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By BETTING UNDER THE CURVE
formula_2002
6/27/2008
8:06:39 AM
Originally Posted by formula_2002 ON the pa board
I've tried the following on a data base of 100,000 + horses.
1. Determine the Z score for each entry in a race.
2. Find the representive area under the curve for each horse in the race.
3. Using the Z score tables, sum all the areas (it sums to about 35)
4. Divide the area found in item #2 by the sum found in item 3.
5. Normalize the value determined in item 4. The normalized value represents the horse’s probability of winning.
------------------
the above showns profits using the Jfactor, the bris prime fig, turn time and another bris factor.
it may show profits for other factors.

best results are attained when the value for the area under the curve is >=.95
only no maiden races.
race booking percentage to be <=1.25 or there abouts.
I would like to know how this works for anyone with a large data base.

thanks
Joe M



Reply
bettheoverlay
6/27/2008
11:54:18 AM
What is the Z score and where are the Z score tables?

Reply
jeff
6/27/2008
12:28:34 PM
There's a thread on the PA site where deriving an odds line using normalized ZScores was being discussed:
http://www.paceadvantage.com/forum/showthread.php?t=41075

I read the thread (post #37) a few days ago and did some R&D. I developed an algorithm that takes a "number" for every horse in a given race and derives a probability using normalized ZScores.

Here is the probability distribution created using the normalized ZScores of my own UPR for calendar year 2007:

Data Window Settings:
Divisor = 999 Odds Cap: None
Surface: (ALL*) Distance: (All*)
From Index File: C:\2008\pl_Complete_History_07_Z.txt)

Data Summary Win Place Show
Mutuel Totals 346722.80 344952.90 342315.20
Bet -453916.00-453916.00-453916.00
Gain -107193.20-108963.10-111600.80

Wins 27794 55312 81505
Plays 226958 226958 226958
PCT .1225 .2437 .3591

ROI 0.7638 0.7599 0.7541
Avg Mut 12.47 6.24 4.20

By: Prob: Normalized ZScore

>=Min < Max Gain Bet Roi Wins Plays Pct Impact
-999.00 0.00 0.00 0.00 0.0000 0 0 .0000 0.0000
0.00 0.05 -31810.90 84882.00 0.6252 1994 42441 .0470 0.3836
0.05 0.10 -28809.10 95964.00 0.6998 2963 47982 .0618 0.5043
0.10 0.15 -27160.30 131658.00 0.7937 7388 65829 .1122 0.9164
0.15 0.20 -12189.10 81856.00 0.8511 7440 40928 .1818 1.4844
0.20 0.25 -5221.10 35136.00 0.8514 4240 17568 .2413 1.9708
0.25 0.30 -915.00 13984.00 0.9346 2040 6992 .2918 2.3824
0.30 0.35 -1087.70 10436.00 0.8958 1729 5218 .3314 2.7057
0.35 0.40 0.00 0.00 0.0000 0 0 .0000 0.0000
0.40 0.45 0.00 0.00 0.0000 0 0 .0000 0.0000
0.45 0.50 0.00 0.00 0.0000 0 0 .0000 0.0000
0.50 0.55 0.00 0.00 0.0000 0 0 .0000 0.0000
0.55 0.60 0.00 0.00 0.0000 0 0 .0000 0.0000
0.60 0.65 0.00 0.00 0.0000 0 0 .0000 0.0000
0.65 0.70 0.00 0.00 0.0000 0 0 .0000 0.0000
0.70 0.75 0.00 0.00 0.0000 0 0 .0000 0.0000
0.75 0.80 0.00 0.00 0.0000 0 0 .0000 0.0000
0.80 0.85 0.00 0.00 0.0000 0 0 .0000 0.0000
0.85 0.90 0.00 0.00 0.0000 0 0 .0000 0.0000
0.90 999999.00 0.00 0.00 0.0000 0 0 .0000 0.0000


to be continued...


-jp

.

~Edited by: jeff  on:  6/27/2008  at:  12:28:34 PM~

Reply
jeff
6/27/2008
1:15:13 PM
The first question I had to ask was: How accurate is the probability expressed by normalized ZScores?

