Which is better?

[Wizard of Odds]

betting with +35% ROI with a 40% win rate (say, betting one horse) or

betting with a +20% ROI with a 65% win rate (say, betting two horses)?

Why?

What formula could be used to compare these two and, more generally, get the mathematically correct trade-off between win rate and ROI?

[Greyfox]

betting with +35% ROI with a 40% win rate (say, betting one horse) or

betting with a +20% ROI with a 65% win rate (say, betting two horses)?

Why?

What formula could be used to compare these two and, more generally, get the mathematically correct trade-off between win rate and ROI?

Am I missing something here?
If you're ROI is 35 % over 1000 bets, wouldn't that always beat a 20 %
ROI using multiple horses for 1000 bets? Conceptually I'm having a hard time connecting ROI to win rate. ROI is what your taking out of the track over a period of time over a series of wagers.

[SMOO]

Am I missing something here?
If you're ROI is 35 % over 1000 bets, wouldn't that always beat a 20 %
ROI using multiple horses for 1000 bets? Conceptually I'm having a hard time connecting ROI to win rate. ROI is what your taking out of the track over a period of time over a series of wagers.
If the lower ROI provides more bets, I could see going that way so you wouldn't have to bet as much.

[Greyfox]

If the lower ROI provides more bets, I could see going that way so you wouldn't have to bet as much.

Anyone averaging 35 % ROI on their investments is going to beat someone making only 20 % ROI on their investments (assuming they are investing the same amount.) Indeed, the guy getting back 35 % will ultimately be in a better position to make more bets.

[Overlay]

As Greyfox indicated, wouldn't the ROI be the determining factor, regardless of the win rate? With a 20% ROI playing two horses, you're betting/risking more for a lower return on investment. Why not just bet twice as much on the one horse producing the 35% ROI? The only justification I can see would be if playing just one horse introduced decision-making/risk-taking issues that affected the psychological side of your game, and thus had a detrimental effect on your handicapping.

[Wizard of Odds]

With the possible exception of SMOO, I think the respondants so far, with all due respect, may have missed the subtleties.

According to Kelly Criteria, the optimal bet of bankroll is edge divided by odds.
Hence, in the Lower ROI/Higher Win Percent scenario, you bet higher amounts as safely as for a lower amount in the Higher ROI/Lower Win Percent scenario.

I think equallizing the % of bankroll to be optimally bet in the Kelly formula above may be the key to answering my question.

[Greyfox]

You didn't ask about optimal bet of bank roll or odds.

[Wizard of Odds]

I aksed which was better - more useful to win money over long run

[Greyfox]

I aksed which was better - more useful to win money over long run

I answered -the method that returns the highest ROI -over the long run.

[hcapperjag]

Dave Schwartz had a fascinating post (may have been on his forum) where he demonstrated that by adding a LOSING but CONSISTENT play into your portfolio, you can up your % of bankroll bet (in his example from 5% to 17%), thereby making more money in the long run, because you are investing much more money, albeit at the lower ROI.

The 65% offers a much lower chance of tapping out - to many this is a more appealing approach, much easier on the temperament. You can churn a vastly larger amount of money through the windows.

I would rather win $200,000 at 20% ROI than $100,000 at 35% ROI. you can't spend ROI - only $$$.

As far as an exact answer, you can't determine it completely without defining confidence levels, full Kelly, half Kelly and so on.

But seriously, if I had either option available to me I would just take the money.

[singunner]

You asked which was "better", "mathematically". Those two words don't really go together. Math is all about being true or false. There is no "more true".

And it's correct that you would want to maximize the ROI, unless an extended losing streak at the higher ROI had a chance of wipping you out, but you didn't provide nearly enough information for that.

[chickenhead]

I thought Kelly is the answer. Whichever bet calls for a higher % of bank is better. That is the whole point of Kelly. To bet most on the best bets.

[JustMissed]

Copied from Turfpedia.com's fine site:

YOUR SKILL
If you know your win percentage and the average odds on your winners, you can estimate your winning edge. Your edge is equal to your win percentage multiplied by your average odds on winners, and that product minus your loss percentage.

The amount of money you can expect to win is equal to the amount you bet during the year multiplied by your edge. So if you have a 22% edge on the game and you bet $100,000 during the year, you can expect to win $22,000. Which is a nice profit from your hobby and an exciting game!

Here are the attainable goals for skillful handicappers:

Win% Aver. Odds Edge
30% 5-2 .05
33% 5-2 .15
35% 5-2 .22
40% 5-2 .40

The average odds are held constant at 5-2 because in reality they do not vary much on key horses to win.

The edge is equal to your return on investment (ROI). If your edge is 20%, that means for every dollar you bet, you can expect to get back $1.20. Investors, savers, and business men and women would be pleased to do as well.

Notice that handicappers who improve their skill by 10%(30% to 32%) have tripled their profits (.05 to .15). How nice! It pays to improve your handicapping.[End Quote]

FYI

JM :cool:

[Wizard of Odds]

I have to say Chicken Head seems right:

To be extreme. Which would you rather have:

1) +10% ROI with a 90% win rate or


2) +50% ROI with a 1% win rate

Isn't the answer now obvious here?

[sjk]

These are serious and interesting questions. I always win around 12% of the races I bet (and probably bet 60-70% of the races I look at). I would not have a clue how to make money if someone told me that a 35% (or 90%) win rate was required.

