testing system results with chi square

[SchagFactorToWin]

The other thread on chi-square testing got me thinking about using it to test the validity of handicapping methods, rather than developing a system. I'm not sure I have the hypothesis set up correctly and may not be reaching the proper conclusion.

I examined one type of bet which resulted in 75 wins over 397 races. I wanted to know if that was significantly better than what would be expected. To calculate the expected wins, I converted the tote odds to decimal for each pick, summed them, and then used SUM OF ODDS/N. That gave me 68.9 expected wins.

The Win/Loss summary table therefore looks like this:

..........W.........L
obs.....75.....322
exp.....69.....328

The research hypothesis is that there is no statistical difference between my system and what the odds would predict.
The null hypothesis is that there is a significant difference.

Applying the chi square formula:
(75-328)2/69 + (322-69)2/328 = 1122.82

With df=1, a=.05, I reject the research hypothesis and accept the null hypothesis.

My conclusion is that this particular handicapping system returns results better than predicted by the odds.

Since this indicates my system may be viable, I'm assuming I made a mistake! Anyone care to check my work?

[BillW]

Would pre-takeout odds be more appropriate for the expected win rate?

[CBedo]

The Win/Loss summary table therefore looks like this:

..........W.........L
obs.....75.....322
exp.....69.....328

The research hypothesis is that there is no statistical difference between my system and what the odds would predict.
The null hypothesis is that there is a significant difference.

Applying the chi square formula:
(75-328)2/69 + (322-69)2/328 = 1122.82
Probably as Bill suggested, using pre-takeout odds to calculate the expected wins seems right.

But using your table, it shoud be [(75-69)^2]/69 + [(322-328)^2]/328
which gives you a chi square of 0.63.

[SchagFactorToWin]

Bill- That makes sense.

Cbedo- I thought the t-stat was weirdly high!

[trying2win]

If I remember correctly, Mark Cramer used to advise crossing off the highest-priced winner after doing a paper test of a system, then review the results again. I think that is excellent advice, otherwise it might give one a false sense of security of future positive results.

T2W