Win % for randomly picked horses

[OCF]

Can any of you database guys give me a win % for picking one horse in a race at random? I suppose ROI would be good to have also.

[PICSIX]

ROI % should equal 100% minus the track take % if the sample size is large enough.

[Magister Ludi]

Can any of you database guys give me a win % for picking one horse in a race at random? I suppose ROI would be good to have also.

What size field?

[OCF]

What size field?

how about calc's for each field size from 5 to 12?

[Will Power]

Can any of you database guys give me a win % for picking one horse in a race at random? I suppose ROI would be good to have also.

It depends how many horses are in the race. The mathematical equation is 1/x, with x being # of horses in race. If there are 20 horses (i.e. Kentucky Derby), a random pick, 1/x = 5%.

The average ROI of betting every horse or random horses over a large sample is actually $1.52, or -24%.

[Magister Ludi]

Lets say 7

1/7 = probability of about 14% of choosing a random winning horse from a 7-horse field. ROI would be approximately equal to -.20.

[OCF]

It depends how many horses are in the race. The mathematical equation is 1/x, with x being # of horses in race. If there are 20 horses (i.e. Kentucky Derby), a random pick, 1/x = 5%.

The average ROI of betting every horse or random horses over a large sample is actually $1.52, or -24%.


Maybe the question should be what is average field size?

[Magister Ludi]

how about calc's for each field size from 5 to 12?

5===.2000
6===.1667
7===.1429
8===.1250
9===.1111
10==.1000
11==.0909
12==.0833

[Magister Ludi]

Maybe the question should be what is average field size?

In the North American market, it is about 7.63.

[OCF]

5===.2000
6===.1667
7===.1429
8===.1250
9===.1111
10==.1000
11==.0909
12==.0833

Thanks for both answers. And ROI would be 1 minus takeout % regardless of field size?

[Magister Ludi]

Thanks for both answers. And ROI would be 1 minus takeout % regardless of field size?

Yes. 1 - (takout + breakage)

[OCF]

Yes. 1 - (takout + breakage)

Got it, thanks!

[Will Power]

Most everybody underestimates the effects of takeout.

Look at Quirin's Winning at the Races, or Michael Nunnamaker's Modern Impact Values and they will confirm what I stated earlier. Random ROI over a large sample size will run -24%.

[GameTheory]

Most everybody underestimates the effects of takeout.

Look at Quirin's Winning at the Races, or Michael Nunnamaker's Modern Impact Values and they will confirm what I stated earlier. Random ROI over a large sample size will run -24%.Yes, all answers above about ROI equaling takeout are dead wrong. You will roughly equal takeout if you choose your horses randomly but with the same probability as the public odds (i.e. stochastically, randomly but not uniformly random, so if the favorite has 25% of the win pool, you would have a 25% chance of choosing him as your "random" choice). But if you choose uniformly randomly (each horse in race has equal chance of being picked, regardless of odds), then you choose many more longshots as your pick and those horses lose much more than the takeout (and many less favorites, who usually lose slightly less than takeout). I would expect losses to be even greater than -24%, but that could well be right...

[Stillriledup]

ROI % should equal 100% minus the track take % if the sample size is large enough.

You know what's funny? Even though that technically this seems correct, it doesnt FEEL like it ever works out that way.

I think if you randomly select NFL teams with coin flips, you'll select 50% because the betting spread is set in stone and it doesnt fluctuate...but in your example, if you're betting random horses that means you know nothing....wouldnt you be losing the takeout PLUS a certain percentage of your bankroll to more informed players?

Don't you have to be skilled in some way to 'just lose the takeout'?

[Some_One]

On a roulette wheel, each number has an undeniable equal chance of hitting and because they all have an equal payoff, the ROI are all the same. What GT was referring to that there appears to be proof (I think especially so in dirt races) that longshots win at a rate slightly lower that the odds would imply so that their ROI is less then a fav's. So if everyhorse had an equal chance of selection, the expectation should be lower then takeout because of the 1 or 2 of 7.5 chance of selection a longshot.

