Archive for March 2010
Regression to the Mean and Owning Some Chumps
Let’s say that you’ve hired a coach to help you improve your Slayer game in Halo 3. I’ve heard of stranger things. Let’s say this coach looks like Mr. Miyagi but he curses WAY more. He uses a variety of training and motivational techniques, ranging from grenade throwing drills to trigger finger sprints, doing everything he can to drive you towards perfection. You notice, though, that he eventually stops praising you whenever you rank at the top of a match. He did at first, but now when you earn more than your usual number of kills your coach stands stoically by, straight faced and not giving you a single word of praise for those outstanding rounds.
Eventually, you ask him why he never praises you when you do a really good job.
“Because,” he says, “I’ve noticed that praise doesn’t work. Every time I praised you for a really good round, your next round is always mediocre. And what’s more, when I yell at you for playing poorly, next round you always do better. Praising not only doesn’t make you better, it makes you worse.”
You pause for a second, then cry “You’re not my real dad!” and run out of the room, bawling like a child. Yes, you do. That emotional outburst aside, though, is your coach’s logic sound, given that you DO in fact perform worse every time he praises you for doing well and perform better whenever he rebukes you for doing poorly? Praise makes you do worse and berating makes you better, right?
Nope. Your performance following stellar rounds of Halo or Starcraft II any other game involving skill can be best explained not by the effects of praise or punishment, but by something called “regression to the mean.”
Let’s assume that if we looked at your performance over a bunch of matches and plotted them out with ending scores along the X axis and how often you end a match with that particular score on the Y axis. They’d probably form something close to a normal, bell-shaped distribution like this:

Figure 1: Your sick skilz, plotted
If we were to pick any single match at random, it’s more likely that your performance would be about in the middle somewhere –somewhere near the “mean,” which is basically another word for “average.”1 In this example, that’s 10 frags. It’s rare that you’re at the very top (17 frags) or bottom (3 frags). In fact, if your performance follows a normal distribution like the one above, then the following will be true:
- 68% of your matches will end with scores between 8 and 12
- 95% will be between 6 and 14
- Only 0.6% will be under 4 or over 162
And even if your distribution is a little skewed because you do well more often than you do poorly, the numbers won’t change much until things get REALLY skewed. At which point no amount of coaching is going to change your game in either direction.
This is the reason that you seem to do worse after good matches and better after bad ones. The particularly good or bad matches are rare, and because they’re rare it’s improbable that you’d have two in a row no matter what your coach does.
So don’t get discouraged when you can’t consistently come out on top multiple times in a row in any game of skill. You may be able to move your distribution up the right-hand side of the scale and/or squish it together so that there’s less variation, but you’re always going to regress to the mean somewhat because every round can’t be your best (or worst) round.
Now go give your dad a hug.
- Actually, in statistical parlance “average” is a vague term, but most normal people use it in the same sense that statisticians use the word “mean.” So let’s not make a big deal about it, okay? [↩]
- For the advanced students in the audience, these numbers refer to one, two, and three standard deviations above/below the mean [↩]
Xbox Game Room’s Dummy Pricing (Not for Dummies)
[Note: A version of this article appeared as my column in Gamasutra and GameSetWatch.]
Microsoft recently augmented their Xbox Live and Games for Windows services with something called “Game Room,” which allows you to buy and/or play classic arcade games like Centipede, Space Invaders, and the like. Basically, it’s just like when we used to hang out at the neighborhood arcade, only with fewer cigarette burns on the machines and no attendants selling weed out of the back office1.
What I thought was interesting, though, was the price structure for the games, which breaks down like this:
- 40 points – Play a game once on either Xbox Live or Games for Windows
- 240 points – Own the game on one platform but not the other
- 400 points – Own the game on both platforms
So if we rate those three options from 1 to 100 on an “Accessibility” metric and plot them out, they look something like this:

Figure 1
I don’t think it takes much insight to guess that Microsoft would rather you not take the first option (about $0.50), since won’t take long to figure out that playing like ONE game of Frogger is quite enough for you. They’d rather you spend the 240 points (about $3) to buy the game on one platform, or even better 400 points (about $5) to buy it on both. But I don’t think these prices are optimal for that. I think there’s a way for Microsoft to actually get more money out of people by raising their prices.