Here, I've taken post time favorites, and broken them out by ZScore probability:

By: Prob: Normalized ZScore

>=Min < Max Gain Bet Roi Wins Plays Pct Impact
-999.00 0.00 0.00 0.00 0.0000 0 0 .0000 0.0000
0.00 0.05 -583.70 1698.00 0.6562 200 849 .2356 0.6838
0.05 0.10 -1182.30 3218.00 0.6326 357 1609 .2219 0.6441
0.10 0.15 -2814.00 12698.00 0.7784 1794 6349 .2826 0.8202
0.15 0.20 -2645.10 16976.00 0.8442 2939 8488 .3463 1.0051
0.20 0.25 -1875.30 11782.00 0.8408 2244 5891 .3809 1.1057
0.25 0.30 -687.50 5994.00 0.8853 1222 2997 .4077 1.1836
0.30 0.35 -606.80 5486.00 0.8894 1209 2743 .4408 1.2794


As you can see, actual win rate was quite different than expected win rate.

It appears that ZScore probability can be used to do a very nice job of classifying favorites as either vulnerable or legit.

But contrast that to something else I've been working on, a Tote Prob using a different type of probability distribution based on my own UPR:

2007 Post Time Favorites

By: Prob: Bettors Tote

>=Min < Max Gain Bet Roi Wins Plays Pct Impact
-999.00 0.00 0.00 0.00 0.0000 0 0 .0000 0.0000
0.00 0.05 0.00 0.00 0.0000 0 0 .0000 0.0000
0.05 0.10 -36.80 56.00 0.3429 2 28 .0714 0.2073
0.10 0.15 -11.40 40.00 0.7150 3 20 .1500 0.4354
0.15 0.20 -563.60 2216.00 0.7457 216 1108 .1949 0.5659
0.20 0.25 -2468.90 9262.00 0.7334 1034 4631 .2233 0.6481
0.25 0.30 -2018.60 10098.00 0.8001 1381 5049 .2735 0.7940
0.30 0.35 -1896.30 12610.00 0.8496 2049 6305 .3250 0.9433
0.35 0.40 -1662.10 9964.00 0.8332 1855 4982 .3723 1.0808
0.40 0.45 -798.30 5480.00 0.8543 1194 2740 .4358 1.2649
0.45 0.50 -367.90 2790.00 0.8681 653 1395 .4681 1.3588
0.50 0.55 -359.40 2740.00 0.8688 724 1370 .5285 1.5340
0.55 0.60 -38.60 272.00 0.8581 75 136 .5515 1.6008
0.60 0.65 -70.20 1062.00 0.9339 339 531 .6384 1.8532
0.65 0.70 -38.00 480.00 0.9208 159 240 .6625 1.9231
0.70 0.75 -69.10 622.00 0.8889 211 311 .6785 1.9694
0.75 0.80 7.20 78.00 1.0923 34 39 .8718 2.5306
0.80 0.85 0.60 6.00 1.1000 3 3 1.0000 2.9028
0.85 0.90 -2.30 42.00 0.9452 18 21 .8571 2.4881
0.90 999999.00 -1.00 34.00 0.9706 15 17 .8824 2.5613


I suspect that normalized ZScores can be used in a number of different ways to rethink (and improve) a lot of the things I currently do. But it's going to take some R&D to do that.


-jp

.

~Edited by: jeff  on:  6/27/2008  at:  1:15:13 PM~

Reply
busseb
6/27/2008
4:34:44 PM
I wish I understood what the hell you guys are talking about.

Oh well, just put it in an update and as long as I can figure out how to make money with it - who cares!!!

ElPaso

Reply
formula_2002
6/27/2008
4:37:25 PM
Jeff,try your top pick only, and your probability is >=track probability*1.5 and the zscore is >=2 for non maiden races.

I set the race book % at <=1.25. It's my way of not betting against low priced entries.




Reply
formula_2002
6/27/2008
4:38:00 PM
just google "z scores"

Reply
jeff
6/27/2008
4:55:24 PM

--quote:
"Jeff,try your top pick only, and your probability is >=track probability*1.5 and the zscore is >=2 for non maiden races.

I set the race book % at <=1.25. It's my way of not betting against low priced entries."
--end quote

Perhaps we should continue this discussion in the Private Section of this message board.

-jp

.


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