regan_antiderivative: Regan Antiderivative

In dryguy/rbitr: Arbiter: One who ensures adherence to the rules and laws of chess

Regan Antiderivative

Description

Calculate the antiderivative of 1 / (1 + abs(x)).

Usage

regan_antiderivative(x)

Arguments

x	A numeric vector of chess evaluations, in centipawns.

Details

This is a convenience function for calculating the definite integral:

di = integral from v0 = eval(m0) to vi = eval(mi) of 1 / (1 + abs(x)) dx

used by Regan, et al., to scale the difference in the evaluation of an engine's "best" move (m0) and a player's actual move (mi). The scaling compensates for the human tendency to evaluate on a log scale.

The antiderivative of 1 / (1 + abs(x)) is:

1/2 * (sign(x) * (log(1 - x) + log(x + 1)) - log(1 - x) + log(x + 1))

Value

The real part of the antiderivative of 1 / (1 + abs(x)).

Note

The antiderivative is undefined at 1 or -1. At these points regan_antiderivative() will return the limiting value (+-log(4)/2).

The input is treated as a complex number with an imaginary component of 0i. The actual antiderivative may have a non-zero imaginary part, but only the real part is returned.

References

• Regan, K. W., & Haworth, G. M. C. (2011). Intrinsic Chess Ratings. Twenty-Fifth AAAI Conference on Artificial Intelligence, 834–839. https://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/view/3779

• Regan, K. W., Macieja, B., & Haworth, G. M. C. (2012). Understanding distributions of chess performances. Lecture Notes in Computer Science, 7168, 230–243. https://doi.org/10.1007/978-3-642-31866-5_20

Examples

regan_antiderivative(c(-100, -10, -1, 0, 1, 10, 100))

dryguy/rbitr documentation built on Oct. 15, 2024, 6:18 a.m.