[Magister Ludi]

Yes, all answers above about ROI equaling takeout are dead wrong. You will roughly equal takeout if you choose your horses randomly but with the same probability as the public odds (i.e. stochastically, randomly but not uniformly random, so if the favorite has 25% of the win pool, you would have a 25% chance of choosing him as your "random" choice). But if you choose uniformly randomly (each horse in race has equal chance of being picked, regardless of odds), then you choose many more longshots as your pick and those horses lose much more than the takeout (and many less favorites, who usually lose slightly less than takeout). I would expect losses to be even greater than -24%, but that could well be right...

You are correct. As a matter of fact, Mr. OCF’s randomly selected horses can be a contributory factor to the favorite/longshot bias.

Random betting, such as on barrier or program number, color of silks, or name, introduces a linear skew to the betting pool. Probabilities > 1/n (where n = field size) will be underbet. Conversely, probabilities < 1/n will be overbet. In other words, there will be a clockwise rotation of the graph of odds vs. return at the point 1/n.

[GameTheory]

You are correct. As a matter of fact, Mr. OCF’s randomly selected horses can be a contributory factor to the favorite/longshot bias.

Random betting, such as on barrier or program number, color of silks, or name, introduces a linear skew to the betting pool. Probabilities > 1/n (where n = field size) will be underbet. Conversely, probabilities < 1/n will be overbet. In other words, there will be a clockwise rotation of the graph of odds vs. return at the point 1/n.Which is why this is such a tough game. I think people intuitively feel like even if they aren't picking well the "bottom rate" they are going to be losing at will be the takeout rate, but that's not true at all. It is much worse than that. Everybody knows you can't win picking the same horses everyone else picks. So you must deviate from the crowd to win. But the more you deviate from what everyone else is doing, the more your ROI is also going to deviate from the takeout (in general) -- you are either going to be winning more than average or losing more than average. So if you take the necessary risk to enable the possibility of winning, you are also opening yourself up to greater losses percentage-wise (that's why they call it risk). And guess which side of that coin of that equation it is easier to end up on?

[OCF]

So would someone with a large database be willing to select one horse at random from each race and calculate the resulting win ROI? I get the impression -24% is good enough for all intents and purposes, but I'm curious how close that is.

[dkithore]

Which is why this is such a tough game. I think people intuitively feel like even if they aren't picking well the "bottom rate" they are going to be losing at will be the takeout rate, but that's not true at all. It is much worse than that. Everybody knows you can't win picking the same horses everyone else picks. So you must deviate from the crowd to win. But the more you deviate from what everyone else is doing, the more your ROI is also going to deviate from the takeout (in general) -- you are either going to be winning more than average or losing more than average. So if you take the necessary risk to enable the possibility of winning, you are also opening yourself up to greater losses percentage-wise (that's why they call it risk). And guess which side of that coin of that equation it is easier to end up on?

I know you guys are heads and shoulders above me in this analysis of racing and risk, so let me ask you Game:

there is no hope to be on positive side for those of us who is looking for a black cat in a dark room, is there?

[Jeff P]

Here's what I have for calendar year 2013... Jan 01, 2013 current through Apr 30, 2013... thoroughbred only - all starters in North America.

First, all starters in the sample broken out by WPS:

query start: 5/1/2013 8:02:23 PM
query end: 5/1/2013 8:04:59 PM
elapsed time: 156 seconds

Data Window Settings:
Connected to: C:\JCapper\exe\JCapper2.mdb
999 Divisor Odds Cap: None

SQL: SELECT * FROM STARTERHISTORY
Where [Date] >= #01-01-2013#
AND [DATE] <= #04-30-2013#


Data Summary Win Place Show
-----------------------------------------------------
Mutuel Totals 143639.70 142903.00 142757.10
Bet -189328.00 -189328.00 -189328.00
-----------------------------------------------------
P/L -45688.30 -46425.00 -46570.90

Wins 12066 24042 35129
Plays 94664 94664 94664
PCT .1275 .2540 .3711

ROI 0.7587 0.7548 0.7540
Avg Mut 11.90 5.94 4.06


Note that a $2.00 bet made on every starter that went to post would have returned a flat bet loss of about 24% in the WPS pools.

