the Art of War: statistics and player rankings

How stats work

These statistics are computed with an ELO-like system. Stats are computed retroactively from the oldest ended game to the newest one. For this purpose, the time is given by the average between the creation time and the time when the game was created (it is assumed that the most crucial choices have been made at half-game). Unfortunately, the system keeps track accurately of the game creation time only for games created after February 2, 2006, 9:13 pm. For all other games, an estimate was made.

• If you score a solo win, you score a double victory against all other players. You don't gain anything from eliminating the other players: the points you gain are independent of whether the enemy is eliminated or survives.
• If you share in a multiple win (by diplomacy), you score:
  • a draw against all the players you share the victory with, and
  • a fraction of a double victory against all other players (that is, 2-way draw: full victory, 3-way: 2/3 of a victory, 4-way, 1/2 of a victory...).
  Again, the points you gain are independent of whether the enemy is eliminated or survives.
• If you survive, you score:
  • 1/2 of a victory against all eliminated players,
  • a draw against all other surviving players,
  • a defeat against winners sharing a multiple win (see above),
  • a double defeat against a solo winner.
  So surviving is slightly better than being eliminated, because you will take some points from the eliminated players.
• If you are eliminated, you score:
  • a draw against all other eliminated players,
  • 1/2 of a defeat against all surviving players,
  • a defeat against winners sharing a multiple win (see above),
  • a double defeat against a solo winner.

And then,

• When you score a victory, you gain some rating points, depending on how strong your enemy is: if he is stronger you gain many rating points, if he is weaker you gain few rating points.
• When you are defeated, you lose some rating points, depending on how strong your enemy is: if he is stronger you lose few rating points, and if he is weaker you lose more rating points.
• When you draw, you will not lose or gain many rating points unless you are much stronger or weaker than your opponent. In extreme cases, a draw can be as good (or as bad) as 1/2 a victory (or defeat).

Important: Here and below we talk about changes in rating. Your actual rating is known only to the system. The system computes and compares all the ratings, and assigns you a rank between 0 and 10,000. Ranking changes are different from rating changes: your rank is affected also by what happens in games in which you are not involved (while your rating isn't).

For example, if a newbie turns out to be exceptionally strong, all players will gradually lose some rank points even if they have never played against the newbie. In essence, even very strong players will not look as strong as they once were.

In games with more players you can score more points if you win, and survival becomes important. Look up the following tables: in the first one you can see what your rating changes are, with your current rating; the following ones give the ratings for different possible estimated strengths.

Rating changes whenever your estimated victory probability against all opponents is 70% (Sabelkatten's mean value)

endgame:	victory	draw						victory
your standing:	win	2-way	3-way	4-way	5-way	6-way	7-way	unique survivor	all survive	unique eliminated
2 players	7.2	-2.4	---	---	---	---	---	-16.8	-16.8	-16.8
3 players	9.6	0.8	-3.2	---	---	---	---	-10	-12.8	-14
4 players	10.8	2.4	-1.2	-3.6	---	---	---	-6.6	-10.8	-12.6
5 players	11.5	3.4	0	-2.1	-3.8	---	---	-4.5	-9.6	-11.7
6 players	12	4	0.8	-1.2	-2.7	-4	---	-3.2	-8.8	-11.2
7 players	12.4	4.5	1.4	-0.5	-1.9	-3.1	-4.1	-2.2	-8.2	-10.8

Rating changes whenever your estimated victory probability against all opponents is 25%

endgame:	victory	draw						victory
your standing:	win	2-way	3-way	4-way	5-way	6-way	7-way	unique survivor	all survive	unique eliminated
2 players	18	3	---	---	---	---	---	-6	-6	-6
3 players	24	8	4	---	---	---	---	-1	-2	-5
4 players	27	10.5	6	4.5	---	---	---	1.5	0	-4.5
5 players	28.8	12	7.2	5.4	4.8	---	---	3	1.2	-4.2
6 players	30	13	8	6	5.2	5	---	4	2	-4
7 players	30.9	13.7	8.6	6.4	5.5	5.1	5.1	4.7	2.6	-3.9

Rating changes whenever your estimated victory probability against all opponents is 50%

endgame:	victory	draw						victory
your standing:	win	2-way	3-way	4-way	5-way	6-way	7-way	unique survivor	all survive	unique eliminated
2 players	12	0	---	---	---	---	---	-12	-12	-12
3 players	16	4	0	---	---	---	---	-6	-8	-10
4 players	18	6	2	0	---	---	---	-3	-6	-9
5 players	19.2	7.2	3.2	1.2	0	---	---	-1.2	-4.8	-8.4
6 players	20	8	4	2	0.8	0	---	0	-4	-8
7 players	20.6	8.6	4.6	2.6	1.4	0.6	0	0.9	-3.4	-7.7

Rating changes whenever your estimated victory probability against all opponents is 75%

endgame:	victory	draw						victory
your standing:	win	2-way	3-way	4-way	5-way	6-way	7-way	unique survivor	all survive	unique eliminated
2 players	6	-3	---	---	---	---	---	-18	-18	-18
3 players	8	0	-4	---	---	---	---	-11	-14	-15
4 players	9	1.5	-2	-4.5	---	---	---	-7.5	-12	-13.5
5 players	9.6	2.4	-0.8	-3	-4.8	---	---	-5.4	-10.8	-12.6
6 players	10	3	0	-2	-3.6	-5	---	-4	-10	-12
7 players	10.3	3.4	0.6	-1.3	-2.7	-4	-5.1	-3	-9.4	-11.6

As you can see from these tables, for below-average players surviving can be an acceptable outcome. Above-average players need to win or share in a draw with very few players to gain some rating points. Keeping a consistently high rank is hard!