How? Well, I’ll get to that. But first let’s talk about magazine subscriptions. In his book, Predictably Irrational2 behavioral economist Dan Ariely describes seeing an ad for the periodical The Economist with the following annual subscription options:
- Economist.com website only: $59
- Print edition only: $125
- Print edition PLUS website access: $125
Bluh? Why would they try and charge $125 for just the print edition and then at the same time offer that PLUS the website access for exactly the same price? It make no sense.
Or does it? These people know economics. It’s RIGHT THERE in the name of their publication! To test things out, Ariely showed The Economist ad to 100 MBA students and asked them which they’d choose. He got the following results:
- 16% chose the Economist.com website access for $59
- 0% chose the print edition only for $125
- 84% chose print edition PLUS website access for $125
Okay, no surprises there. But then he removed the “print edition only for $125″ option and asked the SAME students again. Same people, same choices –the results should have been identical, right? Nope.
- 68% chose the Economist.com website access for $59
- 32% chose print edition PLUS website access for $125
What? They flipped their preference even though the two remaining choices were the same as before! Why? (Click here to read about all this in an excerpt from Ariely’s excellent book, or better yet go buy it –it’s a great read.)
The reason, as usual, is because of how our brains are wired. We simply aren’t very good at evaluating things in absolute terms, like the value of having a subscription to a Web site versus a print magazine. Instead, we tend to compare things to other similar things, especially when trying to quantify something abstract like value or fun. How good is this apartment for rent? Well, it’s better than the last one you saw but worse than the first. How much fun is Game A? Well, it’s more fun than Game B, but not as much as Game C. If you want to see this kind of thing in action, just ask ANY group of nerds to rank the Star Wars movies and then STAND BACK.
Decision making requires more deliberation and data when our evaluation of the options are spread out, as in the graph of Game Room purchase options above. But when some of the options cluster together, our decision-making process tends to exclude or downplay the options outside the cluster because including them in our evaluations makes things pretty complicated. For example, imagine you’re trying to decide between three downtown restaurants for dinner after a movie. Two of them are nearby and one requires a bit of a walk. Let’s assume your feet hurt and you’re on a tight budget, so both distance and price are equally important. Most people will end up making their decision by going to the cheaper of the nearby places, despite the fact that the restaurant farther away may not only be cheaper than either, but enough so to warrant the walk.
Why? Because just using price to decide between the two otherwise most similar options is an easier decision to make than trying to figure out the relative value of proximity and price and combine those values in a precise weighted combination so as to come to a completely rational decision. People’s brains tend to slide into the path of least resistance when making anything beyond the simplest of decisions.3 So savvy companies like The Economist try to frame and simplify their sales pitches so that you glide right to where they want you.
This is why I think Microsoft could alter their Game Room pricing to something like this:
- 40 points – Play a game just once on one platform
- 360 points – Own the game on one platform but not the other
- 360 points – Own the game on both platforms
Which we could graph like this:

Figure 2. Saying things like "Figure 2" makes it sound all legit, right?
Do those two options on the right jump out at you more so than before? They do me. And I’d bet that a lot fewer people would be interested in just dropping two 40 points for a one-time play. Or maybe you could bring the price of both the “own on one platform” and “own on both platforms” option down to 240 points. Your choice! And you could take this concept even further –how do you think a fledgling MMO could benefit from pitching prospective players on monthly, quarterly, or annual subscription packages? Do you think you’re any better equipped to avoid this kind of manipulation after reading about it?
