Author: Stephen A. Boak
Date: 03:03:44 07/29/00
Go up one level in this thread
On July 29, 2000 at 04:29:28, Ricardo Gibert wrote: >The ELO system does not try to model every possible scenario. They could (try) >do that, but instead rely on the rating approaching the true strength >_eventually_. Thus in the above case, the Elo system simply waits for yet >another 9 games to be played. They _could_ model such situations by say giving >more weight to the games played latter on. Huh? Some clarification is in order: 1. A TPR (of formula suggested or perhaps adopted by Professor A. Elo) is used only for a temporary period, to establish first a provisional, then eventually a starting ELO rating. The TPR is based on the assumption that after a reasonable number of games the TPR average (weighted for numbers of games played in each tournament) will approach a new player's 'real' strength (or ELO rating). The TPR is not guaranteed to be exactly equal to a new player's 'real' strength, but it is accepted as reasonably close for a starting ELO rating, after a reasonable number of games has been played and rated. 2. After a start rating has been obtained using the TPR method, a more complex ELO formula (not the TPR formula used to determine starting rating) determines the rating gain or loss on a periodic basis, perhaps tournament by tournament. 3. Elo carefully explained the mathematical foundations for his ELO formula system. The ELO system is based on the accepted notion of natural variability--i.e. that a players rating (measure of strength) will naturally vary randomly above and below his 'real' strength. In simpler but equivalent terms, a player's results will vary randomly, both above and below the player's true (or mean) strength. Sometimes he will score a bit better than his ELO predicts, sometimes he will score a bit lower than his ELO predicts. Per ELO, the standard deviation for an established player's rating is some +/- 100 (or was it 200) rating points. 4. Elo realized that for improving players (perhaps young or new players that improve rapidly) the ELO rating would lag behind 'real' strength. And the reverse would be true for declining players (perhaps old or infrequent players whose strength rapidly falls). But there is no way to tell whether a recent rise or fall in ELO rating is attributable to a normal variation about the 'true' mean or 'true' strength, or is attributable to a greater trend to improve or decline in playing strength. 5. The ELO formulas for established players (those who no longer have a provisional or ELO start rating) indeed gives more weight to more recent games and less weight to older games. It is the recent games that modify the player's last calculated ELO rating, up or down, according to relative results (better or worse) of the player in those newly rated tournaments/games. Anecdote: One time I played a player of approximately 1800 USCF strength. By accident (a typo in transmittal of my opponents USCF ID No.) the tournament results indicated that I had played a player of only 1550, or so, strength. For the USCF version of the ELO rating system, I calculated (at least roughly) that after approximately 50 rated games, that rating data mistake was 'in the noise level', i.e. no longer made any difference. By the time I discovered that mistake, I had essentially played about 50 additional games, after which the initial error was of no consequence--my rating after 50 more games was virtually the same (probably identical, after rounding to the nearest point) as it would have been if the previous mistake had never occurred. So, roughly speaking, after about 50-100 games, whether a person won or lost a particular game in the past is of essentially 'no weight'. Thus your USCF (or similar ELO system) rating is affected by ongoing results, such that after a sufficient number of games has been rated the oldest of your rated games means very little or noting. --Steve Boak
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