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Originally Posted by Rinconpaul
I've googled for a formula to equate the probability of a horse running 2nd or 3rd but the mathematical models requires a phD in mathematics to understand!
Anyone ever come across anything that can predict probability % of a 2nd or 3rd placing based on Actual results?
RP
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Not sure but I've googled some more and will have a crack at a a
highly simplified solution for Horse 1 running 2nd...
5 horse race for simplification:
=> % winning chance(and probability out of 1) for each
1 20% = 0.20
2 20% = 0.20
3 30% = 0.30
4 15% = 0.15
5 15% = 0.15
TOTAL 100% = 1.00
Horse 1 can come 2nd in the following ways... 2-1,3-1,4-1,5-1
So taking each, 1 at a time...
=>2-1: P=0.20 x 0.20/
0.80 = 0.05
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because total probability available for 2nd place getter is reduced by 0.20 given that first place has already happened i.e. 1.0-0.20=0.80)
=>3-1: P = 0.30x0.20/0.70 = 0.0857
=>4-1: P = 0.15 x 0.20/0.85 = 0.0353
=>5-1: P = same = 0.0353
Therefore, probability of Horse 1 running second to 2
OR 3 OR 4 OR 5 ;
P(1 runs 2nd) = 0.05
+ 0.0857
+ 0.0353 + 0.0353 = 0.2063 = 20.6%
Perhaps one of the maths freaks on here can verify the above and compute the equivalent for Horse 1 running 3rd.
If my maths is correct, probability of Horse 1 running 2nd OR 3rd is;
=> P(1 runs 2nd or 3rd) = 0.2063 + P (1 runs 3rd)
Cheers LG
PS would be easier using XL for standard sized field but just an illustration here and frankly.. I can't be jacked whipping up one tonight. Enjoy!
PSS Note Chrome's comment above("It does not just depend on the win odds...") and hence my
highly simplified solution!!