Quote:
Originally Posted by ARAZI91
You can also use those H2H Counts by adding in a losses column and creating an "odds ratio" using a horses Cumulative H2H Win/Loss Ratio over a dataset whilst adding a form of competitiveness or "race strength" by measuring a races geometric mean of each horses odds ratio.The end result is a rating consisting of (5+Rivals Beaten)/(5+Rivals Beaten by)*Race Strength. The additional 5 wins and 5 losses added is a Laplacian prior (Rule of Succession) and results in best predictions. An algorithm called Minorisation-Maximisation(MM) - David Hunter(2004) is used which optimises and exploits convexity and through a process of iteration allows for all Ratings to emerge to a final solution.
The MM algo is an iterative process
1) Start with calculating every horses H2H Win/Loss Ratio to some arbitrary precision(~ 3 dec.points) in the dataset - *note add 1 win and 1 loss to every horse's record at the start. This accounts for non winners etc.
then repeat these steps
2) A Horses revised rating is it's win/loss ratio(including the Laplacian prior above) multiplied by the geometric mean of every horse faced.
3) If ANY horse's ratings have changed(they will have !!),use this new rating in place of Step 1 and return to Step 2. If not go to 4)
4) STOP! this is a horse's final rating.
This set of final ratings maximises the likelihood of the results over the dataset.
This process also works with Impact Values although there is a higher signal using Place Impact Values (including Wins) as that metric is more granular.
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And if using Impact Values make sure it accounts for FS( ie: in Win Impact Values = Actual Wins/Cumulative addition of 1/FS which is just xWins by Random Chance)
