literally all I could ask for.
Then I saw that the sequel was coming out. And I made another snap purchase.
So after singing praises of the first game, lets talk about the core of the game in 2. Yet again, you have hordes of the undead coming to attack you at a very slow pace. The core mechanics had absolutely no changes, which felt like a bit of a missed opportunity. As much as the first game demonstrated how the mechanics could transcend stealth into horror/tension, it would have been great to see a progression of the mechanics against zombies. Some new weapons, tricks, and traps would have gone a long way to make things feel ‘fresh’ after the 10,000th corpse. But overall, the gameplay largely remains the same, and is still incredibly satisfying to shoot zombies in the face. It harkens back to the days of Serious Sam and DOOM, where positioning is more important than twitch reflexes, but with the twist that you have to remain cool and collected enough to land headshots.
So lets talk about the changes. First, the game commits a cardinal sin about halfway through and introduces stationary turrets. Both SENZA and SENZA2 have optional 4 player coop, but the turrets really begin to push the boundary of how optional it is. Several sections are clearly designed to have at least 2 people (one guarding left with a turret, the other guarding right), and having another 2 to defend your backs would be wonderful. There was one section that painfully brought this up, and made the game feel like more luck than skill, and you had to predict which side a special infected would come from. They are a good addition in theory - breaking up the careful, planned sniping with mashing down the trigger can be both refreshing and cathartic, but often with a single player, it just fell flat.
So lets talk about the special infected! All the gang are back from the last time, and are still as fun as ever. Besides your standard zombie, you also get skeletons - who now shamble out of walls or burst out of mannequins, both of which are pretty dang creepy. Then you have suicide zombies, akin to the guys with bombs for hands from Serious Sam, but less obnoxious. There are counter snipers, who make great use of the bullet drop physics. Then there are the machine gun zombies, hulking titans who can shoot back, and require several rounds to the face to take down. Finally, the occult commander makes a return appearance, much to my dismay. It is worth noting that the commander and the machine gun zombie both faced some nerfs between the series, which was more than welcome for the former.
Then there are the new boys, and you know what? They nailed it here. There is a zombie who can explode, converting nearby zombies into flaming zombies who run directly at you. He is annoying as hell to fight, but offers a new, fresh challenge. Then there are the summoners. They do what you would expect, really. The challenge is that they can only be killed with a headshot, and they move their heads around quite a bit. It offers a nice tension to have to get a headshot amidst an ever growing horde of the undead. Later, they start placing them in rather difficult places to account for, and it really winds up being fun.
The atmosphere remains more or less the same as the first game, but they did add in a few unsettling moments into the game. A few points really reminded me of the FEAR series. Wait, scratch that, just FEAR and Extraction Point. You know...the good ones. It is amusing having played SEV2 seeing how often they recycled the assets of the levels to change them around to fit the zombie theme. Sometimes they are well hidden, other times they are wholesale rip offs, but overall it still has more charm than budget. I really would like to see more developers taking note of how they are doing this for future projects similar to SENZA or Blood Dragon. High in charm, and I assume low in work, as models already existed. With all that said, however, the game seems to have lost some of the charm. I can’t put my finger on it, but something about it just doesn’t feel like the same bad B movie feeling. It plays it too straight or something.
So, at the end of the day, it really is more of the same from the first game. If you liked that, I would say that you would enjoy most of the sequel. If the first game just wasn’t your jam though, this offers absolutely nothing new or redeeming. And if you are on the fence...well, wait until it is on sale, grab some friends, grab some beers, and make a night of it. There are only 5 levels, and each level is only about 40 minutes long on average, so it is a pretty short romp. There are collectibles, but I never find those rewarding. After beating the game solo, I do look back on it fondly, and if anyone was getting a group together to four man this bad boy, I would be first to reinstall it.
