Wilson Score (Video Games)

[Eddie W. Shore]

There are various ways to rank games: by the popularity of players or by the custom levels the players (like Little Big Planet and Super Mario Maker). A method to rank is to use the number of likes (or hearts) a player or level receives. Another method is to use the percentage of likes to the number of plays (trials).

Another way to rank is to use the Wilson score interval (Edwin Wilson). The general Wilson interval formula is:

I = ( p0 + z^2/(2*n) ± z * √((p0 * (1 – p0)/n) + (z^2/(4*n^2)) )/( 1 + z^2/n )

Where:

n = number of trials or players
p0 = percentage of likes (successes) = likes/trials
z = z-score of the confidence interval (center of the normal curve)

Matthew Lane, author of Power Up: Unlocking the Hidden Mathematics in Video Games, modifies the Wilson interval to calculate the score with 95% confidence, using the approximation of z ≈ 1.96, as

s = ( p0 + 1.96^2/(2*n) - 1.96 * √((p0 * (1 – p0)/n) + (1.96^2/(4*n^2)) )/( 1 + 1.96^2/n )

The score takes the number of likes and plays into account. The program WILSON calculates the above score.

Code:

EXPORT WILSON(L,T)
BEGIN
// 2017-08-24 EWS
// L: likes,T: trials
// Percentage of likes
LOCAL P0:=L/T;
// Calculation (in parts)
LOCAL S:=P0+1.96^2/(2*T);
S:=S-1.96*√((P0*(1-P0)/T)
+1.96^2/(4*T^2));
S:=S/(1+1.96^2/T);
RETURN S;
END;

Source:
Lane, Matthew. Power-Up: Unlocking the Hidden Mathematics in Video Games Princeton University Press: Princeton. 2017 ISBN 9780691161518

[pier4r]

This is a really interesting input. Thanks for sharing!