#1 · darse
24 Jan 2012
I've written a program that gathers the results of all past Empathy games, and ranks the players according to various scoring metrics. Please provide feedback if you'd like to see other kinds of scoring.
The first list shows the top players over the last 20 games. The second list shows the results over all 748 recorded games to date. [Note: game #749 is now finished, but no results page was found for game #110.]
Both lists are sorted by the win-loss average (over a minimum of 20 games). Sorting by the average number of chips won would also be reasonable, and it tends to favour the winners of the large 100-player games in the past.
The program also produces a one-line summary for each Empathy game, but since the table is quite large, i won't post it unless there is a demand for it.
Here are four of the scoring methods i've computed:
1. The shared win - shared loss score.
All the winners share the win, and all the non-winners share the loss. For example, if there were 20 players, and two of them tied for first, then the 18 non-winners would each earn -1/20 = -0.05 for the loss, and the two winners would each get 0.90/2 = +0.45 points for the win (making it a zero-sum metric). This scoring gives roughly equal weight to each game played, regardless of the number of players. Over many games, we sum a player's win-loss shares, and divide by the number of games played to get an average.
2. The number of "chips" won.
This model is like a poker game: everyone antes one chip to play, and the winners split the pot equally. In the previous example, each of the non-winners would net -1 chip, while the winners would net +9 chips each (they gross 10 chips, but it cost them 1 for the ante). That makes it a zero-sum total again, but winning a game with many players counts for more than winning a smaller game. Over many games, we sum the chip totals, and divide by the number of games played to get an average (also known as the "return on investment", or ROI).
3. The percentage of the top score achieved by the winner.
Here we compare the player's score to the top score by the winner (thus, winners earn 100% for that game). Over many games, we sum the percentages, and divide by the number of games played to get an average.
4. The percentage of the best possible score.
Here we compare the player's score to the maximum score possible (i.e. the sum of the top 10 answers). [1] Since 10 unique answers still earns 10 points, i subtract 10 from both totals to get a fraction in the range 0.0 - 1.0. [2] Over many games, we sum the percentages, and divide by the number of games played to get an average.
I do not sort the player rankings by average percentages, because that statistic depends a lot on exactly which games were played. Some wins will achieve 100% of the maximum, while other games have tough categories where the winning percentage might be only 75%, or less.
The average winning percentage was 88.60% over the last 20 games, and has been 93.54% over all 748 games in the archive.
Footnotes:
[1] If no one had a perfect score, then you could argue that the best possible score was actually a little higher. I ignore that and just use the sum of the top 10 answers as the denominator.
[2] Some players managed to score less than 10 (e.g. an incomplete entry), but they do not score below 0.0.
For the averages, a minimum number of games is required, so that statistically meaningless results don't pollute the top of the list. If a player has played less than the minimum number of games, then their totals are divided by the minimum instead of by the actual number of games (i.e. a true Bayesian average). I've chosen a 20-game minimum, because 20 is a common number for statistical thresholds.
For the player rankings, only the players above the zero baseline are shown (roughly the top 20%). There is a natural break at the zero expected value point, just above the many players who have only played one game.
A total of 1529 players have played at least one game of Empathy in the past, and there were 52 participants during the last 20 games. I haven't shown the whole table because i don't want to risk causing any embarrassment to anyone. If you're not on the list, and would like to know your ranking and stats, send me a message and i'll send you the row.