Monday, September 14, 2009

People who are unintentional "spoilers"

I've noticed some interesting cross-player interactions in game win rates. If a player is good at a particular game, or games in general, you'd expect them their performance to be relatively consistent across opponents. Or, you might reasonably expect they do well against most opponents, but not against others, who beat them more often, even if that opponent isn't as good in general. That is, you might see a rock-paper-scissors kind of effect.

But, in at least two cases, I've observed a different phenomenon, where a particular player "S" has a substantial effect on the performance of player "P", without that performance coming at a cost or benefit in S's performance. Here's the two examples I've observed. All games include me as well, so it may be a three-way interaction.

I have a colleague T who we play a lot of Race for the Galaxy with. He is good at it. He has won 20 out of 46 plays, with an average number of players of 4. But, if you break it down further, there's another person "R" who basically is necessary for T's performance to be high:

T's win rate, games with R: 18/33
T's win rate, games without R: 2/13

Further, while R does better when T is not in the game, the effect on his own play is only part of the change in win rates:
R's win rate, games with T: 5/33
R's win rate, games without T: 6/16

In the other example, the effect seems to apply across all games. "E" does very well overall. In 327 games, he's won 94 games with an expected number of wins of 80, given the numbers of players. But, when A plays, E's performance suffers badly, but it doesn't really help A:

E's wins, without A: 87 wins, 69 expected (276 games)
E's wins, with A: 6 actual, 10 expected (51 games)

A's wins, without E: 22 wins, 23 expected (93 games)
A's wins, with E: 10 wins, 10 expected (51 games)

In both cases the help (R) or hindrance (A) seems mostly distribute wins to other players. Since I'm the only other constant player throughout the games:

My wins (E, not A): 65 (69 expected, over 283 games)
My wins (E & A): 17 (10 expected over 51 games)

My wins (T, not R): 6 (3 expected, 13 games)
My wins (T & R): 6 (8 expected, 33 games)

One more example, lest this all sound like sour grapes; the introduction of R or A helps or impedes the other players as well:

Games with T & !R: T wins 15%, neither I nor T wins 38%.
Games with T & R: T wins 55%, neither I nor T wins 27%.
So, R benefits T and impedes everyone else.

(Limiting to 4 player games with E & A so the percentages can be compared)
Games with E & !A: E wins 42%, neither I nor E win 40%
Games with E & A: E wins 0%, neither I nor E win 53%
So, A impedes E and benefits everyone else.

Further, I'm pretty confident in neither of these cases is the spoiler intentionally helping or hurting the other player. That is, R isn't trying to help T, and A isn't targeting E, it just happens that way.

There's lots of plausible mechanisms, psychological, in-game, and otherwise for what's going on here, for which I don't have any compelling data, but it's an interesting phenomenon, or perhaps simply an anomaly.


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