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Confidence ranges for Win%

PT
5/29/2009
11:37:23 AM

It's funny sometimes how information can find you...I was looking through my racing book collection, browsing for anything that might kick off a UDM idea in my head, and started thumbing through "Horse Racing Logic" by Glendon Jones. In that book, he has a table titled "Confidence Ranges for Winning Percentages by Size of Bet Sample". I'm going to post it up here, with that assumption that it's ok to do that, given that it's generic probability stuff. Jeff, if you feel otherwise, certainly delete it.

code:

                Size of Bet Sample-95% Confidence

Win Pct		20	50	100	500	1000

20%		2-38%	10-30%	12-38%	16-24%	18-22%
25%		6-44%	13-37%	17-33%	21-29%	22-28%
30%		10-50%	18-42%	21-39%	26-34%	27-33%
35%		14-56%	22-48%	26-44%	31-39%	32-38%
40%		19-61%	26-54%	30-50%	36-44%	37-43%
45%		23-67%	31-59%	35-55%	41-49%	42-48%
50%		28-72%	36-64%	40-60%	46-54%	47-54%

This is a 95% confidence table, so, for example, let's say you have a UDM that's giving you 50 plays/month, with a win percentage of 30%. You play it for 100 months. On average, in 95/100 months, your monthly win percentages would fluctuate between 18-42%. In the other 5/100 months, your win% would fall outside of that 18-42% range.

Standard Disclaimer: I'm basically regurgitating this stuff. I haven't verified the accuracy of those numbers. And, this is just fun with numbers, and doesn't take into account what happens when Mountaineer has the owner's nephew driving the tractor this week.

Be right back...I have to download more data.

~Edited by: PT on: 5/29/2009 at: 11:36:43 AM~

-Paul

~Edited by: PT on: 5/29/2009 at: 11:37:23 AM~

ryesteve
5/29/2009
2:56:38 PM

One thing to keep in mind when using these sorts of stats: confidence intervals imply that you're looking at a random set of data. So this means that if you mine your database, find a UDM that looks really good, you can't build a confidence interval around the results you've gotten; what you need to do is run it against fresh, independent data and build a confidence interval around that.

This might be obvious to most people, but it's a trap that I often see people fall into.

PT
5/29/2009
5:04:10 PM

No argument there, good point. That table assumes that the win percentages on the left column are accurate. Ensuring they're accurate is a whole 'nother story.

formula_2002
6/3/2009
1:34:29 AM

the table works well with fixed odds games like craps.
but in horse racing win percentages should be broken down into incremental odds anjusted for take-out.
and you need to generate the win% range with real data. you really want to wind up with two sets of data.
your system results data compared to the publics data.

then find a whole new set of data and repeat the process a few more times.

then dont believe any of it(lol).

i checked a few of the charts numbers and they work out, with an assist using the formula.

sqrt ( win%-(1-win#) x quanity) x 2

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General Discussion -- Confidence ranges for Win%

General Discussion
-- Confidence ranges for Win%