Next, up here's the above sample broken out by RGN. In JCapper terminology RGN is a random number between 1 and 100 auto generated by the interface and assigned to each starter. The interval for each row in the data below is 5 points of RGN. For example, the first row contains starters with an RGN value between 1 and 4 (which is why it has fewer starters than the other rows.) The second row contains starters with an RGN value between 5 and 9... 20 rows in all... The last row contains starters with an RGN between 95 and 100 (which is why it has more starters than the other rows.)

Here's the above sample broken out into 20 separate samples of RGN:

By: RGN

>=Min < Max P/L Bet Roi Wins Plays Pct Impact
--------------------------------------------------------------------------------------
-999.00 5.00 -1824.60 7570.00 0.7590 479 3785 .1266 0.9929
5.00 10.00 -1915.30 9680.00 0.8021 627 4840 .1295 1.0164
10.00 15.00 -2749.40 9428.00 0.7084 586 4714 .1243 0.9753
15.00 20.00 -1587.80 9308.00 0.8294 614 4654 .1319 1.0351
20.00 25.00 -2309.70 9236.00 0.7499 582 4618 .1260 0.9888
25.00 30.00 -2086.20 9450.00 0.7792 601 4725 .1272 0.9979
30.00 35.00 -2167.30 9568.00 0.7735 615 4784 .1286 1.0086
35.00 40.00 -2684.60 9580.00 0.7198 628 4790 .1311 1.0286
40.00 45.00 -1768.10 9582.00 0.8155 644 4791 .1344 1.0546
45.00 50.00 -3197.10 9438.00 0.6613 571 4719 .1210 0.9493
50.00 55.00 -2072.00 9388.00 0.7793 607 4694 .1293 1.0145
55.00 60.00 -3224.80 9570.00 0.6630 598 4785 .1250 0.9805
60.00 65.00 -2520.70 9422.00 0.7325 575 4711 .1221 0.9576
65.00 70.00 -2452.30 9532.00 0.7427 602 4766 .1263 0.9910
70.00 75.00 -1700.00 9476.00 0.8206 619 4738 .1306 1.0250
75.00 80.00 -2776.00 9466.00 0.7067 580 4733 .1225 0.9614
80.00 85.00 -1584.20 9586.00 0.8347 606 4793 .1264 0.9919
85.00 90.00 -1917.00 9256.00 0.7929 628 4628 .1357 1.0646
90.00 95.00 -2097.00 9516.00 0.7796 601 4758 .1263 0.9910
95.00 999999.00 -3054.20 11276.00 0.7291 703 5638 .1247 0.9783


Note that while some of the above RGN samples have higher (and lower) flat bet win bet roi than the overall sample, the player's expectation in the WIN pool across the entire sample is a loss of about 24%. Also note that NONE of the 20 separate RGN samples have a positive roi. That should drive home the point that betting horses at random is a VERY bad idea (financially.)