OH! Also! I recorded my entire playthrough of the series! First video for SENZA is here:
As is the case with the previous blogs, I ran into a question that I had to answer by using spreadsheets, math, and prayer. This time around, the question came up from the wonderful game Path of Exile. In Path, you have 4 damage reduction systems: armor, block, dodge, and evasion. Armor and evasion come from the gear that you are wearing, block comes from your choice of shield, and dodge comes from passive skills. Block, dodge, and evasion all negate the attack you are taking, whereas armor will reduce the damage by a set amount, based on math (more on that later). Now because I didn’t feel like messing around with 4 variables, and because only 2 come up very often with every class, I wanted to figure out:
What is the best combination of block and evasion?
Now, obviously, 100% of both would be the best, so it becomes rather important to phrase the question. Basically, there is armor that has about both stats in about half the amount of ‘dedicated’ gear. So would you be better taking 50/50? Or maybe 70/30? Or just not worrying about one at all? My mental roadblock with all this was that it seemed like there might be a sweet spot of reducting the damage that you don’t take.
So lets talk about the math required to figure out the first part of this challenege. We know that evasion has a chance to proc each time, so it will fall into normal distribution, whereas armor is conistent. Now as you SHOULD REMEMBER FROM THE LAST TIME, the difference is negligible in the long run, but is rather swingy in the short run...in theory. Path actually does use psuedo random distribution (a method by which they force the ability to proc after X events, in a way that still results in approximately the same odds). For the purpose of the math I’m doing though, this doesn’t matter. In fact, I can treat block and evasion as exactly the same! The reasoning is that if you took 100 attacks at 100 damage with 50 of either armor or evasion, the armor would block 50 from each, for a total of 5000 blocked, and the EV for evasion would be ½ of all attacks, for 50 blocked attacks by 100 damage for, you guessed it, 5000 damage. So by putting 10% block to 90% evasion, and increasing/decreasing by 10, I get something like y=x^-2 : an inverse parabola.
Probably about the 3rd saddest time in my life to see a parabola, really
Oh. Well. Looks like this week is pretty short, huh? Assuming each attack coming at you hits for 100, that means that the 50/50 block gives .5*.5, or 25% total damage received. 90 by 10 gives 9%. So really, there is no sweet spot. It is always better to focus on one or the other. Really obvious in hindsight.
In a vaccuum at least. In reality, it gets a little bit more complicated than that, but not by a whole lot. The assumption made throughout that process is that you have access to whatever gear you would need, and the resources to get it all - more often than not, this is not the case. So then we have to understand the value that we are getting from each piece of armor, and in order to get that, we need to know how many pieces, and in order to get that, we have to build a model! Yay!
So lets talk about how these mechanics scale. We would need a curve that start at 0, and infinitely scales at either 100 or 90 - I still haven’t figured exactly how Path does this, as the math that the wiki provides does one thing, but says the other. Path has a 90% cap on the damage you can reduce, but the theoretical amount you can block actually scales to 100%. For reference, the equation I found is “Armour / ( Armour + (12 * Damage) )” So as armor increases, it grows ever closer to being 1, but even at millions of armor, you still take a teensy bit of damage. Evasion’s calculation is actually a lot more complicated, because it uses an enemy’s accuracy stat, so I am going to again make a large, sweeping assumption, and say that evasion scales the exact same way that armor does. Now, you can rearrange the above equation to get Total Armor = (12*Damage*Desired Reduction%)/(1-Desired reduction%), which lets us figure out how many units we would need for any given reduction.
Diminishing returns apply both to how much armor you have, and how much you pay attention to me
So applying this formula to our ratios gives 134 armor required to get to the 10% threshold, and 10800 to get to the 90% threshold, if facing 100 damage. That is an 8,000% increase to get a 900% gain! Hooray! Math! So the same thing applies for evasion. This means that in order to get the 90/10 split, we would need to have a total of 10,934 points. However, in order to get to the 50/50, we only need 2400 points (as 1200 is the 50% point for both). So, we would have to increase our total stats 4 times over to get 2.7 times the gain. Ok, cool. Now we are getting somewhere!
