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\n ![\"Philip](\"https://neuralswarm.com/assets/images/authors/plyleung.jpg\")
\nAnalytics Competition
\nAdvanced horse race tactics using Trakus coordinate data
\nThe impact of drafting percentage, path efficiency, race strategy and speed fluctuation on horse race tactics.
\n\n\n\n\n \nKey Takeaways
\nObservation
Horses with a meager drafting percentage have a much higher chance of winning the race than other horses. This is likely because these particular horses are front-runners with no one ahead. Interestingly, the win percentage of horses with a high drafting percentage increases for longer distances which means that a high drafting strategy is more effective for longer distances. Also, the low drafting percentage advantage is especially significant when the going is fast or firm but less significant when the going is more wet.
Observation
Horses with a higher path efficiency generally have an advantage over horses with a lower path efficiency. This advantage is true across different distances and goings. Saving that extra 1% or 2% of the race distance compared to other competitors increases a horse’s win percentage.
Observation
Once again, front-runners are favoured to win the race. However, it is challenging to implement a strategy to ensure that a horse leads 20 seconds into the race because many other horses are fighting for the front position. In addition, the advantage of being an early horse seems to decrease for longer distances and when the going is more muddy.
Observation
Horses with a lower speed fluctuation perform significantly better across all different distances and race goings and is something that trainers and jockeys should prioritise. A lower speed fluctuation likely means that the horse has had a smooth race without being unexpectedly blocked or pushed by other horses.
Multinomial Logit Explanation
\nThe Multinomial Logit model was first applied to horse racing by Ruth Bolton and Randall Chapman [3] and further improved by William Benter [2] who went on to amass a \\$1bn fortune betting on horses in Hong Kong [4].
\nThe model works by weighting the features and adding them up to create a performance rating for each horse. The stronger the horse, the higher the performance rating. Afterwards, we group the performance ratings by race and use the softmax function to transform these performance ratings into probabilities. Finally, we use the Maximum Likelihood Estimation (MLE) technique to adjust the feature weights by maximising the log likelihood of the win probabilities of the horses that won.
\nMathematically, let $X_{ijk}$ represent the $k$-th feature of the $j$-th horse of the $i$-th race, $\\mathbf{1}_{ij}$ represent an indicator function which returns 1 if the $j$-th horse is the winner of the $i$-th race and 0 otherwise, and $\\alpha_{k}$ represent the weighting of the $k$-th feature. Then we have $U_{ij}$, which represents the performance rating of each horse:
\n$$U_{ij} = \\sum_{k}\\alpha_{k}X_{ijk}$$
\nTo convert the performance rating to probabilities, we need to compare it with other horses in the same race. We group the performance ratings by race and perform the softmax function to convert them into win probabilities. Now, we have $p_{ij}$, which is the win probability of the $j$-th horse of the $i$-th race:
\n$$p_{ij} = \\frac{e^{U_{ij}}}{\\sum_{j}e^{U_{ij}}}$$
\nTo get the maximum likelihood, we want to maximise:
\n$$p = \\prod_{i}p_{ij}\\mathbf{1}_{ij}$$
\nWhich is the same as maximising the log likelihood function:
\n$$L(p) = \\ln\\left(\\prod_{i}p_{ij}\\mathbf{1}_{ij}\\right) = \\sum_{i}\\ln\\left(p_{ij}\\mathbf{1}_{ij}\\right)$$
\nPyTorch Model
\nWe turn to PyTorch to implement the Multinomial Logit model, since adjusting the feature weights to calculate the performance rating is the same as adjusting the weights of a single nn.linear layer neural network. PyTorch also comes with useful functions like F.softmax, which can be used to transform performance ratings to probabilities, and F.nll_loss which can be used to compare the predicted and target win probabilities.
The data is loaded into a PyTorch Lightning data module which applies min-max normalisation to all non-odds features and pads races, since the number of starters in each race varies between 3 and 14. The data is divided into 5 folds for cross validation.\n
A PyTorch Lightning trainer is used to find the ideal weights by training the neural network using an Adam optimiser with learning rate of 1e-3 and L2 weight decay of 1e-4, and letting it run for 200 epochs.
\nObservation
The predictive power using our four features is significantly better than the baseline model with the baseline giving a loss of 2.639 and our combined model giving us a loss of 1.965. We can analyse the weightings of the features to help inform racing tactics and decisions.
The feature weights inside the combined model, indicate the following, in order of significance:
\nObservation
The mean loss for both models are very similar which means that adding the two extra features of draw and weight_carried did not improve the odds probabilities significantly. The public odds have already factored in the two extra features which means that the odds are already efficient enough to reflect all the starter-specific pre-race information provided in the NYTHA/NYRA dataset.
Observation
When we add all four features to the odds, there is a significant improvement in accuracy, dropping from 1.618 to 1.468. If we can forecast these features with reasonable accuracy, we can produce more accurate probabilities than the ones implied by the odds. Out of the four features we added, the one that helps improve the model the most is the speed fluctuation feature. This means that public odds largely undervalues the performance benefits of reduced speed fluctuation.
The feature weights inside the combined model, indicate the following, in order of significance:
\nKey Takeaways
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