I have a data set containing over 5 000 soccer matches (1X2 odds and results). I would like to test some strategies but Im not quite sure how to test whether the strategies are statistically significant. I hope somebody could guide me with this simple example so that I could try to get the hang of it.
I have calculated returns of various simple strategies where one places one unit (1$) bets on the outcome that fulfills certain conditions. A simple example is a strategy of always backing the home team.
Example of how I have calculated the returns:
12.8.2007 Manchester U – Reading 0-0 - 1.22-6.80-23.00 => return on 1$ bet: -1$ or -100%.
16.9.2007 Manchester C – Aston Villa 1-0 – 2.92-3.15-2.92 => return on 1$ bet: 1.92$ or 192%
Then I have calculated the historical average of these returns (over all matches).
Now, is there a way to test whether the average return is due to chance or whether it is statistically significant?
I googled and searched this forum and noticed that people suggest z-test.
Can I for example use the Central Limit Theorem to calculate the normal test statistic Z? At least one problem though is that I do not know the mean. I think the relevant benchmark should be a mean return of 0%. So in this particular case, can I do as follows:
average return ~ N(µ, s^2/n)
Z= [ 0 - (realized mean return) ] / (realized standard deviation of the mean returns) ?