This year, MoS Funds have for the first time been wagering with other than the TAB. It seems obvious that adding a second bookmaker must be beneficial to a bettor unless that second bookmaker offers identical prices to the first. The question is: how beneficial?

In this post we'll look at this issue by calculating the vigorish (or bookmaker edge) in:

• The synthetic market formed by taking the better of the two prices

As an example, imagine a game for which:

• The TAB has prices \$2.75 and \$1.45 (and hence overround of (1/2.75 + 1/1.45 - 1) = 5.3%, and so vigorish of 5.4%/105.4% = 5.1%)
• Centrebet has prices \$2.90 and \$1.42 (and hence overround of (1/2.90 + 1/1.42 - 1) = 4.9%, and so vigorish of 4.9%/104.9% = 4.7%)

Our synthetic market then would be, taking the higher price for both teams, \$2.90 and \$1.45, for which the overround is of (1/2.90 + 1/1.45 - 1) = 3.4% and the vigorish therefore 3.4%/103.4% = 3.3%.

In this example, by availing ourselves of two bookmakers, we have reduced the vigorish we're facing from, minimally, 4.7% to 3.3%, which is almost a 30% reduction.

The table at right shows the results of performing this same calculation for every game from Rounds 1 to 17 of the 2017 AFL season and reveals that, on average, using two bookmakers rather than one has reduced the average vigorish faced by about 17%, from 4.9% per game (had we wagered solely with the TAB) to 4.1% per game (by taking the better of the TAB and Centrebet).

That's quite a significant reduction and means, for example, that we should expect almost a full 1c in the dollar better return from our head-to-head wagering, even if our probability-estimating abilities are no better, on average, than the bookmakers.

It would be interesting to see how this diversification benefit scales as more bookmakers are added, which is an exercise I might undertake during the off-season. Practically, there must surely be some asymptotic limit to the benefit because, as the portfolio of bookmakers increases in size, it will become more and more difficult to find new bookmakers that, at least occasionally, provide a better home team or away team price than any other bookmaker already in the portfolio. In reality, of course, there are also considerable transaction costs in maintaining a float with a large number of bookmakers.

In the meantime, it's eye-opening (to me at least) just how significant the benefit of adding a single additional bookmaker can be.