For those of you who have complained that the TAPL rewards negative skill, I have developed a new metric, the Convolution Integral, that measures only one skill: the ability to gain Elo points.

The Convolution Integral (CI) is a fancy name for a simple concept: the best linear estimator of a player’s potential Elo gain per game.

The formula for the CI is

10.23p1 + 6.93p2 + 3.63p3 + 0.33p4 – 2.97p5 – 6.27p6 – 9.57p7

where p1 is the percentage of first place finishes, p2 the percentage of second place finishes, etc. from your current month’s profile. These numbers are the best fit from the stats for the 33 contestants for the lifetime TAPL competition. I used only the last month’s stats because I want this metric to measure the _current_ strength of each player.

You may say to yourself: “These numbers look anemic. Only 10.23 points for a win? The typical winner may get +30, +35, or +40 points!� The answer is that the 10.23 is the skill part of the win. The rest is good luck, likely arising from good initial placement. Likewise for the -9.57 for seventh place. If you lose 30 points on a seventh, 9.57 points is for bad play and the rest is bad luck. Since the numbers in the CI are roughly one-third of the score changes we see in a typical game, your finishing first (or second, or whatever) is likely due to skill a third of the time and luck two-thirds of the time.

These numbers are likely biased somewhat because they are not derived from a random sample of players but from the 33 contestants in the TAPL competition.

You will notice that a fourth place finish is not neutral but has a small positive component. This is due either to how the dom scores work out or because the percentages do not always add to 100.

Here are the current top 25 players ranked by their CI’s. The CI’s are at the end of the strings.

25 (0.66) algios 25 2244 (5th) 10 60% 0% 0% 0% 20% 20% 0% 4.29
7 (2.07) Tom-ster 0 2241 (7th) 33 21% 45% 12% 3% 6% 6% 6% 4.14
10 (1.27) morb0 0 2226 (12th) 26 34% 15% 15% 7% 11% 7% 7% 3.09
3 (2.96) Cleopatra -33 2225 (14th) 28 25% 25% 17% 0% 17% 3% 10% 2.64
13 (0.97) XCRobin 0 2236 (9th) 24 33% 16% 8% 8% 12% 8% 12% 2.49
11 (1.13) udbking 0 2220 (17th) 24 29% 16% 8% 16% 8% 12% 8% 2.34
4 (2.53) Somis 0 2246 (4th) 52 23% 13% 21% 21% 7% 5% 7% 2.12
5 (2.41) Waveman -60 2200 (23rd) 17 29% 11% 17% 5% 11% 17% 5% 1.87
20 (0.77) Mrdanger 0 2121 (92nd) 34 17% 17% 11% 17% 17% 11% 5% 1.27
14 (0.93) ManOMan 54 2211 (19th) 27 25% 11% 18% 14% 3% 11% 14% 1.23
9 (1.42) mihai777 0 2184 (31st) 17 23% 17% 17% 0% 11% 17% 11% 1.09
6 (2.17) wowimbad -3 2130 (80th) 52 15% 21% 15% 11% 9% 17% 9% 0.82
16 (0.87) sarahxxx 0 2194 (27th) 55 23% 7% 18% 12% 9% 20% 9% 0.48
8 (1.52) petomni 0 2175 (33rd) 88 12% 18% 17% 14% 18% 9% 10% 0.45
21 (0.72) jschelz 0 2098 (133rd) 58 20% 13% 15% 13% 10% 5% 20% 0.45
2 (3.39) rnd -57 2239 (8th) 7 14% 28% 0% 14% 0% 28% 14% 0.28
1 (3.63) Mikeypoo -15 2124 (90th) 167 13% 14% 15% 16% 19% 10% 10% 0.18
12 (1.00) X LUCK X 0 2356 (1st) 0 0% 0% 0% 0% 0% 0% 0% 0.00
17 (0.85) Vohaul 30 2174 (34th) 51 21% 13% 5% 9% 15% 13% 19% -0.02
23 (0.70) hatty -27 2133 (75th) 24 12% 8% 16% 12% 29% 12% 8% -0.57
24 (0.67) leekstep -4 2151 (50th) 29 13% 20% 3% 10% 13% 13% 24% -0.78
18 (0.83) gcn05 0 2064 (187th) 79 5% 11% 16% 24% 21% 12% 8% -0.82
15 (0.87) smanzer 74 2164 (42nd) 74 17% 6% 12% 14% 12% 20% 16% -0.97
19 (0.78) Rsquared 43 2082 (162nd) 41 4% 12% 19% 9% 21% 24% 7% -1.54
1450 (0.01) skrumgaer 44 1624(3816th) 16 12% 0% 18% 18% 18% 18% 12% -1.55
22 (0.71) redsox5445 0 1234 (28320th) 78 11% 8% 8% 3% 14% 19% 33% -3.08

Notice that redsox5445 is rewarded with a large negative CI for having tanked his score.

The CI does not replace the TAPL; it is a complement to it. A better measure of current