Originally Posted by
hutennis
As far as calculation itself, it goes as follows
variance = (bet_size)^2 * (decimal_odds - 1)
SD = sq. root of variance
Profit (in standardized units, NOT in $$)
Z Score = (profit - ev)/SD
If your null hypothesis assumed % edge ≠ 0, then your formula for variance would be a bit off. The correct formula should be:
variance = (bet_size)2 * (decimal_odds - 1 - Edge) * (1 + Edge)
Originally Posted by
hutennis
What REALLY concerns me, is an overall validity of making statistical arguments about SB results assuming that the Central Limit Theorem applies to them simply.
If you search the Think Tank forum you'll find a simple Monte Carlo simulation program I wrote in Perl. You could compare that to results obtained using a Z-Score.
If you're comfortable with programming, hacking together a VB script to traverse the entirety of the binomial outcome tree should be a straightforward exercise in combinatorics. Provided you had manageably few bet classes, this would represent a faster computation than a Monte Carlo Sim.
Originally Posted by
hutennis
For example, I would never ever, ever put any trust in any z score
That would generally be a wise decision.
In sports betting, one real problem with frequentist-style hypothesis tests and confidence intervals is that of selection bias.
One form of this is often seen when investigating multiple models. For example, if you intended to perform hypothesis tests on 10 (orthogonal) models then the probability of at least one null rejection at α = 5% would be 1-95%10 ≈ 40.1%.
To get this meta-Type I error probability down to the generally accepted level of 5%, you'd actually need to use a per-test value of α = 1 - 10√95% ≈ 0.512%.
And many other potential problems exist with this methodology taken as given. If you're interested, search the Think Tank (or inquire here) for some examples.
Oh, and do check out Bayesian inference as seasoning (or an alternative) to the frequentist flavors.