Hot Hand Fallacy and Kill Streaks in Modern Warfare 2

What do basketball free throws, Modern Warfare 2, and murdering 11 people in a row have in common? Read on to find out.

In psychology, there’s a phenomenon called “the hot hand fallacy” (a.k.a., “the gambler’s fallacy” or “the hot streak fallacy” or “the clustering illusion”). The seminal work on this kink in the human mind was done by thee guys named Gilovich, Vallone, and Tversky and published in a 1985 edition of the journal Cognitive Psychology. 1 These fellows weren’t much into online shooters, but they had noticed something about basketball. Specifically, a belief among fans and players in the “hot hand” phenomenon, which dictates that a player’s success in sinking one basket is determined in part by his making the previous shot –success feeds on success and creates a type of momentum or streak.

The problem, though, was that when the researchers studied records of the Boston Celtics and Philadelphia ’76ers making shots, they found that the idea of a hot hand was a fallacy. In fact, if anything, a player’s success on a previous shot slightly predicted the failure of a subsequent shot, perhaps because overconfident players were taking riskier chances. So the idea of a hot hand was all in your hot head.

What does this have to do with video games without “NBA” in the title? Enter Modern Warfare 2 (MW2), Infinity Ward’s military first person shooter. The multiplayer side of MW2 has a feature called “kill streaks” that, as far as a player motivation tool goes, is fairly reminiscent of the hot hand phenomenon. In short, killing a certain number of opponents in a row without dying yourself rewards you with powerful perks like dropping supply crates, calling in heavily armed gunships, or at the extreme end bringing down a nuclear strike to cut the match off at the knees.

Modern Warfare 2

This guy is just one kill away from his killstreak bonus. Unfortunately the guy behind him beat him to it.

To be sure, some players get lots of kill streaks because they are tiny, radiant gods of destruction whose skills at the game put every last member of the Boston Celtics to shame (who prefer Halo 3, after all). But skill aside, does the kill streak system in MW2 work in the sense that it gives players some momentum that propels them towards otherwise unreachable acts of virtual carnage? Is a player who has 10 kills in a row any more likely to get the 11th one needed to unlock a kill streak reward than he is to get the first kill?

Nope, says the science of psychology and basic probability theory. It’s all in their head because splash damage and javelin glitch abuse aside, each shot is basically an independent event. For any given player, any perception of kills clustering together more than usual is just a product the human brain’s tendency to see patterns where there are none –a phenomenon called “apophenia” by psychologists trying to win at Scrabble.

In fact, I’d wager that MW2 players are less likely to get those capstone kills than they are to get the first few in a streak. Interestingly, Microsoft, Activision, Infinity Ward, or someone else connected with the game probably has the data to directly test this kind of thing –they track everything these days. It’s be really neat to recreate Gilovich, Vallone, and Tversky’s 1985 study of basketball shots using data from Modern Warfare 2 to see if someone is more likely to kill or be killed as they approach the killstreak payoffs. Heck, somebody get me the data and I’ll do the analyses myself!


1. Gilovich, T, Vallone, R, & Tversky, A. (1985). The Hot Hand in Basketball: On the Misperception of Random Sequences. Cognitive Psychology 17, 295-314.

24 thoughts on “Hot Hand Fallacy and Kill Streaks in Modern Warfare 2

  1. Pingback: The Psychology of Video Games blog (Madigan, 2009) « VG Researcher – Psychology

  2. Did any of the studies of the “hot hand fallacy” delve into the sense of confidence that is gained once someone perceives they are on a streak? For example, in basketball, sensing you are “hot” often is accompanied with an adrenaline rush, a burst of energy, and a sense that you’re “on” and can suddenly do more than you thought you could. This could be bad and good — you’re more likely to take intangible risks, or you could be more likely to play aggressively and succeed in other ways besides shooting.

    The same could be said for gaming — because you’ve got the “hot hand,” you might change your playing style in intangible ways that have ancillary benefits, such as not camping too much, moving around and becoming a more difficult target, attacking an advantageous position, etc.

  3. I’m not sure they examined confidence per se, but as I said they did find that success on a shot actually slightly predicted failure on a subsequent shot. Presumably because the players were more confident and went for harder shots.

    Some of the players were apparently hard to convince. Andrew Toney had to be shown the data proving that his success rate of 46% overall dropped all the way to 34% when you looked only at shots made after sinking the previous three. And, more bizarrely (from his point of view), his success rate shot up to 52% when you only looked at shots where he had MISSED the previous three.

  4. There may also exist an important difference between making shots in basketball and playing an online shooter in terms of streaks. And that’s the perceptions of one’s opponents. In terms of free-throws, the basket has no reaction to you just scoring a series of shots.

    In MW2, it’s obvious to people you’ve killed and potentially other players (if your streak is announced) that you’re a skilled player, or that’s the perception. This perception of you as the predator and them as the prey is likely to cause a moment of fear when they encounter you, causing a potentially significant delay in their proper reaction. In that fight or flight scenario, the brain is more likely to tend toward flight, at least for a second, which spells death, since rarely is flight a viable option in an online shooter.

