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A new measure of skill for the new scoring system--the PRoot!
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skrumgaer wrote
at 1:50 PM, Sunday September 9, 2007 EDT
Under the new scoring system, the score of a player who is playing other kdicers of equal skill would follow a random walk. The average straight-line difference between a player’s score and zero will be proportional to the square root of the number of games (see Wikipedia http://en.wikipedia.org/wiki/Random_walk) for a given level of table. So I propose as a measure of a player’s current standing the player’s score divided by the square root of games played (Points/RootGamesPlayed or PRoot for short). A player with skill will tend to have an average straight-line difference from zero that is greater than average random walk.
The advantages of the PRoot are as follows: 1. It is easy to calculate. 2. It is a fair balance between rewarding games played and rewarding points per game. 3. Playing at higher level tables is rewarded. 4. Players who horse around when their scores are zero are penalized. The one disadvantage of the PRoot is: 1. Luck is not eliminated. There will be considerable variation in a player’s PRoot. To eliminate the luck factor, we would need the average of the PRoot, but the data are not available to calculate this. The following table shows the current top 25’ers, their scores, games played, percentage profiles, and PRoots. I had the take the diamonds out to convert the scores to numerical fields. I express my appreciation to mrMichaels and RedSox 5445 for comments regarding scoring. 3 rnd 761 127 25% 18% 9% 6% 6% 9% 23% 67.53 8 Yce 538 71 26% 25% 9% 11% 9% 8% 8% 63.85 2 wishbone 771 156 21% 18% 19% 12% 11% 10% 7% 61.73 11 I'm Lost 505 67 37% 20% 11% 11% 5% 7% 4% 61.70 10 petomni 520 101 22% 16% 16% 12% 9% 14% 5% 51.74 1 Vohaul 905 339 19% 12% 10% 9% 11% 15% 19% 49.15 6 Phoenix37 581 153 21% 19% 11% 11% 5% 12% 17% 46.97 4 Zosod 624 187 20% 14% 17% 11% 9% 13% 12% 45.63 13 DoobiusMalcor 457 104 27% 12% 7% 10% 13% 12% 15% 44.81 18 SodaPop 403 81 19% 20% 11% 11% 11% 14% 11% 44.78 5 ProxyCheater 583 210 17% 17% 14% 11% 10% 17% 11% 40.23 15 Danny_DCB 413 112 22% 11% 12% 13% 15% 12% 12% 39.02 23 Cleopatra 380 96 23% 13% 13% 17% 16% 5% 9% 38.78 20 pUPAS 389 110 20% 21% 11% 8% 12% 8% 16% 37.09 14 Vermont 425 141 21% 17% 9% 19% 14% 10% 7% 35.79 7 Jos�lito Michaud 580 264 16% 21% 15% 16% 9% 9% 10% 35.70 19 XxDiceyGirlxX 399 133 18% 21% 12% 13% 12% 9% 12% 34.60 9 Ssergio 522 229 23% 15% 16% 14% 12% 10% 7% 34.49 21 Whitehawk 382 163 14% 22% 10% 8% 9% 17% 15% 29.92 16 jss 413 229 17% 16% 10% 13% 12% 12% 17% 27.29 25 Kehm 372 189 16% 13% 11% 8% 14% 15% 19% 27.06 12 GronamOx 491 343 19% 15% 10% 16% 12% 12% 13% 26.51 17 fandango1 407 286 14% 15% 13% 15% 15% 13% 12% 24.07 24 sisu 375 286 16% 18% 10% 10% 11% 14% 18% 22.17 22 Polamalu 380 305 17% 12% 15% 13% 14% 14% 12% 21.76 3813 skrumgaer 0 167 12% 10% 17% 16% 16% 14% 11% 0.00 |
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Replies 11 - 19 of 19
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Disasterz wrote
at 11:49 PM, Sunday September 9, 2007 EDT Is math a big part of your profession?
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Barkindji wrote
at 12:17 AM, Monday September 10, 2007 EDT What's mine?
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DoobiusMalcor wrote
at 12:26 AM, Monday September 10, 2007 EDT skrum:
I think you have made a mistake. For instance, Player A: Hits a homerun for every 2 at bats Bats 10,000 times Your score for him is a 50. Player B: Hits a homerun every 10 at bats. Bats 1,000,000 times. Your score for him is a 100. Is Player B twice as good as A? Is he better at all? Clearly, this is not a case where either player was simply lucky we are talking about a LOT of at bats. The confidence interval is quite narrow, and yet your system says Player B is better. What gives? PPG FTW. |
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DoobiusMalcor wrote
at 12:27 AM, Monday September 10, 2007 EDT Or, in simpler terms, rnd is #1 on your scoring.
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nuflis wrote
at 4:20 AM, Monday September 10, 2007 EDT @Doobius:
Central limit theorem helps to determine a minimum sample size, as skrum needs little sample sizes to make the system easily available to the community, CLT helps to establish an inferior limit. That’s all. In your example, the calculations are right, but I find two problems: 1/ Difference of the sample sizes: there is a relationship of 100 to 1 between the 2 sample sizes. In kdice, if calculations start in 30 games, I guess it’s difficult to find that difference (a player with 3,000 games in a month needs professional help). 2/ PRoot (or PPRG) rewards the number of games played (as the old system did). I find this fair, why not?, helps to minimize random effects and is a way to “remunerate†the “jobâ€. Otherwise a player with 30 games and a good score could be 1st and he hasn’t any incentive to stay playing. People would create new accounts and try again with an alt. |
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skrumgaer wrote
at 5:22 AM, Monday September 10, 2007 EDT Doobius:
Supposing I can employ both hitters and they bat 1,000 times in a season, and supposing the discount rate is zero, I would offer player A a contract of 50 zillion dollars for 10 seasons and player B a contract of 100 zillion dollars for 100 seasons. |
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DoobiusMalcor wrote
at 7:56 AM, Monday September 10, 2007 EDT nuflis:
Look at the solution I gave, which solves the small sample size problem while also making sense with large samples (games played). This skrum approach does not converge on 'best player' IMO. skrum: I am not following your reasonings. If the answer to 'which is a better player?' requires you to say 'well for X seasons at a time, it's player A, but for Y seasons at a time, it's player B' then its not really much of a collapsed single-value ranking. |
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unlucky9999 wrote
at 8:51 AM, Monday September 10, 2007 EDT Doob, superb comparison :) ure absolutelly right
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skrumgaer wrote
at 8:53 AM, Monday September 10, 2007 EDT Doobius:
You are the one who made up the problem, you have to live with it. In baseball, since all active players have approximately the same number of games and at bats, Player B would be employed over a larger number of seasons. But the number of seasons is actually not relevant. Suppose Player A is a pitcher and there are 100 pitchers on the roster. So he has only 1/100 of the at bats of Player B. I would offer him 50 for the same number of seasons I offered player B 100. |
