Open BenoitLondon opened 11 months ago
Thanks for opening the issue. I do not think this would be too hard to implement. I have two requests, however:
bashsm
for "BAcon-SHone Soft Max".)I saw this is in this chapter
https://onlinelibrary.wiley.com/doi/10.1002/9780470400531.eorms0386
but the references are:
Lo, VSY; Bacon-Shone, J; Busche, K. (1992). A modified racetrack betting system. 18, 1–14. http://hdl.handle.net/10722/60980
Lo, V. S. Y., Bacon-Shone, J., & Busche, K. (1995). The Application of Ranking Probability Models to Racetrack Betting. Management Science, 41(6), 1048–1059. https://doi.org/10.1287/mnsc.41.6.1048
For the implementation, I am not sure we need a new name, it's just an extension of your Henery model as I see it.
maybe just an argument like gamma_method = c("discrete", "LBS")
discrete being the current implementation and LBS the power shape, not sure about how to handle the number of runners though...
The Lo et al 1995 article talks about a "discount model", introduced in their 1992 paper. The discount model depends on some parameter r
which would have to be fit. However I do not see the mu^k
approximation there.
yeah me neither I could not find that exact formulation of mu^k
in the references...
For example, gamma's seem to decrease with the position, and I've read they could depend on the number of runners as well in an article form John Bacon-Shone (I can't find the reference) cf: LO(i, j|k) = λ(k,n) log(pi/pj), with λ(k,n) ≈ μ^k in Bacon-Shone article where lambda is gamma in your formulation of Henery's model
Not sure how doable it is as it can't be too complex I guess?
but the dependence on number of runners makes sense to me
Thank you for that cool package! I might open more issues... :)