82.1.49.233: Probability of Win (2020-07-27 16:04) [#11551]

In 2010 I undertook an analysis of the winning statistics tables in E.G.D developing a model for the probability of win in even games as reported in ^[3]. I recently revisited this analyis and found that the old model no longer fits so well. The reason is that in the early days of the E.G.D, the winning probability of SDK players showed expected behaviour down to 16k, and it was reasonable to attach less weight to players below this level (there were only 15% of players below 12k). The current tables show a marked difference - see the plot in ^[6]. There are now about 30% of player below 12k and these cannot be ignored in the analysis. The effect is that departures from expected behaviour now start at 8k continuing down to 20k.

I have recently analysed data for handicap games covering the period 1996 to 2018 - this analysis is reported in ^[7]. It contains quite a few interesting plots (worth a look), even if you wish to skip the maths!

Handicap data is much more sparse than even game data, and so the raw data for probability of win is rather noisy. In handicap games it is expected that on full handicap Black should win 45% of games, independently of absolute grades. In a McMahon tournament, where handicaps are assigned according to the difference in McMahon score, the handicap is often well below the full value - there is a handicap deficit.

The work in ^[7] concentrated in developing a local model for the probability of win in terms of the handicap deficit (d) and Black's grade, for fixed values of d from 0 to 3. The data I had was too sparse to capture the case d = -1, in which black gets one more stone than expected. The model at the moment is local, because it was not clear how some of the measured parameters vary with d.

Nevertheless a reasonable fit was obtained (producing a residual better than 5%). With more data it is expected that the range of d can be widened, and a sensible model produced in which the model parameters vary with d in a smooth way. The form of the model will also fit the curves shown in ^[6].

The other main conclusion demonstrated is that for full handicap (d=0) and handicap -1 (d=1), the values for the win probability vary substantially with time - illustrated for 15k,13k, and 10k players.

All of these conclusions are tentative and will be revisited with an improved model based on better game data.