Did you ever try extending it out to other methods of probability estimation other than the forms of regression? I have only skimmed your excellent article, but I think you are first calculating the average probabilities from a regression model and then minimizing the loss to calculate Harville corrections for place and show markets? Is that correct or am I missing something here? I guess I am curious if there has been any improvement on using regressions for combining the various initial odds as I don't really follow the literature anymore.
Yes! There have been big improvements since then but they are beyond the scope of the post. I just wanted to reproduce the calculations in the paper using PyTorch.
Bill Benter subsequently replaced the multinomial logit model with a multinomial probit model, which assumes Normally distributed errors rather than errors that follow the Laplace distribution.
Sorry - to be clear this is just re-running the model detailed in Bill Benter’s 1995 paper (he uses the time period 1986-1993) on more recent time periods (1996-2003, 2006-2013, 2016-2023) using PyTorch.
Nice work. Have you made available the CSV of this data, or is it easily obtainable using horse racing information online? I didn't see how that HKJC site offered it in CSV format. Perhaps you scraped the data to generate your CSV? Thank you.
Please read the first paragraph of the post again. The original author of the paper is Bill Benter, and the GP is the author of this excellent writeup.