Next up, here's the above sample broken out by odds range in intervals of 2.5 points of odds:


By Odds Range:

>=Min < Max P/L Bet Roi Wins Plays Pct Impact
--------------------------------------------------------------------------------------
0.00 2.50 -4717.00 29914.00 0.8423 5374 14957 .3593 2.8189
2.50 5.00 -6693.10 35888.00 0.8135 3270 17944 .1822 1.4297
5.00 7.50 -4275.90 23700.00 0.8196 1370 11850 .1156 0.9070
7.50 10.00 -3720.40 16896.00 0.7798 692 8448 .0819 0.6426
10.00 12.50 -2710.00 12832.00 0.7888 421 6416 .0656 0.5148
12.50 15.00 -2076.00 9430.00 0.7799 254 4715 .0539 0.4226
15.00 17.50 -2540.40 7514.00 0.6619 144 3757 .0383 0.3007
17.50 20.00 -2281.40 5922.00 0.6148 93 2961 .0314 0.2464
20.00 22.50 -1318.30 4998.00 0.7362 83 2499 .0332 0.2606
22.50 25.00 -1083.70 4554.00 0.7620 71 2277 .0312 0.2446
25.00 27.50 -531.10 3788.00 0.8598 60 1894 .0317 0.2485
27.50 30.00 -450.50 3348.00 0.8654 49 1674 .0293 0.2296
30.00 32.50 -700.80 3078.00 0.7723 37 1539 .0240 0.1886
32.50 35.00 -760.00 2620.00 0.7099 27 1310 .0206 0.1617
35.00 37.50 -1010.80 2428.00 0.5837 19 1214 .0157 0.1228
37.50 40.00 -767.00 2110.00 0.6365 17 1055 .0161 0.1264
40.00 42.50 -732.00 1912.00 0.6172 14 956 .0146 0.1149
42.50 45.00 -566.60 1728.00 0.6721 13 864 .0150 0.1180
45.00 999999.00 -8753.30 16668.00 0.4748 58 8334 .0070 0.0546

Note that when the player does ZERO handicapping: Return expectancy gets excessively worse the higher the odds.

Hope I managed to get most of that out in a way that makes sense.


-jp

.

[Jeff P]

Looking closer at the odds range sample I posted above, I noticed what appears to be a short term blip in the numbers (specifically the roi in the 25/1 to 30/1 odds range.)

Not wanting anyone to come away with the impression that the 25/1 to 30/1 odds range is somehow a magic sweet spot, I decided to run a larger follow up sample.

Below is what I have for calendar years 2011 and 2012 combined... thoroughbred only... all starters at all North American tracks during the two year period.

First, all starters in the database broken out by WPS:
Data Window Settings:
Connected to: C:\JCapper\exe\JCapper2.mdb
999 Divisor Odds Cap: None

SQL: SELECT * FROM STARTERHISTORY
Where [Date] >= #1/1/2011#
AND [DATE] <= #12-31-2012#


Data Summary Win Place Show
-----------------------------------------------------
Mutuel Totals 1184181.40 1187791.40 1186915.80
Bet -1574070.00 -1574070.00 -1574070.00
-----------------------------------------------------
P/L -389888.60 -386278.60 -387154.20

Wins 100278 199588 292713
Plays 787035 787035 787035
PCT .1274 .2536 .3719

ROI 0.7523 0.7546 0.7540
Avg Mut 11.81 5.95 4.05


Next, all starters in the database broken out by odds range - 2.5 points of odds per row:
By Odds Range:

