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Originally Posted by davew
I have been trying to devise a method using standard deviations, but still have some snags. If you did probabilities by hand (from your numbers) what would you get? I guesstimated a probability line, but would have to see a few thousand races (with results) to see correlation with your numbers and results -> what percent of time would 2,3, or 9 win? Being able to go to the tenths would really help in lower odds horses...
#1 -- 72.65 -- 2
#2 -- 101.06 - 16
#3 -- 104.32 - 20
#4 -- 87.72 -- 9
#5 -- 89.90 -- 10
#6 -- 10.20 -- 1
#7 -- 75.89 -- 4
#8 -- 79.96 -- 6
#9 - 105.25 -- 22
#10 - 77.95 -- 5
#11 - 73.84 -- 3
#12 - 69.82 -- 2
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Obviously, at least to me, if the ratings are fairly accurate, then the top 3 horses should win about 60% of the time, over time. Your line has them at 58%, that's very close. Based on that, how did you differentiate between those 3 horses to get their portion of the 58% total probability? It appears that the relationships are not linear, but I haven't a clue as to how to come up with that non-linear scale/slope.
This set of numbers seems promising, regarding the separation/relationship between the 3 ratings. I found the average and then subtracted the 3 ratings from that average.
#2 _ -2.483333333
#3 _ 0.776666667
#9 _ 1.706666667
Based on those numbers this is what the probabilities percentage would be:
16.85
20.11
21.04