- Or maybe not; I’ve never been to your place [↩]
- Ariely, D. (2008). Predictably Irrational: The Hidden Forces that Shape Our Decisions. New York, NY: HarperCollins. [↩]
- c.f., “Why We Love Genres So Much” [↩]
Framing and World of Warcraft’s Rest System
One of my favorite things about human psychology is how a punishment can be turned into a reward just by changing the way it’s framed. A few years ago a friend of mine was serving on the board for a large conference and negotiating a contract with the hotel where the event would take place.1 Part of the contract dealt with giving hotel room discounts to a limited number of attendees, but they were first come first served, after which the room price would go up. My friend wrestled with how to present this to attendees, grumbling about how he was having to tell people he was punishing them by raising the prices if they made last minute plans to attend the conference.
“Dude,” I said, ’cause I really do say things like that, “It’s not a penalty for late registration, it’s a reward for people who register early.” And with that, the wording on the conference registration changed from “late registration fee” to “early registration discount.” And nothing else changed, except that people probably thought it was more fair.

Word of Warcraft framing. Get it? Eh? Eh? Eh, yeah, you're right, it's not that funny.
In a recent episode of the nifty Idle Thumbs podblast2 Gamasutra’s Chris Remo articulated another great example of this kind of simple framing in how World of Warcraft’s “rest bonus” system came about:
In World of Warcraft what they did when they first designed the game was they had an experience system that would, over time, lower the amount of experience you got because [Blizzard] wanted to encourage people to play for like two hours at a time instead of twelve hours at a time. So the longer you played you’d get this experience degradation and then it would bottom out and at that point it would be a fixed rate of experience. And people just hated it.
And so they went back and [Blizzard's Rob Pardo] was like allright, basically what we did was we made everything in the game take twice as much experience to achieve as before and then we flipped it. So actually what happens is you start getting 200% experience and eventually it goes back down to 100%. So that effectively now how they spin it is that if you log out for a while you get this 200% boost when you log back in! And then over time it goes away and you just get regular 100% experience. It’s EXACTLY the same as it was before, except NOW everyone is like “Fuck yeah, Blizzard, this is exactly what I want!”
So, in other words, people hated the system when it was presented as a penalty for playing too long at a stretch, but they loved it when it was framed as a reward for taking a break. Even though the results were exactly the same. Such is the magic of framing.
Et Cetera, March 2010
And now comes the time again where I dump a bunch of little stuff I didn’t want to make individual updates for.
ONE: The website is getting more attention than I thought it would, so a big thank you to everyone who linked here from your blog, Twitter, Facebook, or wherever. I even got huge a traffic spike the other day from Metafilter, so OH HI to everyone who came from there. Grab the RSS feed before you leave. Now, next on my checklist is getting onto the front page of Digg.com…
TWO: On a similar note, I’m really impressed with the quality of comments people are leaving. I learned long ago to accept having my ideas debated (if nothing else, grad school familiarizes you with the art of ruthless critique), but what really impresses me is that when people disagree or offer a different interpretation, they’re doing it in a civil and thoughtful way. This is generally true, but the stories on the glitcher’s dilemma, genres, and attraction-selection-attrition are particularly good examples, both of differing views and people expanding on my own initial thoughts. Go read those comments if you haven’t.
THREE: I’m taking this show on the road! In collaboration with some of my buddies at GameSpy Industries I’m presenting a lecture at the Login 2010 conference in Seattle come this May. The title is The Psychology of Games: Why We Do What We Do With Friends (and Screw That Other Guy). Here’s the abstract:
What can decades of research by psychologists tell us about how gamers behave differently when playing video games with strangers versus with friends or alone? Under what conditions will grown men and women in multiplayer games do things like cheat, abuse glitches, hurl vulgarities, form allegiances, return favors, play fair, welcome newcomers, and form communities that persist outside of your game?
Hey, this stuff is human nature, and psychologists and behavioral economists have been looking at these kinds of things in other contexts for a long time. They just use their own jargon –stuff like prospect theory, deindividuation, reciprocity, game theory, social identity building, decision-making heuristics, person-organization-fit, distributive justice, and other fancy terms. Sometimes they even draw diagrams.
