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Skrumgaer on Ratings II
skrumgaer wrote
at 6:35 PM, Friday March 2, 2007 EST
As we approach the end of the first month under the new scoring rules, I thought I would provide more data on how the top scorers fare under the various goodness-of-fit-tests.

First, my own scores. With a rating of 1576, my profile is 160 games, 10-10-19-23-12-13-10. My score for the test against plain luck (TAPL) is 1817, for the test against my own worst rating (TAOWR), 792, and for the test against my most recent 1500 profile (TAO1500), 200.

I have developed two new tests: the test against a sample of 1500 level scorers (TAS1500) and the test against a sample of 1400 level scorers (TAS1400). I lurked among the tables until I had collected a sample of 5 players with scores within 20 points of 1500 and a sample of 5 players with scores within 35 points of 1400. I took the weighted average of the profiles for each sample and came up with 93.8 games, 12-10-15-15-14-15-14 for the 1500 sample and 274.8 games, 11-14-12-13-15-15-16 for the 1400 sample.

I do not trust the 1500 sample because, more players being in the vicinity of 1500, the sample size is too small. It would be better to do a test against your own last 1500 profile than to use the 1500 sample test.

I think that the 1400 sample is more reliable. There are fewer 1400-level players to sample from, and the ones I found tended to play a larger number of games.

Both samples show some lumpiness and we probably have to wait another month to get more reliable profiles.

I worked up the stats for the top 5 players as of 6 p.m. on March 2. In comparison to these, my TAS1400 score is 2755.

rewind, 115 games, 23-14-13-08-17-09-13, TAPL = 1257 TAS1400 = 1951

yoshiko, 183 games, 16-21-15-18-15-09-03, TAPL = 2837 TAS1400 = 3824

barbarian, 39 games, 35-17-12-05-07-07-12, TAPL = 1775 TAS1400 = 2467

sixaushoj, 62 games, 22-19-17-09-12-11-06, TAPL = 0886 TAS1400 = 1388

Wicked! 50 games, 28-26-04-06-26-06-04, TAPL = 2900 TAS1400 = 3214

Replies 1 - 2 of 2
joshuaxls wrote
at 6:51 PM, Friday March 2, 2007 EST
What are these algorithms you're using -- TAPL, TAOWR, TAO1500, TAS1500, TAS1400, etc.? I don't really understand what you're talking about without being able to see these equations.
skrumgaer wrote
at 6:27 AM, Saturday March 3, 2007 EST
joshuaxls:

The formulas measure the deviation between the actual distribution of first, second, third, fourth, fifth, sixth, seventh places and an expected distribution. If the place of finish was a matter of pure luck, the distribution would be even (14-14-14-14-14-14-14 in percentages). For each of the seven numbers in the distribution, take the square of the difference of the actual number of finishes and expected number of finishes and divide by the expected number of finishes. For background, check Wikipedia on "goodness of fit test". For the test against pure luck (TAPL), use 14-14-14-14-14-14-14 as the expected frequency. For the other tests, use the other frequencies given. In the calculations, use the actual number of games, not percentages. The numbers I report have been multiplied by 100 to eliminate decimals and make the numbers comparable in magnitude to the Elo ratings.
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