    So the sequence goes:

    Perception of stronger opponent –> inclination toward flight –> no option of flight available –> resolve to fight

    Where for the person with the kill streak the sequence is:

    Perception of weaker opponent –> resolve to fight

    This alone could continue the person’s kill streak and give them a significant advantage. It would be interesting to see this study repeated in more direct competitive environments than simply manual skill based ones.

  5. You do realize that these kill streaks do lead to other kill streaks as well? If you get a predator missile at 5 kills, you will most likely get a harrier strike at 7. This is because you have a much better chance of getting 2 kills from the predator missile than running around trying to get 2 more. This adds to momentum, and a general strategy of using kill streak rewards. For example, if I have my loadout at 5 kills (predator), 7 kills (harrier), and 11 kills (chopper gunner) I will be able to get to the chopper gunner much easier than if I had to kill everyone on the ground.

    Also the inclination of the kill streak rewards is welcome, especially in Team Deathmatch. With a reward for not dying helps the whole team. Instead of some idiot running out in the open to die, they might be much more careful knowing they can reach a kill streak reward.

    In other words, I would bet that they would most likely reach those other kill streak rewards because they would have assistance to reach that goal.

  6. Hrm. The subsequent kill streak rewards are a wrinkle I hadn’t realized. You’re probably right about subsequent kill streaks. The point still stands for the first one, though.

    Not sure about teamwork being a factor, though. Wouldn’t a good team always be assisting each other and not just when someone is nearing a killstreak goal? Suggesting that a team focuses on covering the members who are nearing a killstreak payoff implies a pretty darn impressive amount of teamwork. Maybe at the very top end of competitive play, but certainly not in pickup games.

  7. I’m going to have to agree with Mark here. Jamie, while your thesis is interesting and certainly does apply to many video games, I think citing MW2 was a poor choice. As Mark noted, this game is designed to truly give the player an advantage if they are doing well, and in fact make the probability of getting subsequent kills increase. While I suppose you are correct in saying your theory still holds true leading up to the first kill-streak reward, this pretty much ends after 5 kills, which, in the scheme of things, is pretty insignificant.

  8. Is it? I totally concede the point that calling in a gunship, for example, invalidates the “scoring each point is a unique event unrelated to all other points” assumption. But given that the killstreak counter resets when you die, I’d guess that people are going for the 5th kill a lot more often than they’re going for the 11th or beyond.

  9. I just need to call a time-out to reflect on this and just say how cool what you are doing with this site is. It’s now in my favorites. Most people, at least on Xbox Live, play Modern Warfare while shouting profanities and racial slurs. So I just need to say ho great it is to be able to step-back and reflect on all of this, and do so in an intelligent and seemingly friendly place. Now, back on topic! If we were discussing any other game, Halo for example, there would be no disagreement from me. I completely agree with the idea that the excitement and momentum of a kill does not by itself increase the probability of any amount of following kills, be it one or a series. I just disagree with supporting this by using Modern Warfare’s “kill streak” rewards. For example, “Is a player who has 10 kills in a row any more likely to get the 11th one needed to unlock a kill streak reward than he is to get the first kill?” Yes. Because for your first kill, you must rely solely conventional weaponry. But at a 9 kill streak, the player has the option to call in a Pave Low. If the player is careful and takes cover, that’s pretty much an automatic 11 kill steak, resulting in a chopper gunner or ac130, which then results in the player being ever closer to the 25 mark. Let’s look at it in very simple terms. With the kill streak rewards implemented, it is difficult, but very possible for a player to obtain the 25 kills needed to drop the nuke. Now imagine getting that streak without the kill streak rewards. Possible, yes, but only for the most insane players. And I have to disagree that people, at least those who have been playing for a little while, are going for the predator missile, and not the chopper gunner.

  10. Thank you for some VERY cool reading. I noticed that when I’m playing (and I’m not that great) I do seem to be on self momentum if I get to a 5 kill streak. I am lucky to get two or three kills in a row but, if I get to a point where I need three more to get a chopper gunner, I seem to always get there (this is after the gracious kills awarded by streak equipment). So for me, I feel that I do a little better as momentum kicks in. It really seems to ring true when your on the other side of the fence. If your losing via killstreak awards, the momentum effect seems to rain down making any effort to regain momentum almost useless. Thanks for a really cool topic.

  11. The hot-hand fallacy applies to statistically independent probabilities, which doesn’t apply in the case of most videogames. As @Brian Newton observed in a previous comment, players make decisions based on a constant flow of new information. Beyond this, one can observe that players in a skill-based game use information (such as the strengths of opponents, situation, the map they’re on, etc.) to decide whether they’re doing well or not.

    A related question that might be interesting to explore: what’s the tendency of players to ascribe “luck” (things beyond their control) versus “skill” (ability to dominate weaker players) to whether they get a kill-streak (or any other form of in-game recognition)? Does the perception of luck vs. skill have an impact on how the player values the recognition/achievement/badge/loot/reward/whatever?

