# How to calculate the FIDE Percentage Expectancy Table

Section 8 of the FIDE Rating Regulations provides the following table I understand that dp=800 and dp=-800 are arbitary caps at the top and bottom of the table.

However, in relation to the other scores, what's the formula for the conversion of p into dp, and vice-versa?

As noted in the comments, the regular Elo formula almost works but does not quite work. Does anyone know what the formula is for the adjustment made in the tails?

It's basically just table 8.1a with the columns switched. E.g. the entry in table 8.1b with rating difference 92-98 and expected score (for the higher rated player) of .63, corresponds with the entry (.63, 95) in table 8.1a.

That table is based on the expected score formula mentioned here:

If Player A has a rating of RA and Player B a rating of RB, the exact formula (using the logistic curve) for the expected score of Player A is

EA = 1 / (1 + 10 (RB - RA) / 400)

but it's also possible to directly generate table 8.1b from this formula. For example, a rating difference of 92 points (in A's favor) leads to EA = 0.6294.

The inverse formula, calculating the rating difference which corresponds to a certain expected score, is RB - RA = 400 log10(1 / EA - 1).

• I checked some calculations in MATLAB. I get that if I enter for example 1/(1 + 10^((300-392)/400)) it equals 0.6294 just like you said. However, if I enter 1/(1 + 10^((300-838)/400)) I get 0.9568, when the table seems to indicate that a difference of 538 rating points should accord to .97. The table seems to be slightly 'out' in relation to your formula as soon as we get into high probabilities. Oct 31, 2018 at 7:49
• Yeah, maybe they have a slightly different formula for the tails. It could be that they don't want people to gain rating from playing a lot of games against much weaker opponents, and therefore using a slightly higher expected score. Oct 31, 2018 at 7:53

As stated in 12.1 the formula above gives a close approximation to tables 8.1a and 8.1b. However it does not explain the precise construction of the table. Take fore example Rb-Ra = -736. According to the table 8.1b, the resulting expectation equals 100%. But according to the formula, the expectation is 98,57%.