First, I am not good at statistics. Therefore, the following article may include incorrect description. OK?
In the comments for the previous article, rating system was mentioned:
Enhancements of Elo rating system is used by TopCoder and Codeforces. TopCoder uses normal distribution. On the other hand, Codeforces uses logistic distribution.
In Elo rating system, expected score, that is probability of winning plus half probability of drawing, is assumed. The expected score is described by ratings and this is (one of) the formula using different distribution between TopCoder and Codeforces. So, I am interested in the actual result.
This scatter chart shows rating difference of two participants and probability that the participant having higher rating gets higher score. It is calculated as follows:
- For all not-team contests, any pair of participants is chosen.
- For all pairs, difference of ratings before the contest is calculated, ranks in the contest is compared and the result of comparison is classified to win, draw or lose.
"Logistic" is calculated by the formula (RB-RA means negative of rating difference and EA means expected score):
"Normal" is calculated by the formula:
μ is 0 and σ is adjusted to pass through the point (x, EA) = (400, 10/11).
According to the chart, it seems that both of distribution does not fully capture the characteristics of the actual curve and that normal distribution is near form the actual curve though it is little difference..