This means that each piece of armor is contributing less ans less as we add more and more. Specifically, our best case example has each piece of armor protecting us from .0313 damage, or 32 units to block 1 damage. The 90/10 example, however, is .0083 or 120 untis to block a single point of damage, supporting our previous 4 to 1 numbers. Neat! So for right now, it looks like it is all up to context right?
Its been too long since I have thought of this scene, or this movie. Needed to be fixed. By math.
So far, I assumed you had a tradeoff between armor and evasion, but what if we lifted that restriction. Well, you wind up with the 60/60 build, which offers 84% damage reduction. This happens to be the same as the 80/20 split, however it does it with 1,500 (!) less units of armor, with an efficiency per unit of .0233, or 42.86 (comparable to 70/30)! Whoa! Then we can step it up to 70/70, which gives 91% (the same as the 90/10 split), for 5,600 units (efficiency of .0163, or 61.54 units per damage reduced). Then we have the 80/80, offering up a hearty 96% reduction at .01 per unit...which is both more reduction than the 90/10, and less cost!
Now unfortunately, I am writing this up late and don’t have access to Excel (or the effort to boot up my work computer to get it), just Google’s charts, so I can’t do a proper regression to figure out all the math for it, so I cant tell you if it is some super cool exponential curve, or something like that, but what I can tell you, for sure, is that it is 100% better to scale your stats equally is possible. Because the systems are set up the way that they are, you are losing value the more armor that you take. However, by abusing the relationships between the two curves, you can make significant gains by balancing your stats. In context, this may be tricky - A vendor may not have a 700/700 armor, only 500/500 or 1000/0. Now, can you imagine what this would have looked like if we had included another system, such as blocking or dodging? What a headache!
In addition, the games methods may not match what this math is exactly...for instance, Path starts each character off with a base 5% dodge meaning that my treating dodge and block as the same is a little bit faulty, plus the enemy accuracy plays a large part into how the mechanic works. Further clean up and asterisks, I did use 100 for the base damage of an attack, and using any other number changes the exact numbers that will come up. However, the scaling is set up in a way where the damage to armor required ratio scales linearly - so the armor required to soak 90% of 300 damage is exactly 3 times the armor required to soak 100 damage.
Other than that though, there you have it! The answer to a question, as solved by math! And your professor said it didn’t have any real world applications.
I was talking out loud to myself while playing a videogame, and I had an interesting question come up, one which could only be solved by using the worst of all demons: Math. So let me phrase the situation for you guys...You are playing an RPG. At the beginning of the game (or whenever, really, but my numbers use a level 0 assumption), you can take a perk that offers you an extra 10% on every single experience granting transactions. Is it worthwhile to take this perk?
Now, the gut feeling towards this changes day to day. Clearly, the earlier that you take the perk, the more effect that it has, meaning you should take it is as early on as possible. Second, that’s an extra ten percent, baby! One tenth of each level is free! However, what exactly does that imply...that means that I will not have a significant experience advantage over anyone who didn’t take the perk until level 11 - they will still be at ten. This continues for each ten levels. At level 20, I have only managed to eke out an extra 2 levels over my theoretical friend. So would I have been better off to have taken another skill in its place?
Both of those arguments are easy enough to conceptualize, but the benefit that you are getting from either decision is actually pretty hard to quantify without using some math. The reason? We all know that RPGs are drip fed - the difference between level 1 and 2 is nowhere close to the difference between 20 and 22. This is largely in part to the way that experience is curved out. Because of this, I couldn’t come up with a satisfactory answer and I had to do some math. To start with, I had to design an RPG Exp curve, along with average monster exp. Having no background in game design, this is something that has always fascinated me...how do they know how much gold and exp to hand out in any given area, but still maintain balance? In my mind, there was some master spreadsheet kept in the back that told them, similar to an actuary table. In reality though, calculating this is quite easy! So I wanted to dedicate a lot of space to how I set up this example…
Or I could just...you know...plagiarize one. But where's the fun in that?
