@mikeywilding Hi Michael. Further to your excellent training earlier this week, if when developing a microangle , could it be that a very low Chi2 number indicates that the microangle is overfitted?
If the answer is yes, is there a Chi2 value below which you wouldn't want to go when developing microangles?
Interesting question. To be honest I've never actually thought of considering whether a very low Chi2 could be the result of overfitting. I would say that it could be, but would be dependent on the amount of selections. If the selection number is very small and the Chi2 is effectively 0, then I'd be wary and would prefer to expand the number of selections and see a small rise in Chi2. On the flip side, if I was getting the same results in an out-of-sample test, I'd be less concerned and more tempted to ride the wave.
Thanks Michael. Good suggestion re out-of-sample trst. Just need to think about how to do it. Cheers
Yes absolutely, a low Chi square (pronounced 'Kai' after the Greek letter, with a hard c and open i as in Kayak and Kite) could indicate overfitting.
Chi square measures 'goodness of fit' to a hypothesis but cannot determine what this is due to. In statistics the sample is usually random and the hypothesis is, 'given the overall sample, this particular sub-group is exactly what is expected'.
In our case, you can view the hypothesis as, 'given the accuracy of the market over a large sample this number of winners is exactly what the market expected'. We hope the answer is, 'no, it's significantly different from what the market expected' and this would be the case with a Chi2 figure below 0.05(5%). However, Chi2 says nothing about why this is the case nor that it will be the case in future.
I think A/E and Chi2 are most useful when they are both close to 1 at BSP but greater than 1 and closer to 0.05 to 'the prices you took'. You have the same number of 'actual winners' but the 'expected winners' is different. You are measuring the significance of the prices you are getting rather than the number of winners. When all is said and done, it's all about the prices you take and beating BSP.
So, with 1,000 bets and 200 winners with an A/E =1 and Chi2 =1 at BSP (or 100% if converting to percentage) you should not be thinking, 'bugger, that's exactly what the market expected, I'd better look for some other method'. Rather you should be thinking, 'I needed too have taken prices that gave 176 'expected winners' or 'I needed to have taken prices 13.6% above BSP (an expected of 176 is what would have given an A/E of 1.136 and a CHi2 of 0.046).
(pronounced 'Kai' after the Greek letter, with a hard c and open i as in Kayak and Kite)
I never knew that, I've always pronounced it wrong! Amended as of today 🙂