From: Larry Kaufman COMCAST NET>
Date: 2 jun 2003
Subject: Re: Dual ratings
----- Original Message -----
From: "Ross Dickson" ACHILLES NET>
To: TECHUNIX TECHNION AC IL>
Sent: Sunday, June 01, 2003 10:52 PM
Subject: Re: Dual ratings
> It is with some trepidation that I present the least mean square results
> for the enlarged data set Larry has produced.
>
> Pan-Atlantic = 0.6 times ShogiClub24 + 1100 is a close approximation to
the
> linear regression (lms slope = 0.5962 , lms intercept = 1118.7).
The slope of .6 is much more plausible than the earlier numbers. If
you force the slope to .6 (in the interest of ease of calculation), the
intercept should drop to about 1113. By a curious coincidence, if I
multiply my very latest ShogiDojo rating (2010) by .6, and add 1113, I get
2319, which happens to be my exact up-to-the minute Pan-Atlantic rating! I
feel that we are getting quite close to the "true" formula, given the
limitations of a linear formula. Note that since ShogiDojo ratings are not
allowed to go negative, the formula would imply a minimum rating of 1100 (or
1113) on Pan-Atlantic, but in fact we have many players rated below that
level. So either the true slope is higher than .6, or else the formula
breaks down below about 5 or 6 kyu Pan-Atlantic. Maybe we need a non-linear
regression, but perhaps that's getting too complicated for our needs.
I note also that the formula implies that the two systems converge at
2750 (or 2783 if we use 1113), which agress almost perfectly with my
previous states opinion.
Until further notice, I suggest we adopt Ross's formula (.6 SC24 +
1100 ) (or 1113 if you want to be exact) for setting the rating of new
players in our tournaments who have ShogiDojo ratings.
>
> The original data is in the first two columns, sorted in order of
> SHogiClub24 score, the calculated Pan-Atlantic follows, and then the
> difference between the calculated and Actual values of the Pan Atlantic
> scores.
>
> Actual Shogi Calc Actual
> PanAtl Club24 PanAt - Calc
> 2422, 2284, 2485, -63
> 2455, 2118, 2386, 69
> 2255, 2013, 2323, -68
> 2285, 1993, 2311, -26
> 2174, 1925, 2270, -96
> 2195, 1753, 2167, 28
> 2094, 1555, 2049, 45
> 1980, 1513, 2024, -44
> 1660, 1507, 2020, -360
> 2118, 1455, 1989, 129
> 2101, 1465, 1995, 106
> 2012, 1453, 1988, 24
> 1926, 1378, 1943, -17
> 1852, 1377, 1942, -90
> 1973, 1312, 1904, 69
> 1809, 1298, 1895, -86
> 2044, 1181, 1825, 219
> 1908, 1161, 1813, 95
> 1599, 1157, 1811, -212
> 1769, 1149, 1806, -37
> 1924, 1124, 1791, 133
> 1827, 1091, 1771, 56
> 1791, 1072, 1760, 31
> 2074, 1064, 1755, 319
> 1784, 993, 1713, 71
> 1772, 933, 1677, 95
> 1620, 797, 1595, 25
> 1272, 789, 1591, -319
> 1505, 635, 1499, 6
> 1138, 336, 1320, -182
>
> The large (and possibly periodic) deviation of a number of points is
> interesting. Perhaps the starting rating does have some effect.
>
I don't think starting rating is the problem. For the SC24 ratings,
the 80 game requirement virtually rules that out as a factor. For
Pan-Atlantic, it may be a problem for fast-improving players, but not for
the majority of players on the list, who are veterans.
The two very large negative deviations belong to the only two Swedes on
my list. This offers strong support for the
claim that Sweden is substantially underrated (on Pan-Atlantic) relative to
the rest of Europe (and the U.S.). The two largest positive deviations
belong to older Japanese players living in the U.S., who are more likely
than others to play on ShogiDojo during breaks from work (where they may be
interrupted) or to play after drinking alcohol at night (at least that is my
perception), so my guess is that these nationality factors may be the prime
cause of large deviations.
Thanks Ross for your statistical help.
> Ross
Larry Kaufman