If I rate a runner in a field of 30 as a +1600 chance, and have these options to bet on them, how do I calculate which one is the Better Value?
Win only: +2000
Top 3: +520
Top 5: +310
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Win
Top 3
Top 5
If I rate a runner in a field of 30 as a +1600 chance, and have these options to bet on them, how do I calculate which one is the Better Value?
Win only: +2000
Top 3: +520
Top 5: +310
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Angelman
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1.18% of BR on the Win, or 2.57% on Top3, or 9.1% on the Top5 bet.
Wow Ganchrow, thankyou. And double thankyou for explaining it so well.
Intuitively, I had expected the order of value to come out; Win, then top 3, then top 5. Being so wrong with that guess reinforces how important this is for me.
Hope you don't mind a couple of follow up questions.
1) Is this logic correct? Runner A has a 92.94% implied chance of beating any other, Runner B has a 91.73% chance. Meaning A has 1.21% more chance in a 1 on 1 matchup than B? Therefore ((10.0121)/(0.0121+1))+1 = $1.98 is the implied fair odds on the underdog? (or should I be looking at the ratio of their probabilities?)
2) I'd very much like to know how to calculate this out when I don't "judge them all to be equally matched each with the same probability of losing" too, if you have the time and patience to set that out as well.
Last edited by Optional; 061510 at 03:12 PM. Reason: typo
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Very good observation. I doubt the effect will be anywhere near as marked in NASCAR, because everyone races an entire season, aims to peak at the same time and goes out to spell at the same time.
I'm not sure the sample size will be enough with only 36 races per year, but I've just added it to my todo list to check out anyway. Sounds like something that might at least help improve my handicapping, if I can spot any individuals that trend that way.
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Thanks again Ganchrow. I had to read that lot several times, but have got it now.
3more quick follow up questions though, if you don't mind.
1) A NASCAR field has 43 starters. When I do my handicap ratings, I generally end up with 5 to 10 drivers on zero rating. In my calculations I have treated it as field with however many runners I've actually rated with some chance. The combined probability of the remainder of starters is likely well under 1%.
For best accuracy, should I ignore them completely as I am now? Or should I be calculating the above equations with the full 43 starters, including those with 0% rated prob?
2) I have intermediate experience with PHP, and I 'think' I can come up with the program you describe. (with a bit of research beyond my high school math education) But...
Should I be looking at trying it with a different language that might prove more suitable for this type of work in future?
3) How much utility would you give to the current figures that don't take into account the relative probability of each runner? Can I rely on them as being useful at all?
Last edited by Optional; 061610 at 10:36 AM.
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Do these figures look right to you Ganchrow?
With the original calcs the distribution looked a lot more like reality, and not evenly graduated. The third ranked runner's probability to finish 3rd was highest, and fell away either side for instance.
I've triple checked my work, so guess it's right, but just thought I'd ask.
(BAO = Beat Any Other)
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Last edited by SBR Jonelyn; 041615 at 02:06 PM. Reason: image does not exist
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Each of the runners are sorted by a handicap rating I gave them. (I probably should have included that column too, to help make better sense of it)
BAO refers to the calculation you gave above for "the probability of the good runner beating any any other given runner". It wasn't necessary for me to include it there, I was really just asking about the distribution of the Win thru 5th columns.
The table includes the 36 of 43 runners I had rated >0 in the race only. The others are not factored into any calculations there.
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Thankyou. You just saved me many hours.
I'm still surprised by the result distribution there too though. I guess my intuition was wrong, that the 3rd ranked driver would have a higher probability of finishing 3rd than 2nd or first.
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My PC is a lot slower than yours. I ambitiously started a test to calculate the top 10 places about an hour ago and it's reporting only 40% done so far.
You have taught me a lot, and left me with exactly the calculation solution I set out looking for, plus more.
After looking at the output, I think I will try refining my handicapping system to exclude even more runners from the final calculations, as I think the lower probability results are just creating unnecessary noise when it comes to the more important top 15 ranking.
I'm in your debt.
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