For the first time the leaderboard has a comprehensive set of stats for all the players in the roster. I will be able to answer questions like: Is there any relationship of luck to rank? Or score to kills per game?

I will start by developing a set of characteristics for what could be called the zero datum player: a typical player drawn from set of all players with score of zero or nonpositive PPG. This datum can be used to calibrate other measures, such as the TAPL.

To get a rough idea of the zero datum, I took the bottom 107 players in the leaderboard who had played at least one game. The percentage stats for 4 of the players were corrupted (they add to more than 100%, sometimes much more). I eliminated these. For the remaining 103 players, I obtained the following averages:

Kills Dom Luck 1st 2nd 3rd 4th 5th 6th 7th
2.31 22% 49.04% 6% 6% 9% 18% 24% 22% 13%

These are not weighted by games per player, but a few results emerge even from this sketchy start.

1. The number of seventh place finishes is not significantly elevated.

2. Even zero datum players have an average of two kills. Is this because players like to accumulate kills even at the risk of their scores? Or is it because the zero datum will always contain some good players who are temporarily down on their luck?

As I accumulate more data I will amplify this post.

Update 6 Nov.

For the same group I have developed the weighted-by-game percentages: They are

9% 9% 11% 15% 17% 18% 19%

The distribution is flatter, with more fat in the tails. The game-weighted number of kills per games is

0.14

and individuals' average points per game is

-23.0

Update 7 Nov.

The Return of the Convolution Integral

The convolution integral (CI) is a fancy name for the weighted sum of a player's percentage profile as a predictor of that player's PPG. For a player that plays only at zero level tables, where there is no dom, under the current scoring system, the convolution integral would be

PPG = 50p1 +35p2 +25p3 +0p4 -25p5 - 35p6 - 50p7.

I have run a least-square check of my sample of 107 and the actual and predicted PPG's are fairly close, but there is some error because some of the sample have played at higher level tables and the percentages don't always add to 100.

A comparison between a player's PPG and what the CI says his PPG ought to be if he had played only at zero level tables can be used as a measure of the average level of table a player plays at, hence a measure of the risk that the player is willing to take. It can be used to compare two players with the same score.

[update 12 Nov]

I took a bigger sample of zero-score players. Of the bottom 1,005 players on the leaderboard, 181 had played no games and 59 had corrupted percentage profiles, leaving me with 765 players. Of these, the game-weighted percentage profile is this:

1st 2nd 3rd 4th 5th 6th 7th


10.0% 10.0% 10.3% 12.9% 15.5% 17.2% 19.4%

These can be used as a basis for a new test: the Test Against Zero Datum (TAZD). Substitute these percentages for the expected percentages of 14% in the TAPL to get a test that gives a bigger reward for players whose profiles are more unlike than that of the zero datum.

[Update 17 November]

I have developed a stat that measures players' devotion to the game. It also measures their gutsiness, or total buy-in.

The stat is the player's earned points divided by the convolution integral. Earned points is the product of PPG and games played. It can be either negative or positive. The convolution integral is the weighted sum of the player's percentages if he had played all this games at the zero level table. The greater percentage of the time the player risks his points at higher tables, the greater his ratio of earned points per game will be to his convolution integral. This ratio I call the guts-per-game (GPG). This should always be a positive number. The total amount hazarded, or buy-in, is the product of the GPG and the number of games.

In calculating the convolution integral, I add 0.01 points to it to avoid a zero value (it has a resolution of 0.05 points). In a few cases, because of truncation of percentage points, a negative GPG might result. I set a minimum of 1.0 for GPG for all players.

Below is a listing of top 25 players whose percentages are uncorrupted, along with members of my 765-player data set whose names may not be seen very often. A greater buy-in indicates a greater devotion to kdice.

Incidentally, the buy-in stat may be a way to spot pga's. Since two players have to risk the same number of points in a game to pga, the buy-in stats of players who pga consistently are more likely to move in sync with each other than the buy-ins of players who are not pga's.

Rank Player Games PPG CI GPG BUY-IN

11th MadHat_Sam 37 85 0.4 229.03 8474
8th Bombardier DS 65 116 110 5.9 18.69 2168
9th riccardo 321 36 8.4 4.31 1382
5,863rd Mr. Freud 67 -8 -0.5 17.27 1157
14th yellowfin 112 85 8.6 9.92 1111
5,598th Chaos§theory 80 -34 -2.8 12.28 983
23rd XxDiceyGirlxX 33 231 10.0 23.08 762
12th CuteKittens 151 45 10.5 4.30 649
5,423rd Zamorano 68 -6 -0.7 9.00 612
16th Flying Dutchman1 113 57 10.7 5.33 603
5,720th ScotsLaw 71 -36 -5.4 6.66 473
5,663rd apignarb 171 -6 -2.2 2.68 459
5,774th bugra7 155 -3 -1.2 2.45 379
5,654th logicom 122 -4 -1.4 2.85 348
5,034th phuze 97 -4 -1.2 3.40 330
5,542nd ??? ? 269 -16 -14.4 1.11 300
5,867th lmm 146 -5 -2.5 1.99 290
5,558th hextall 50 -5 -0.9 5.62 281
5,743rd junobeach 260 -16 -14.9 1.07 279
5,121st Bö bö 130 -3 -1.4 2.09 272
5,399th Sorin 241 -12 -11.1 1.08 260
5,707th timingo 207 -11 -8.8 1.25 260
5,740th Spuh 90 -7 -2.6 2.67 241
5,261st gaialovesyou 117 -6 -2.9 2.05 240
5,728th weedeater 221 -13 -12.4 1.05 232