TI-84 Plus CE and HP Prime: Wilson Score
Introduction
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)
Some values of z:
99% confidence: 2.575829303
97% confidence: 2.170090375
95% confidence: 1.959963986
90% confidence: 1.644853626
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.
TI-84 Plus CE Program WILSON
Input "LIKES:
",L
Input "TRIALS:
",T
L/T→P
P+1.96^2/(2*T)→S
S-1.96√((P(1-P)/T)+1.96^2/(4*T^2))→S
S/(1+1.96^2/T)→S
Disp "SCORE:
",S
HP Prime Program WILSON
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;
Example
Here is a comparison of ranking methods for five levels for
a given custom level of the making game Super Mario Maker (https://supermariomakerbookmark.nintendo.net/?difficulty=normal
Retrieved August 25, 2017)
|
Level
|
Likes
|
Plays
|
% of Likes
|
Wilson
Score
|
|
Castle Of Bomb Spin Jump
Arts
|
1024
|
6169
|
0.1659912466
|
0.1569147894
|
|
Smb3 the mini game Cave 5
|
3468
|
20423
|
0.1698085492
|
0.1647212552
|
|
Stepping Stones 101
|
31
|
176
|
0.1761363636
|
0.1269508811
|
|
Squid Sisters & The
Flooded Cave
|
90
|
518
|
0.1737451737
|
0.1435495995
|
|
Tower of challenges 2
|
244
|
1394
|
0.175035868
|
0.1559880745
|
Source:
Lane, Matthew. Power-Up: Unlocking the Hidden Mathematics in Video
Games Princeton University Press:
Princeton. 2017 ISBN 9780691161518
Eddie
This blog is property of Edward Shore, 2017.