Criterion Xi^2

[ihraf]

Hi ALex,

I still can't understand the relation between the Success rate % , the entropy and the Criterion Xi ^2

For this example I see that the Success rate % and the entropy are good but the Criterion Xi ^2 is too High

And as you said , the value must be small.

Please can you explain

[Alex]

Statistical criterion Xi^2 is calculated as a N * Sum((P-W)^2/P), where P is an average computed probability of given correct score, W is actual relative frequency of given correct score. Summation is made over all possible scores from 0:0 to 10:10. This criterion measures difference between actual and computed probability distributions.

Success rate and Entropy rely on the "successful" probabilities of outcomes. I.e. probabilities (P1-PX-P2) are counted when they are consistent with the actual outcome of an event (home win - draw - away win). Otherwise they are ignored. N1, NX, N2 - actual number of "successful" home wins, draws, and away wins.

SuccR = Sum(P1)/N1 + Sum(PX)/NX + Sum(P2)/N2, commonly used Success rate.

Entropy = (Sum(-ln(P1)) + Sum(-ln(PX)) + Sum(-ln(P2)))/(N1+NX+N2);

The problem is that all these criterions are not consistent with each other. For instance, good small value for Xi^2 does not mean highest value for SuccR and smallest value for Entropy, and vice versa. It is the reason that we still continue research on this subject.