I started messing around with each level being exponentially far away from the previous level, but wow, that gets out of control quickly! I have never seen an exp bar go into scientific notation, so I clearly had to use a different approach.
I decided that first, the RPG system is a drip feed so the time it takes to reach a level should increase at each level. After messing around with some models for a bit, I discovered that the time to level is probably the first factor that you want to decide on. I figured that if you added an extra 15 minutes to each level, that would probably be enough to keep things balanced - 15 minutes to level 1, 30 to level 2, etc.
Next, you have to know the average amount of experience you are giving out per level. I decided to make an assumption that the exp per monster would also increase in a linear fashion - 50 at the first level, 100 at level 2, and 150 at level 3. These numbers could be anything and it should all still work out. Next, I made yet another assumption that each fight would take exactly one minute. I guess you could replace the minutes with encounters and it would still be the same, but for some reason I was hellbent on using fractions of hours in Excel, so...it stays as minutes.
So what does that let you do? Well, now you can take the total experience per encounter, and multiply it by the encounters to level up! This gives the experience gap between levels! In our case, it takes 750 to reach level 1, an additional 3000 to reach level 2, then 6750, and so on (spoilers if you figure out what ‘and so on’ means here, I suppose!). Taking the cumulative values of all of these gave me an exp curve that starts at 750 for level one, and ends at 7 million for level 30, after a hefty 116.25 hour journey!
Now here is where something happened that blew my mind...I had created an RPG curve that I was satisfied with, and wanted to know how it was modeled. I took the data for cumulative experience and put it on a plot, tried some regressions, and nothing quite matched. It looked close on one or two, but the fit wasn’t perfect. Maybe it just wasn’t that mathematical. Then, because I was bored/wanted to be thorough, I put a regression on the experience between the two levels, and discovered that it fit a 2nd order power regression perfectly. Not ‘really really well’, not ‘pretty close’, but 100% perfection. Then I thought about what that meant. If I had the value between two points on a chart….and it was represented as aX^2+bx+c….then that is the integral of the experience curve! And sure enough, the experience curve comes up as a 3rd power regression, with a 100% fit, whose derivative gives the fit of the exp between charts (+ c, naturally)! Holy crap! Thats awesome! That also means that I can take the derivative of the experience between levels to get….something….related to the experience...I didn’t actually figure out what that would give me as it has been a while since I have performed a calculus, much less on a real world example.
Pretty much 'mfw'
After this, it becomes pretty simple to figure out how the scaling works. Just slap on an extra 10% to the exp per fight, and do the division. And what do we get? Well, the initial assumption actually holds true...the player with the extra 10 percent hits level 22 at 57.5 hours of play, at which time the player without the perk is just barely level 20. The comparison for 10 and 11 is 15 and 13.75, so it isn’t quite a clean cutoff, but the marginal gains are clearly there. So it really doesn’t seem like much, does it? Maybe you could take a perk that gives +20% damage which pays off at every single level instead of getting an extra level every 10 levels…
...Except the way that the levels are curved out showed me something different. In order to reach max level, it takes the player with the perk 105 hours, and the player without 116 hours. In fact, it is taking the second player an average of half an hour less past level 20 to level up. So it isn’t what you are gaining in levels over another player, but perhaps the time you are gaining back from the game. If a perk said ‘save you ten hours of leveling’, would that be worth it?
But then this is where things get extraordinarily more interesting (or more boring, but if you think that and you made it this far...uh...thanks?) Because of the way that the experience scales, you save less time in the early levels as opposed to the later levels. From levels 1 to 7, you only save half an hour by taking that perk. From 23-30, you would save 5 hours, which is to say 10 times more time! So this is where the final wrinkle of this puzzle is introduced..in fact, you do not get more value by taking the perk early, as logic might dictate. While it is true that having it wouldn’t be a bad move at early levels, its effects are most pronounced in the late game. This is again because of how the experience distribution curve is calculated - for lower levels, the difference between 1.1 and 1.0 multiplied by x^3 makes less of a difference, but for higher levels, it suddenly becomes a much larger gap.