In this session, a Ph.D. in psychology who also happens to be an avid gamer will bridge the gap between these two worlds by looking at what the science of psychology has to tell us about why gamers do what they do when they’re in groups and how game designers might leverage these kinks in the human mind to design better experiences for everyone involved. Each topic will be accompanied by a review of relevant scientific research from the fields of psychology and behavioral economics, as well as real-world data from actual gamers to back up the claims and test the hypotheses.
I’m going to post a more detailed outline of the lecture soon, and hopefully after the conference I’ll be able to point you to where you can get a recording of the presentation. But if you’re going to be at the conference, please come see me! Shout “UNEXPECTED HOT POCKET!” in the middle of my talk and we’ll share a laugh.
FOUR: Thanks to Alex for hitting the PayPal donation button and buying me a copy of the book Nudge: Improving Decisions about Health, Wealth, and Happiness by Richard Thaler and Cass Sunstein. I’ve referenced the book once or twice already on this site, plus I have at least one other article idea drawing from it. Want a review? Lucky day! I wrote a full review of Nudge over on my personal blog.
Picking Your Guildies: The Role of Attraction, Selection, and Attrition
What leads gamers to join one guild in a massively multiplayer game or one clan in an online shooter over another guild or clan? Why do you post on the gaming messageboard that you do as opposed to one of the other countless alternate ones? And once you’re in a group, what kind of things make you leave?
Industrial-organizational psychologists, who use the tropes of psychology to study people in the world of organizations and work,1 have come up with a lot of theories on why people choose to work for one company over another, why they leave, and how those things affect the “culture” of the place –the shared understanding of what is expected and rewarded within that group. Some of these models lay more credit at the feet of organizational structures, and some credit the environment. But another view known as the Attraction-Selection-Attrition (ASA) model,23 says that it’s the people that determine the culture of whatever organization you’re looking at, be it guild, clan, messageboard, or mod team.
In brief, ASA says that it’s the people in the group that define the culture4 , not just the environment, structure, or rules of the game. It does this through a three-step cycle:
- New members are attracted to the group by what they perceive to be similarity in values, goals, and interests
- When petitions are made for membership, the gatekeepers in the organization select would-be members based on who is most similar to them
- Attrition happens when people who don’t fit in so neatly after all find better things to do than hang out and deal with the guild drama

Figure 1: The ASA cycle. Also, this whole thing is moderated by lolcats. Somehow. Science is still working on that part.
This isn’t exactly mind blowing, but it has implications if you think it through. One being that it explains the three-pronged mechanism by which cohesive, like-minded groups of people develop over time. People that are at odds with the culture within the guild or clan tend not to want to be a part of it. And if they do, they tend not to be selected for membership. And if that happens, they tend to rage quit over time.
For example, back when I was playing lots of Team Fortress 2 I hung out a lot with guys from a website called “Portal of Evil.” These were guys who ran goofy game mods, played on experimental and occasionally awful maps, and who broadcasted obnoxious music and trash talk over allchat. I played with them regularly because I thought all of this was hilarious and fun. But if hadn’t wanted my Engineer wearing a jaunty party hat or couldn’t tolerate hearing “Baby Got Back” on allchat FOR THE FIFTIETH TIME THAT NIGHT, I would have found someone else to play with or been mocked for complaining.
Likewise, guilds in massively multiplayer games are sometimes interesting in how they evaluate petitions for membership. A friend of mine who wanted to join a hardcore raiding guild in World of Warcraft once described this process as an audition where he was grilled about his play style and history, his character build, his equipment, and how many hours a week he was willing to devote to to the guild. He was then taken along on an actual raid where the guild’s recruiter used UI mods to track his performance in the game along very strict measures to see if he could properly play his role. In the industrial-organizational psychology parlance, we call that kind of thing a job interview and a work sample test. It’s exactly the kind of thing that the “S” part of the ASA model describes. (And if you, dear and handsome reader, have personal experience with this kind of thing, I’d love to hear about it in the comments section.)
