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G.S.,
Thank you for the formula !!
However I would like to point out a problem with your example. You wrote
" As an example, a 20% win rate, coupled with a 1.20 ROI and an average mutuel of $15 would result in the following:"
There is a relationship between win rate, ROI and average mutuel, which this example violates.
Here are some definitions and the simple formula:
HIT Frequency (H) is how often the particular wager in questions pays off in the form of a percentage (%). This could be a Win wager, a WPS wager, Triple Box Wager, on and on. We originally used the term WIN Frequency, but people confused that with a Win Wager Frequency. Using HIT Frequency avoids that confusion.
Avg Odds (O) is the Odds to 1 (expressed in decimal form) for the respective Wager in question.
ROI (R) is Return On Investment, in other words profit or loss on the respective wager. We shall normalize this value such that an ROI of $1.00 means you break even. We settled on this to keep away from negative numbers for loss situations, and to make the math simpler. For example, an ROI of $1.38 means 38cents profit on a dollar. An ROI of $0.78 means 22cents loss on a dollar.
With the definitions established, here is the simple but very useful formula presented in 3 formats:
H = HIT Frequency
O = Avg Odds
R = ROI
R=H(O+1) When you want to find ROI as a function of HIT Frequency and Avg Odds
H=R/(O+1) When you want to find HIT Frequency as a function of Avg Odds and ROI
O=(R-H)/H When you want to find Avg Odds as a function of HIT Frequency and ROI
Therefore, for a Hit Frequency of 20% and an ROI of $1.20, the average odds must be 5.00 which is an average mutuel payoff of $12.00 assuming the mutuel payoff is for $2.00.
So to run this example through your formula again with the correction:
E = H - [(2 x ROI) / AvgMutuel]
E = .20 - [(2 x 1.20) / 12] = 0
If my relationship for H, R, and O are correct, I believe E comes up zero for all cases.
Is there a flaw in the E formula?
Do I have a misunderstanding?
Can you help me out on this?
Thanks, FH
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