I described how to calculate the significance of a set of uncorrelated bets in
this post.
Using this methodology, however, would tend to overstate your variance (thereby understating significance) because many of your wagers will be negatively correlated (insofar as you're placing mutually exclusive outcome wagers on the single winner of a given race). Therefore, rather than simply summing variances to determine a total grouped variance you'd also need to include
covariances in your analysis.
Given two
fairly priced bets on two
mutually exclusive outcome events of size x
1 and x
2, respectively the covariance between the two bets would be given by -x
1*x
2. So if we assume that the two bets are offered at decimal odds of d
1 and d
2, respectively, the total outcome variance would be given by:
σ2 = x12*(d1-1) + x22*(d2-1) - 2*x1*x2
And generalizing across N mutually exclusive outcomes:
[nbtable][tr][td]σ2 = [/td][td][/td][td]{xi2*(di-1)} - 2*[/td][td][/td][td] [/td][td][/td][td]{xi*xj}[/td][/tr][/nbtable]
Of course this neglects the possibility of non-binary outcome bets (e.g. show or place bets), correlated bets that aren't mutually exclusive (e.g., a trifecta and a win bet), as well as bets known to be -EV but placed as hedge bets (as Kelly would dictate). These issues (notably the 1st, that of non-binary outcome bets)
significantly complicate the problem and are probably better posed on a quantitative horse racing forum, where a suitable approximation of the solution is likely well-known.