What’s even more interesting to me is to consider is how game designers and community managers might use something like this model to guide their efforts if community is a big part of their game.
First, the ASA model points to providing players with tools that they can use to communicate their goals, values, and desires to each other. Allowing players to formulate and share a charter that signals these things would be great, as would communication channels like messageboards and private chat to which prospective members could be invited to eavesdrop. Statistics about guild/clan activities could also provide a strong signal –things like rankings, achievement counts, manhours played, headcount, or other metrics could be invaluable to people shopping for a group to become part of.
And this information works both ways –people who aren’t as into PvP combat could self-select out of the process while those who are will find it easier to find guildies who share those values. Heck, what if you borrowed another idea from the world of Industrial-organizational psychology and allowed players to submit anonymous responses to standardized surveys asking about what values their guild or clan holds? “On a scale of 1 to 5, my guild is forgiving of people who miss scheduled events.” Useful.
Game developers might also want to provide tools that team leaders can use to evaluate potential members. Gameplay stats and standardized application blanks could be really useful, as could be information on complaints filed against that person by other players. If you provide a useful tool, players won’t have to rely on third-party tools. Or maybe THAT IS your plan, and you can facilitate it by providing data and APIs upon which players can build.
The point is that both current and potential group members are going to be looking for information about those shared expectations (i.e., organizational culture) in order to make decisions about each point in the Attraction-Selection-Attrition cycle. To the extent that a game or a service outside of a game facilitates that, people will find it useful.
- Hey, I’m one of them guys! [↩]
- Schneider, B. (1987). The people make the place. Personnel Psychology, 40, 437-453. [↩]
- Schneider, B., et al. (1995). The ASA Framework: An Update. Personnel Psychology, 48, 747-761. [↩]
- it also acknowledges the disproportional weight of the organization’s founders in determining culture, but that’s another article [↩]
The Glitcher’s Dilemma: Social Dilemmas in Games
Note: This article is also published in my columns on GameSetWatch.com and Gamasutra.com.
Soon after its release, some players of the online first person shooter Modern Warfare 2 discovered what became known as “the javelin glitch.” Someone, somewhere, somehow figured out that through a bizarre sequence of button presses you could glitch the game so that when you died in multiplayer you would self destruct and murder everyone within 30 feet, often resulting in a net gain in points. It wasn’t long, though, before the method for creating this glitch spread through the Internet and servers were filled with exploding nincompoops. In fact, it quickly got bad enough that developer Infinity Ward had to rush out a patch to fix it.
The javelin glitch presented players in the know with an interesting dilemma: they could either abuse the glitch to boost their own rankings and unlock new perks, or they could abstain and preserve the game’s fair play. Of course, the problem is that if they abstain, someone else may abuse the glitch and dominate the match. The middle ground is when everyone glitches, but the resulting pandemonium isn’t as much fun as fair play for most normal people.
Let’s simplify the discussion by assuming a two-player deathmatch game in Modern Warfare 2. Look, I’ve created a table to summarize the dilemma for you! It’s suitable for framing.

Figure 1: The Glitcher's Dilemma
So what do you do? Psychologists and economists who study this kind of decision-making call it a “social dilemma.” In these situations, intentional griefing notwithstanding, each person has what’s called a “dominating” alternative where they’re most likely to win (in this example, abusing the glitch) but most people REALLY want the “nondominating” alternative produced when everyone chooses to abstain from it. Especially once the novelty factor wears off.
