r square figures

[jazzfish]

hi alex,

i am a loyal odds wizard user and am very keen to understand the predictive performance of the odds wizard a bit better and have a question to that end. what is the r square of the system. ie what percentage of variance does the system explain in regression terms?

kind regards,

jazzfish

[Alex]

For the English Premier League which is one of the most balanced (in the sense of 1-X-2) league, the figures for algorithm of 2007 are:

Total variance 299.2
Explained variance 81.0
Residual variance 218.2

For the Highland Scottish league (the highest value of explained variance):

Total variance 243.9
Explained variance 120.7
Residual variance 123.2

For Mexico:

Total variance 194.3
Explained variance 15.7
Residual variance 178.6

All these figures are indirectly reflected by the performance values presented in the Performance tool: Tools -> Performance analysis.

It must be noted that algorithm of 2007 deals with transformed (by certain function) input data rather than with raw data as in the algorithm of 2002.

[jazzfish]

Hi Alex,

So are you saying that for the English Premier League the OW statistical model explains 81.0/299.2 variance (27%). Please forgive me if I seem negative, but is that not rather low? That means that 73% of variance in results is unexplained by the model. How can the results be relied upon in this case? Perhaps I am missing something.

Kind regards

Sam

[Alex]

That's right. Explained variance is rather low, and there is a natural explanation of that fact. Imagine that all teams are of equal strength. What explained variance is expected to be? The answer is zero! Therefore, the higher difference in the teams' strength, the higher explained variance can be expected.

In particular, the above example means that Mexican Primera Division teams are rather closer to each other by their strength as compared to Scottish Highland league teams.

Of course, the better statistical model may result in the higher explained variance in the league with weak and strong teams. I can assure you that this is a subject of constant research in Newhaven Software.