While discussing this with one of my coworkers, he actually brought up an excellent point, which I had not initially considered when writing this, but was actually the very thing that brought it to my mind: In some RPGs, traditionally the western RPG, enemies scale with the player! This means that you are actually inflating the difficulty at a rate which it should not be inflated, and losing a perk in the progress! At level 10, you only have 9 perks working for you if you took the extra level, making you 1 perk behind the slower player! So all of the sudden you are trading a decrease in time for an increase in difficulty! Oh no! The example that brought this to mind was actually Dead Island: as far as I could tell, the zombies 'leveled' with you by gaining new abilities, such as increased mobility, better climbing, larger numbers, things like that. So I constantly felt that, while I was better off in total exp, I was actually playing a much harder game than I should have. And we call this the Ayn Rand paradox of game design, wherein the player who made the 'smart' decision to have more exp is punished by the unflinching machine of poor game design.
Now obviously, this is just an example of what an experience curve could look like, and most of the numbers were chosen by an arbitrary method, but the principles still apply. So what can we draw as a conclusion? Basically, taking the perk early isn’t actually that important...in fact, you get more value from it the later that you take it, on a per level basis. As long as the early grind isn’t that bad, it is totally worth holding off. And as far as being worth it in general, it comes down to a matter of the value of your time. If the game is something like Final Fantasy where you are expected to grind out between levels, it is probably going to be worth it. But if the game is something like Fallout where having levels is nice, but not required? Maybe just enjoy the sights. Certainly, dont waste your perk to make the game harder - most games have a slider for that! In any event, you should now be more prepared each time you face that decision!
So a while ago, I was browsing some site on the internet, probably pornagrophy of some sort. I guess I must have become side tracked, because I encountered a hypothetical videogame situation: after slaying 1000 hyperdemons, you have been given a choice of rewards. You can either select the Red Sword, or the Blue Sword. The red and blue sword both deal the same amount of damage, but here is the catch: the Red sword hits 100% of the time, Blue hits 50% of the time but can attack twice as often. Which sword do you take, and why?
Now, obviously, this situation has 3 choices:
A. The Nihilist Approach - “it doesn’t matter which one I take”
This seems like it should be obvious, right? After all, you just have to do some basic math in order to come to this conclusion. Lets say both swords do five damage. In 100 attacks with the red sword, I will do 500 damage, and with the blue sword I get half of 200 attacks by five, for - wait for it - 500 damage. So, as long as its better than my other gear, my choice, much like every choice in life, has no meaningful impact.
B. Team Red- “I have terrible luck”
Yes, you nihilist, on paper, given a large amount of trials, the two will be equal. But this sword relies on a RNG when it decides to hit. This means that in theory I could miss more than I hit with the blue sword, because this stupid game is rigged! If I pick the red sword, I am guaranteed my 500 damage. The blue sword is eventually going to fail me if I take it, it is only a matter of time.
C. Team Blue- - “Maaaaaaybe”
There are a lot of maybes in the game. Maybe an enemy dodges. Maybe I get lucky. Maybe I crit! Maybe I can buff the sword! (For the purposes of discussion, neither of these are true. Sorry.) Bummer...well, at any rate, maybe every once in a while I can get really lucky and do some serious damage.
D. None of the Above
Wait...what? How did you….nevermind. You know what? You have to re-choose. House rules.
So which option would you end up picking? From what I saw, it was about 40/50/10 between A B and C. What would I pick? Well, the answer depends a lot on two different things: Statistics and context. Lets look at the former first.