Back in the 1960s research on these kinds of dilemmas exploded and out of it came what’s known as “the prisoner’s dilemma” based on an anecdote about getting confessions from two prisoners held under suspicion for a bank robbery. In his book, Rational Choice in an Uncertain World1 Robyn Dawes summarizes the classic scenario thusly:
Two men rob a bank. They are apprehended, but in order to obtain a conviction the district attorney needs confessions. He succeeds by proposing to each robber separately that if he confesses and his accomplice does not, he will go free and his accomplice will be sent to jail for ten years; if both confess, both will be sent to jail for five years, and if neither confesses, both will be sent to jail for one year on charges of carrying a concealed weapon. Further, the district attorney informs each man that he is proposing the same deal to his accomplice.
Here are those choices in table form:

Figure 2: The prisoner's dilemma
In this case, both prisoners will probably confess if they’re rational about it. Why? Because each prisoner get a better (or no worse) payoff by confessing no matter what the other guy does. Prisoner A thinks, “I don’t know what B is going to do, so if I confess it’s the best way to keep myself from getting screwed. If he keeps quiet, I go free. If he also confesses, I get 5 years instead of 10.” In other words, confessing is the only way to keep the other guy from being able to screw you over. Notice how this mirrors the javelin glitch dilemma, only with fewer explosions.
Now let’s take another example from the golden years of PC gaming. In the early days of Starcraft, a strategy called “Zerg rushing” emerged where at the beginning of the match players would quickly build lots of cheap Zerg units to overwhelm opponents before defenses could be constructed. Counter strategies developed,2 but for a good chunk of the player base Starcraft became a game of seeing who could Zerg rush faster, which wasn’t nearly as much fun as choosing from any other number of play styles or even races. So the dilemma was:

Figure 3: The ...Zerg dilemma?
Again, the dominating strategy was to Zerg rush, because if you didn’t and the other guy did, you lost, which was worse than any of the alternatives. This despite the fact that what you really both want is a varied, fun game. It’s a design issue that still plagues strategy game developers today.
Prisoner’s dilemmas and social dilemmas in general can similarly be used to illustrate the reasons for “ninja looting” in World of Warcraft where one player exploits the “need/greed” loot distribution system to get a piece of equipment:

Figure 4: Oh, you know what? Forget it.
Or you could apply it to “tick throwing” and “fireball trapping” techniques in fighting games. I could go on, but I think you get the idea. My 2×2 table making machine burnt out, anyway.
What’s really more interesting and useful, though, is to look at what psychology has to show us about when people DON’T choose the purely rational option of abusing a glitch or a winning but boring strategy. Generally, people are more likely to do this when:
- They know they will be playing against their opponents in the future and face retribution
- They expect to interact with their opponents outside the game
- They don’t expect to remain anonymous
- They don’t know how many games will be played with the same person
Under these conditions, many players will adopt a strategy where they cooperate at first (for example, they don’t glitch or rush), then if the other player abuses that trust they retaliate in kind. This is known as the “tit for tat” strategy. Some researchers with lots of time on their hands even organized tournaments where people were invited to write computer programs to play iterated prisoner dilemma games, and the programs that adhered to the “tit for tat” strategy tended to do the best.
This is why things like playing with people on your friend’s list, Steam community group, guild/clan, or a favorite dedicated server is good. And it’s one reason why random matches between strangers or pickup groups can be infuriating. Making it easy to submit ratings to the profiles of people you just played also helps resolve these dilemmas to everyone’s benefits. It’s also the reason that I love the way that Halo 3 lets you remain in a lobby with the people you just played and go straight into another round with them.3
People being the complicated beings they are it’s not a perfect system, though. Some people are just griefers out to disrupt the game no matter what. Some people won’t abuse a glitch out of a sense of honor. Some will value their ranking on a leaderboard more than a sense of fair play for any individual match. But even if none of the suggestions above is a silver bullet, they help across large numbers of games.
- 1. Dawes, R. (1988). Rational Choice in an Uncertain World. Fort Worth: Harcourt Brace Publishers. [↩]
- as well as a game-balancing patch or two, I believe [↩]
- Ringing a bell? You may be thinking about my article on how deindividuation fosters antisocial behavior and how to similarly deal with that [↩]
