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According to this article in league of legends matchmaking there's an average of 50/50 chances of winning or loosing a game based on how system ranks a specific account (player skill). However this implies that a player is expected to loose at least half of his games (provided that he's not a student of the game) or at most he'll win 75% of the games (that's ranked top rated guys and the highest win rate I've seen in my region, so should be a feasible boundary).

However, the latter is rather rare since not so many people actually achieve that skill level (that can also be observed by going through ranked statistics) and the former is also not a constant since a) it's also in the algorithm and a queue of 1 min is most likely not a 50/50 and b) there are situations where it is extremely obvious that a player was placed against a way stronger team or vice verse.

An example from my practice is that I had a win rate of 88% which severely dropped after about one ore two weeks (to around 71%) and it rose again in a week or so with me learning nothing (I literally didn't). So, during such drops a player reward expectation is not met which results in negative attitude (taken to extreme in some cases, as was also observed). Some people were literally saying: "I hate the game" and they kept playing.

So the question is: why? why is it that with such reward volatility people still keep playing? (please, give a rigorous proof, if any, supplied with references presumably from behavioral psychology)

P.S.: I do not have any empirical data, so I realize this might be only a feeling as well as the fact that mostly I observed it through my account (not even lvl 30) and in my region. I also understand that most likely they are using statistical learning algorithms which obviously require data and will put a player to his actual rating as number of games grows (theory of big numbers).

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If you win every game, there's no challenge. If you lose every game, there's no reward. I don't think there's anything magic about an average of a 50/50 win-loss rate being "optimum," but it's in the middle of those extreme "no fun" cases. –  Cameron Fredman Mar 14 '13 at 18:01
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3 Answers

If you want a behavioral psychology answer, then here's one - if the player isn't sure if he'll win the next game, he's more likely to try one more game. If he lost, he thinks "Maybe this I'll be lucky". If he won, he thinks "Ooooh that was awesome, one more".

You actually need a 50/50 win/loss ratio to keep the players engaged. The effect is basically the same as with slot machines, and is known as a variable-ratio reinforcement schedule. Of course, slot machines don't have a 50/50 ratio; there are other effects with slots (like the chance of a huge win, and very fast play time).

The crucial element in a variable ratio schedule is uncertainty - the brain never knows what the result of the current match will be. This is what keeps the game exciting, whearas a fixed-ratio schedule would just mean "every second game is a win", which is just... plain boring.

While not really used in LoL, the other common schedule in games is variable-interval. For example, in MMORPGs you can farm monster for an hour or a day before you get the uber-loot you are looking for. The activity is more or less constant, you just don't know how long it will take.

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Well that's not exactly how slot machines work (I make them at my company) what we do is try to give people small wins. While they overall lose money, they might win back 10% of what they threw in to make it seem like they are winning. –  Benjamin Danger Johnson Mar 14 '13 at 20:31
    
+1 for the link, even though I'd presume at the end of the day it sums up to 1/2 victories (+/- extremely small % ) out of all games played thus resulting in a fixed-ratio schedule. –  Denys S. Mar 14 '13 at 20:46
    
@BenjaminDangerJohnson, obviously, if there's a 50% win chances on a slot machine with sufficiently big number of games on it there is merely no profit for the supplier. –  Denys S. Mar 14 '13 at 21:01
    
@DenysS. sorry I was trying to point out the fact that the idea of small victories can also keep people playing. For example (I've never played the game so I don't know what they do) maybe you gain xp or in game money for participation you can use to buy upgrades or make your self stronger online. Even if you lose the game, so long as you get closer to some minor goal it can be motivation enough to continue. –  Benjamin Danger Johnson Mar 14 '13 at 21:18
    
@BenjaminDangerJohnson well sure, 50/50 ratio doesn't apply to slot machines. I'll edit the answer to reflect. As for losing games in LoL, last time I played you gained a little but only about 5x less than for a win. –  Liosan Mar 14 '13 at 21:51
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There are other, more powerful factors than just "reward". In the case of competive multiplayer games such as LoL the most important one is the social component, you will likely have friends who play LoL too, and that alone will make the player much more likely to continue playing even if they are fed up with it. Another is the overcoming of challenge, and competition. You want to become better so you play more. And you want to show others how good you are.

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A win rate of 50% is the only number a matchmaking system can possibly aim for. As an example, if the system were set up to create matches in which players have an estimated 60% chance of winning, then from the pigeonhole principle, it follows that there must be a probability of at least 20% of the match ending with both teams victorious. League of Legends, as most competitive games are, is zero-sum. For every match you win, someone else must lose.

Regardless of how your matchmaking system works, if the total number of wins equals the total number of losses, the average win ratio will always be fixed to exactly 50%. That doesn't mean everyone is winning only half the time, but if your win rate is above average, someone else's must be below.

Better players will naturally gravitate towards high numbers, worse players to low. That's fun for neither. It means better players are insufficiently challenged and are conditioned to expect a win, decreasing the rewarding experience when they do and increasing the frustration when they don't. On the other end of the spectrum, frequent losses disappoint, people feel they are not given a fair chance to compete and new players are alienated from the game.

Generally, the less certain the outcome of a match is in advance, the more exciting the game will be. That is what a matchmaking system hopes to achieve. By putting players against opponents of their own skill level, it does not ensure the win rate averages close to 50%, but it lowers the variance in win rate across skill levels.

Not necessarily to a minimum, by the way. A matchmaking system could actively have new players face veterans instead of other rookies, so their win rate starts off low and increases as they get better at the game. This pushes the ratio of seasoned players to an optimum between 50% and 100%, whereas new players experience a sense of progression.

In conclusion, why aim to keep everyone winning only half the time? The alternative is to have some win too often, others not enough.

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Can you please explain the quantitative part of the pigeonhole principle applied to the problem? (20%?) –  Denys S. Mar 14 '13 at 20:55
    
@DenysS.: Both team A and team B win sixty out of one hundred games. That's 120 victories total that need to be distributed over 100 games. Given that when two compete, you can't have three winners, at least twenty matches (holes) must have had more than one winner (pigeon). It might not be the most obvious metaphor, but that's what my mind jumped to. –  Marcks Thomas Mar 14 '13 at 21:45
    
@Marchs Thomas, thank you for your clarification of the Pigeonhole. I am currently developing such matchmaking algorithm and I noticed that clearly the sum of two players to win/lose is more than a 100%. So, can these 20% be draws as well? –  user33961 Aug 8 '13 at 16:14
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