Now that the 2013 season is over, it’s time for us to recap our gambling year at AFLpredictions.wordpress.com. To remind everyone, I have developed a model that predicts the margins of AFL games by giving each team a rolling rating and taking into account home ground advantage and some other factors. The past accuracy of the model is then used to convert a predicted margin into an actual chance of winning for both teams. For example, if I predict Team A have a rating of +12 and Team B have a rating of +5, and they are at a neutral venue (suppose both Team A and Team B’s home ground is the M.C.G.), then I predict Team A to win by 7 points. The past performance of the model tells me that 40% of the time, a team supposed to win by 7 points or less will actually lose, so I give Team A a 60% chance of winning.
For a game with known chances of winning for each team (given by the model) and a given set of odds (given by the bookmakers), there exists an optimal amount to bet. For instance, if we think a team is a 10% chance to win, but they are paying $20 for the win, then we want to bet a small amount on them. That is because they will probably lose, but they only need to win more than 5% of the time for us to make a profit in the long run. As you can imagine, this betting strategy only works if we do it over many games. This strategy is known as Kelly betting.
According to how the model has performed retrospectively since 2005, it appears that we make all our money betting on home teams. That’s not to say we bet on all home teams, but when the model suggests a bet on a home team we take it, and when it suggests a bet on the away team, we ignore it. Why this happens isn’t entirely clear, but it is empirically well-established!
Profits using Kelly Betting
In line with the long-term trend (retrospective profits since 2005), we turned a decent profit from Kelly betting on home teams. For a $1000 bank and a Kelly factor of 5 (i.e. only betting the fraction of 1000/5 dollars), this how our bank would have evolved this season (including finals).
You will notice that betting on all games, we about broke even, suggest that our model performed roughly equivalently to the bookmakers this season. Also, in line with the historical performance of the model, we lost money betting on away teams. And also in line with the long term trend of the model, we made a tidy profit betting on home teams. In fact, betting on home teams gave a total profit of $326.20 on an initial $1000 investment (and without ever running out of money!). Why do we make all our profit on home teams? Is this just a case of the bookmakers underestimating the home ground advantage?
Profits using flat, home-team betting
Well, if we bet a flat amount of money on the home team in every game of the season (say, 10% of our pot), our profits would look like this,
This means that if you just bet on home teams, you would lose a little bit of money. This is expected because the bookmakers don’t give quite fair odds (they take a cut). This highlights the value of Kelly betting – when we pick which games to bet big on, and which to put a small bet on, we comfortably beat the bookmakers. This still means that we give away teams a better chance of winning than they truly have. This is particularly peculiar because the distribution of errors in our model is symmetric. In other words, the away teams outperform our predictions just as frequently as the home teams do.
Profits betting on home underdogs
Another intriguing betting strategy is to use Kelly betting, but only on home teams and only when they are underdogs. Here are the 2013 profits if we use this strategy,
As we can see, we invest less money in fewer games, but return more. In fact, we have a whopping return on investment of 28%! Over the past eight years of betting, though, this would have netted us less total profit at a slightly higher return-on-investment (16% as opposed to 14% with Kelly betting on all home teams). This implies that while we don’t make as much money on home team favourites (and why would you – they pay worse than underdogs!) , we still profit from them.
Profits from home underdogs playing an interstate team
Finally, it seems that we outperformed the bookmakers in a specific subset of games – those when we want to bet on the home team and those when the home team is the underdog. To take this concept to its logical conclusion, let’s see what happens when we bet on only home teams when playing an interstate team and only when they’re underdogs.
We see that we get a massive return on investment (53%). Before we get carried away, though, it’s worth pointing out though that while this flatters the 2013 season, there’s nothing to suggest that this is indeed the optimal betting strategy. If the goal is to maximize total profits, then this strategy fails in the long run – we make more by betting on all home teams. The above plots probably flatter this past season because there were one or two very big wins which happened to be a home team playing an interstate team. Furthermore, the reduced number of games bet on increases the volatility and Poisson noise in the profits. That is to say, betting on more games means a dodgy umpiring decision or a missed goal that decides a game means less to us, because we have lots of other games which we bet on. If we are reliant on only 25 games a year, these become big differences in the end and make our profits quite uncertain.
By next season, I hope to have further improved the accuracy of the mode, predicting more correct tips and and reaping larger profits. I also hope to diversify the suggested bets, branching out from just head-to-head predictions.