While doing some research to (hopefully) arrive at a personal line-making methodology I realized that I need to know what I am up against, i.e. how well bookmakers can predict the outcome of a game. I would like to know good ways to assess the predictive performance of a wagering strategy. Below I explain one approach which I think makes sense for a higher (season) level analysis, please suggest alternatives that you might think is more appropriate.
This was explained to me by a Phd friend and I am pretty sure it has a fancy statistical name (like log-likelihood test or something like that). As a performance measure it would be interesting to analyze how far off one is in its prediction of the outcome in terms of probabilities.
For example, if a bookmaker posts a Money Line odds at +120 for a certain game, it implies that the bookmaker thinks the fair value is a 45% probability that the certain outcome will occur. If the outcome does occur, the amount the bookmaker would be off in its prediction regarding the outcome of the game would then be |0 - 0.45| 0.45. On the other hand if the outcome did not occur the amount would be |1 - 0.45| 0.55. The "|" here represents is an instruction to evaluate the absolute value.
To assess the predictive performance of multiple games would then a matter of getting the product of the distances which the prediction is off. E.g. if we are looking at two games with MLs posted at +120 (45%) and -110 (52%) respectively and the result of the games is that bets on both odds pay off. The overall prediction of the bookmaker would then be evaluated to
|0-0.45|*|1-0.52| = 0.216
Since evaluating many such games would result in a very very tiny number, a trick one could use is to take the logarithm of the expression, giving a more manageable number. In the example above we would then be looking at:
ln(|0-0.45|*|1-0.52|) = ln(|0-0.45|) + ln(|1-0.52|) = -1.5325
This is a nice number indeed, but what does it tell us about predictive performance? Not much really. So we need to benchmark the number against the predictive performance of an more "basic" strategy. This could be the equi-probable strategy, i.e. to say that in any given game each team has a 50% probability of winning. It could also be something slightly more sophisticated such as, "if the team is playing home field then its 55% probability to win, otherwise its 45%". Assuming we use the equi-probable approach to benchmark our results above, the resulting number would then be
ln(|0-0.45|*|1-0.52|)/ln(0.5*0.5) = [ln(|0-0.45|) + ln(|1-0.52|)]/[ln(0.5)+ln(0.5)] = 1.1054.
This measure will then be portable to any game and any scenario in which one wishes to assess the predictive ability of its method against an opponent, just like what I would like to do against bookmakers.
As I do not have the opening lines, which are available from sources like www.donbest.com I am interested to know the predictive performance of bookmakers (ball park measure) over the basic equi-probable strategy and possibly also when accounting the home-field advantage. Anyone that has these numbers at hand for a MLB season I would very much appreciate if you could share them here.
Note that the approach to evaluate the performance above does not say anything about the profitability of your wagering strategy as it only analyzes your performance on an aggregate level. Averages can certainly be misleading and it is really how your prediction against the bookmaker in each game falls out that really counts.
This was explained to me by a Phd friend and I am pretty sure it has a fancy statistical name (like log-likelihood test or something like that). As a performance measure it would be interesting to analyze how far off one is in its prediction of the outcome in terms of probabilities.
For example, if a bookmaker posts a Money Line odds at +120 for a certain game, it implies that the bookmaker thinks the fair value is a 45% probability that the certain outcome will occur. If the outcome does occur, the amount the bookmaker would be off in its prediction regarding the outcome of the game would then be |0 - 0.45| 0.45. On the other hand if the outcome did not occur the amount would be |1 - 0.45| 0.55. The "|" here represents is an instruction to evaluate the absolute value.
To assess the predictive performance of multiple games would then a matter of getting the product of the distances which the prediction is off. E.g. if we are looking at two games with MLs posted at +120 (45%) and -110 (52%) respectively and the result of the games is that bets on both odds pay off. The overall prediction of the bookmaker would then be evaluated to
|0-0.45|*|1-0.52| = 0.216
Since evaluating many such games would result in a very very tiny number, a trick one could use is to take the logarithm of the expression, giving a more manageable number. In the example above we would then be looking at:
ln(|0-0.45|*|1-0.52|) = ln(|0-0.45|) + ln(|1-0.52|) = -1.5325
This is a nice number indeed, but what does it tell us about predictive performance? Not much really. So we need to benchmark the number against the predictive performance of an more "basic" strategy. This could be the equi-probable strategy, i.e. to say that in any given game each team has a 50% probability of winning. It could also be something slightly more sophisticated such as, "if the team is playing home field then its 55% probability to win, otherwise its 45%". Assuming we use the equi-probable approach to benchmark our results above, the resulting number would then be
ln(|0-0.45|*|1-0.52|)/ln(0.5*0.5) = [ln(|0-0.45|) + ln(|1-0.52|)]/[ln(0.5)+ln(0.5)] = 1.1054.
This measure will then be portable to any game and any scenario in which one wishes to assess the predictive ability of its method against an opponent, just like what I would like to do against bookmakers.
As I do not have the opening lines, which are available from sources like www.donbest.com I am interested to know the predictive performance of bookmakers (ball park measure) over the basic equi-probable strategy and possibly also when accounting the home-field advantage. Anyone that has these numbers at hand for a MLB season I would very much appreciate if you could share them here.
Note that the approach to evaluate the performance above does not say anything about the profitability of your wagering strategy as it only analyzes your performance on an aggregate level. Averages can certainly be misleading and it is really how your prediction against the bookmaker in each game falls out that really counts.