If the odds of the blue sword hitting are forced to be 50%, then anyone who picked A would be correct in that it doesn’t make a difference. But if we assume that the RNG behind the scenes runs an independent check before the next number, that means that a series of coin flips will be normally distributed. However, because a coin only has 2 outputs, a graph of that looks pretty darn lame:
So lame, in fact, I'm not even giving it real data
Where it gets interesting though, is when you perform multiple trials of multiple coin flips. So, for example, lets say you expected to be able to survive 100 turns against a monster. That means that you get 100 coin flips throughout the course of the battle. And you could say that you will fight, for the purpose of example, 500 encounters. Some encounters will result in more hits landing, some will result in less hits landing. But what is neat, is the pattern that these observations create. Because all the coin flips were independent, we expect them to fall in to a normal distribution, along a bell curve.
Oh sweet Jesus, normal distribution.
This is where things get amazing! Because bell curves have already been analyzed to death, I don’t have to do any dirty work, and can just spit out numbers from any statistics textbook and/or website! The average for this curve, based off 100 coin flips, is going to be at the center with a value of 50. The chart can be broken down by standard deviations to figure out what percent of the area is made up by what values. If we know the standard deviation of the data, we can figure out how much area is under each section of the curve, and so, how unlikely it would be to see that value come up. As it turns out, for 100 random trials the standard deviation would be somewhere in the ballpark of 5. For the first 5 in either direction from the median, we cover 34% of the area under the curve, because math. Neat stuff, right? (You can say no...I don't mind...but I think its neat)
So how does this affect our two swords? Well, it means that there is only a 32% chance for us to be outside of 1 standard deviation of hits, so either above 55 and below 45. It also means that there is only a .26% chance of being outside of the 45 to 65 range. In fact, out of 10,000 simulated trials done in excel, only 360 were outside of +/- 10 from the average, as we would expect with the math.
So with that somewhat explained, how does it apply to the situation at hand? First, you would need to know how many rounds you have against each monster, and how much health they have. Then, you have to figure out your level of risk. So assuming that we are only fighting monsters that kill us at exactly at our previously selected arbitrary limit of 100 turns. If they have 500 health, in the long run, it doesn’t matter which sword we pick... but half the time, we will probably die. Not looking great for the blue sword. It can take out enemies with 45 health 85% of the time, though, but that is nothing compared to Red’s 100% win rate!
...but what happens if a monster has 505 health? Red’s win rate drops to 0%, while Blue’s is just barely under 50 percent. Suddenly, we made up a ton of ground. Or if we have to deal the same damage within a shorter time limit? Again, Red suddenly has no choice but to resign to never beat the game without better gear, whereas Blue can suddenly begin to shine. In fact, if we had infinite time, we could kill a monster that has a full 1000 health! It would be like winning the lottery while getting eaten by a rabid shark that was just struck by lightning, but theoretically...it could happen!
Now, you won’t always get 100 rounds against your opponent, which affects some of these numbers. As the number of rounds increase, the effect of the variance decreases thanks to the Law of Large Numbers. This means that as the number of turns decrease, the variability is more pronounced. So lets look at what happens with ten turns instead of 100. The average damage is still where we would expect it to be at 5, but the standard deviation changes to be 1.5. This means that our 68% is now within 3.5 to 6.5, and our .26% is now at .5 to 9.5. Suddenly, it doesn’t look like quite the best option yet.
Now here is one final thing to consider about the two swords, and is something that I have yet to mentally reconcile, to be honest. If you have 2 attacks at 50% to hit, the expected result would be that, on average, 1 attack hits each time. But consider this: each turn has 4 possible outcomes, each with equal odds of happening: both miss, only the first hits, only the second hits, or both hits. 3 of the 4 outcomes are equal to or better than the Red sword, so you have 3:1 odds of Blue being the same or better!
But ultimately, math cannot make this decision. In the end, you have to go with your gut as to what ‘feels’ the best, and a lot is to be said for the context. However, I hope that this has helped in your consideration when encountering similar scenarios. Or at least you’ll have an ethos.