  12. @Jon Radoff – The tendency of players to ascribe luck vs. skill to their successes or failures is an interesting one. And it seems to be quite complex, because it’s socially mediated. Dan Cook wrote about this in an excellent post about Testosterone and Competitive Play. When you’re playing with friends, there’s an inclination to ascribe your own success to luck, because socially it’s important to limit your dominance displays when they’re aimed at people you actually care about. So winners tend to say things like “Oh, I was just lucky” when playing with friends.

    On the other hand, when playing with strangers, it’s the *losers* who tend to ascribe results to luck, because this undermines the dominance of the person who just pwned them (at least in the loser’s mind).

    I’d recommend Dan’s post, it’s a fascinating read.

  13. Aside from killstreak bootstrapping (the classic 5-7-11 sequence mentioned by Mark), there are other factors that create relationships between kills in MW2 which make it a poor comparison to basketball.

    Often you can get a killstreak by “rolling up” an enemy team from behind. If a group of four or five enemies are entrenched in a static battle with your friends, it’s not that uncommon to be able to walk up behind them and wipe them all out, especially if you use a silencer.

    Also, your broader team could have the enemy team “on the run” if the momentum is going a certain way. If the enemy team can’t reform and claim some safe territory, they are at a significant disadvantage because their backs will tend to be exposed. This situation is continued when they’re getting killed over and over again and respawning in random locations too often to form a group or a front.

    Finally, if I am one kill away from a streak, I can start using tactics that increase my chance of getting the next kill. This is especially true in objective games in which I can choose to stop taking risks to get the objective and switch to pursuing kills alone. This means camping in a spot that has no relevance to the objective (so enemies won’t predict me being there) or following a teammate (who I’m hoping will get shot first).

    MW2 is generally a very dynamically complex game so it is hard to analyze (and very interesting to play).

    A better comparison than the team modes would be Free-For-All, in which kills are much more independent events, and killstreaks are somewhat less common.

  14. Hey I am enjoying the site and I just want to drop in on this topic since my counter now says over 5 days playtime in MW2 and I also have a very strong interest in psychology. I do not think that if I get 2 or 3 kills in a row I am likely to get more. There is always a chance you will be shot down. Which is probably why they added the buzzkill which gives an enemy player more exp for killing you if you are 1 off of a killstreak. However, the killsteaks themselves help you get more kills. If I get up to a predator missile at 5 kills, I can almost guarantee I will have a harrier as soon as get to deploy the missile. Why? Because the predator is player controller and the player decides to deploy it. So, you can watch the ticker to see when a couple enemies die and it is likely they will respawn together. Boom, double kill, harrier incoming. Unless the enemy team is all using cold blooded, or the map is just not good for air support it is very likely that your kills plus the harriers will carry you to 11, or whatever your choice may be. There are many ways of intimidating in mw2, most notably the title and emblems which your enemies see whenever you kill them. In closing I would say that when I play I am going for 11 because I enjoy the AC-130 so much. The others just help me along the way. I can see players keeping counters in their heads and when they get so close to something I enjoy as much as the AC-130 often doing like me, choke.

  15. There is a similar mechanic in Team Fortress 2. When you manage to kill a certain enemy 3 times without him being able to kill you, you DOMINATE said opponent. You become his NEMESIS, which is accompanied by a sound cue and a semi-transparent flag above your avatar’s head.

    In my experience, this works as a hot streak breaker, if anything. I found that your nemesis is more likely to focus fire on you, because he gets points for breaking the domination and has a strong(er) visual cue to kill you.

    Valve, if you read this, let me have your data! 😉

  16. I believe the effect of self-confidence plays a heavy role here.

    Anyone attemting to do a task is much more likely to succeed at it if he genuinely believes he is capable of succeeding. Thus succeeding the 6th time is more likely after five previous successes, because the person no longer doubts his own ability.

    Of course this can lead to failure due to overconfidence, but i believe this to be a relatively minor effect compared to self-doubt(just consider what if the person FAILED five times – this would make failing the 6th time even more likely, as trying to win seems to be a futile effort – a downward spiral)

    Of course, the basketball research shows something different. I’d say this is because the players, being pros, did not have any doubts about their abilities, so the effect of gaining confidence did not affect them(as much as, for instance, a casual MW2 player). So i’d say whether the hot-hand theory is a fallacy or not probably depends on the target group.

  17. Unlike other posts this was complete faile. In MW (I dont playe mw2 – no dedicated servers , no buy) the streaks are engineered event.

    When you want them you play a specific play style. It all aimed at killstreak whoring, for example I could find nice safe spots and camp people, I could get my airstrike to strike on enemy spawn area( on top of that I can deliberately die just after getting airstrike and get another airstrike after death )

    Kill streaks in MW have absolutely NOTHING to do with probability or “hot hand”

    Killstreaks is a feature I actually dislike 9and it completely ruined all hardcore servers due to airstrike/nade whoring) . I mean in CS with quake mode killstreaks are just announcement but I enjoy it more cause there is no deliberate farming for them

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