>=Min < Max P/L Bet Roi Wins Plays Pct Impact
--------------------------------------------------------------------------------------
0.00 2.50 -38894.20 249470.00 0.8441 44863 124735 .3597 2.8229
2.50 5.00 -54188.40 297586.00 0.8179 27113 148793 .1822 1.4302
5.00 7.50 -39617.80 196946.00 0.7988 11174 98473 .1135 0.8906
7.50 10.00 -28658.00 142432.00 0.7988 5959 71216 .0837 0.6567
10.00 12.50 -25789.30 106062.00 0.7568 3335 53031 .0629 0.4936
12.50 15.00 -20117.60 80196.00 0.7491 2064 40098 .0515 0.4040
15.00 17.50 -14992.20 62674.00 0.7608 1397 31337 .0446 0.3499
17.50 20.00 -12149.00 49988.00 0.7570 966 24994 .0386 0.3033
20.00 22.50 -12618.40 42222.00 0.7011 672 21111 .0318 0.2498
22.50 25.00 -10080.00 36090.00 0.7207 530 18045 .0294 0.2305
25.00 27.50 -9808.90 31536.00 0.6890 401 15768 .0254 0.1996
27.50 30.00 -9047.90 27172.00 0.6670 307 13586 .0226 0.1774
30.00 32.50 -8687.50 24036.00 0.6386 240 12018 .0200 0.1567
32.50 35.00 -8375.80 21646.00 0.6131 194 10823 .0179 0.1407
35.00 37.50 -5884.00 19208.00 0.6937 180 9604 .0187 0.1471
37.50 40.00 -5691.40 17348.00 0.6719 147 8674 .0169 0.1330
40.00 42.50 -6560.90 15704.00 0.5822 109 7852 .0139 0.1090
42.50 45.00 -5789.80 14448.00 0.5993 97 7224 .0134 0.1054
45.00 999999.00 -72937.50 139306.00 0.4764 530 69653 .0076 0.0597



-jp

.

[Stillriledup]

Excellent stuff Jeff.

Here would be my question.

If the average win takeout across america is 17% to 20%, why would the loss be 24 percent?

Is the random player essentially losing 17-20 percent to the actual takeout and an extra 4 (approx) percent to the 'winning players' for a total of about 24 percent?

[Overlay]

Excellent stuff Jeff.

Here would be my question.

If the average win takeout across america is 17% to 20%, why would the loss be 24 percent?

Is the random player essentially losing 17-20 percent to the actual takeout and an extra 4 (approx) percent to the 'winning players' for a total of about 24 percent?
The additional loss is the result of dime breakage (rounding $2.00 payoffs down to the nearest multiple of twenty cents).

[OCF]

Thanks jp, the results are interesting. The -24 number held up well.

[Ray2000]

Similar results in Harness

Randomly betting on a number puts you on a 20/1+ horse too often and the favorite/longshot bias drops the ROI below take + breakage.

data from 2012

[flatstats]

One thing to note about examining prices is that there are more opportunities for selecting a random big price than a random short price.

There is only one favourite in a race (if you split co / joints) whilst there can be many 20/1+ or higher). Thus charting on prices creates it's own bias.

---

Here's some figures from British flat turf racing for the past 5 years / 19,600 races:

Bookie SP: -21% ROI, 0.87 A/E
Betfair SP: -3.5% ROI, 1.00 A/E
Tote: -16.2% ROI, 0.86 A/E

Bookies include over-round, which is their percentage profit per runner. It's usually around 2% per runner.

Betfair SP is much more fairer because it's a 100% book. You do pay commission on winning bets (fixed 5% used for this test)

The Tote is the PM. The takeout used to be 13.5% but increased to 16.5% a few years ago. The ROI figure is pretty much the same as the take out.

[OCF]

I don't thoroughly understand everything set out above by flatstats, but I'm fairly certain it says British bettors start out with a better chance of success than U.S. bettors.

[OCF]

If average field size is assumed to be 7.63 (see post #9), expected win rate for a horse picked at random, without factoring in odds, would be 13.11%

In jp's results tables the win rates are 12.74% and 12.75%, which are closer to 13.11% than I would have expected after comparing average ROI to 1 minus takeout %.

In other words, the effect of the odds seems to be greater on the ROI than it is on the win rate. Hope that makes some sense.

What gives? Breakage? Maybe we should have a thread "The dramatic effect of breakage"?

[MightBeSosa]

makes perfect sense. the win rate on a random horse is insensitive to any other factor. the odds reflect numerous bias.

[OCF]

makes perfect sense. the win rate on a random horse is insensitive to any other factor. the odds reflect numerous bias.

true, i also just noted that the roi is better than 1 - TO, but still negative, on the lowest odds horses, but gets progressively worse, much worse than 1 - TO, as the odds get higher