Sports betting mathematical models in science

That title of the paper is a whopper, for sure. And they started making money. And that — the limiting of winners — was the second part of the title, the rigged part. Jack Andrews, a seasoned veteran of the sportsbook world. However, getting the money down is where the art of sports betting comes in. The academics never get their heads out of their collective classes to see how it all really works.

The picture is very similar when backing the longshot instead. In this case, the ensemble method requiring all five models to agree is the only one to produce a positive return across the seven-year period. Notably, bets are only placed in 0. Panel a refers to betting on the favorite, panel b to placing bets on the longshot. This figure shows the outcome of the most successful betting strategies as per Tables 5a and 5b. The vertical dotted lines indicate the seven annual periods spanning through Using average bookmaker quotes, figures a and b reflect the results from backing the match favorite [ensemble method with four members; variance-optimized money management strategy] and the match longshot [ensemble method with five members; wagered amount as a fixed proportion of the bankroll], respectively.

When relying on the most advantageous bookmaker quotes for each match, figure c shows the results of backing the favorite [ensemble method with four members; variance-optimized money management strategy] and d those for betting on the longshot [ensemble method with five members; money management based on fixed expected returns].

Another prominent observation pertains to the fact that, for the majority of cases, the returns are lower more negative when backing the longshot rather than the favorite. This is consistent with the well-studied longshot bias, i. It has been confirmed many times for the tennis market as well. Franke argues that the favorite-longshot bias is due to a misperception of probabilities rather than risk preferences.

However, he also reveals evidence that bookmakers bias odds in order to protect themselves from adverse events. As in the case of using average bookmaker quotes, no single model stands out versus the others in terms of performance. The same applies to the used money management strategy. The two most successful strategies deliver returns of 1.

The corresponding graphs in panels c and d of Fig. In spite of combining signals from different approaches, a lot more bets — 18 to 30 times as many — are placed compared to panels a and b. However, when taking the wagered amounts into account and working with returns, the outcomes are comparatively less favorable. As in the case of average betting odds, there were annual periods with negative returns or hardly any wins.

Overall, the picture is mixed. The tennis betting market as a whole leaves hardly any room for con-sistent positive returns for a bettor. Even more sophisticated machine learning models struggle with this goal. Model ensembles are comparatively performing the best, but even when using those, one needs to be prepared to invest over longer horizons since there can easily be periods with zero or even negative returns.

When risk-adjusting betting returns, these are far less attractive than those of typical financial investments. Market liquidity constraints are another factor to consider in a practical application. The presented results are consistent, for example, with studies such as the one in Lyocsa and Vyrost : when applying various betting rules based on odds and rankings, they find at best weak evidence for market inefficiency and cast doubt on literature that cites attainable profits in the professional tennis betting market.

The used dataset combines player, match, and betting market data and constitutes one of the most comprehensive research undertakings in this sports discipline. The study extends previous research by applying established statistical and machine learning techniques including model ensembles to investigate a the informational content of betting odds and historical player and match data with regard to predicting future match outcomes and b the ability for bettors to achieve consistently positive risk-adjusted returns.

It is found that the official player rankings and bookmaker odds together encompass most of the information for a model-based prediction of match outcomes.

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