Some things are clearly impossible although all I have is simple heuristic arguments. It can't be possible to bet all the races, win 90% of your bets and make money.

Why: Most horses are underlays, most favorites are underlays, most winners are underlays, nobody gets ahead by betting on underlays, if you are winning almost all the races the drain on your return from all of those underlays takes you down.

If you are getting all of these winners by being selective in the races you bet the question of how many races you pass and how much you can put into the pools without ruining your edge becomes relevant.

If you are actually playing all of the races the actual odds of the historical winners (5.33-1 if I remember from another thread) is relevant.

I have no idea how to calculate it but I have no doubt that there is upper limit to ROI if you bet all the races. The upper limit will increase if you are selective in the races you bet but total profit may not increase.

There are answers to these questions that take some mathematical firepower to derive.

That reminds me of another thread. If every question had a simple answer scientific journals would be far thinner and better popular reading. Some questions are deep.

[chickenhead]

it gets more complicated when you want to add differing amounts of plays, and different pool sizes into the mix. i.e. the real world.


It has always seemed to me that the final answer is: how much total inefficiency have you uncovered that you can exploit? Its a pretty straight forward thing to calculate. Let's just say we set it to a break-even return.

Using whatever strategies you can find, betting however many or few horses, however many of few races, what is the total amount of money you could push through the windows in a year, while acheiving exactly breakeven ROI. Some of you might be saying, "Breakeven, my ROI is much higher!", then keep adding more money into the pool until the ROI is lowered to zero. Sum up all those bets for the year.

Whatever method can push the most money through the windows in a given timeframe, while acheiving a given return (breakeven makes everything easier to figure, and makes the most sense) is the better method. By definition I believe. It has uncovered more inefficiency than the other method.

I have no idea what the upper limit of that number is..but its really really big, I know that.

[Overlay]

Dave Schwartz had a fascinating post (may have been on his forum) where he demonstrated that by adding a LOSING but CONSISTENT play into your portfolio, you can up your % of bankroll bet (in his example from 5% to 17%), thereby making more money in the long run, because you are investing much more money, albeit at the lower ROI.

Sounds similar to Mike Pascual's group overlay method, where he showed that it's possible to increase the expected return from a wager on a group of overlaid horses by including a horse that has a high true probability of winning, even if the high-probability horse is slightly underlaid on an individual basis.

[Overlay]

I have to say Chicken Head seems right:

To be extreme. Which would you rather have:

1) +10% ROI with a 90% win rate or


2) +50% ROI with a 1% win rate

Isn't the answer now obvious here?

I agree that the optimum wager size is determined by Edge/Odds. But to me, the issue you're addressing with your original stipulations, and with your conditions above, is still the bettor's comfort level with the length of the runouts he is likely to experience, and with the relative probability that he will lose his entire bankroll, rather than the profitability of the system itself. To use your original example: after, say, 100 races, you will have bet $200 with the first method (one horse per race), won 40 of those 100 races, and gotten back $270 (a +35% ROI), for an average mutuel of $6.75. With the second method, you will have bet $400 (two horses per race), won 65 of the 100 races and gotten back $480 (a +20% ROI), for an average mutuel of $7.38. Yes, the average mutuel and total return are higher in absolute terms, but you're risking twice as much to achieve it, and the return is not commensurate with the risk. Similarly, with your first example above, after 100 races, you would have bet $200, and gotten back $220 (a +10% ROI), for an average mutuel of $2.44 on your ninety winners. With the second example, you would have bet $200, and gotten back $300 (a +50% ROI) on your one winner. The second method presents a much greater risk of runouts that will cause you to lose your entire bankroll (which gets back again to the bettor's comfort level, rather than profitability), but it is still more profitable in absolute, long-run terms.

Or am I misunderstanding how you are calculating ROI?

[Wizard of Odds]

If the objective function is to doubling your bankroll with a fixed percent bet of bankroll per race, then option 1 crushes option 2 with the same safety level of not losing your bankroll.

This is a fundamental corallary of the Kelly Criterion:cool:

[singunner]

Is it just me, or did you ask a question, absolutely sure that you knew the answer and then shoot down everyone who offered a contrary opinion? (Often a mathematically proven, logical, contrary opinion)

[Wizard of Odds]

Singunner - that's a fair point- it not just you.


I want to hear contrary opinions although, at this point at least, I think the mathematics of the Kelly Criterion makes the contrary opinions incorrect.

One way to check this empirically is Monte Carle simultation.

[thaskalos]

I think that by betting 2 horses to win you would probably find at least twice as many plays as you would if you were waiting for a standout bet, which would mean that your long run profit would be bigger even with the lower ROI.

[RXB]

I have to say Chicken Head seems right:

To be extreme. Which would you rather have:

1) +10% ROI with a 90% win rate or


2) +50% ROI with a 1% win rate

Isn't the answer now obvious here?

Well sure it is, when you take the profit down to almost nothing. That is a far cry from your original question. Knock the win rate down to 1% on your 90% profit expectation, and how do you feel about that now?

Regarding your original premise-- probably nobody is winning 60% of their bets, making 20 cents on the dollar and able to find enough plays to make it worth their while, so the whole hypothesis seems rather pointless. If the question is win % vs. profit expectation, that's always a matter of degree.

[raybo]

I aksed which was better - more useful to win money over long run

ROI, to me, doesn't count unless it IS "over the long run". ROI is everything, assuming you have been doing it long enough to call it a realistic ROI. If you're talking about short-term ROI, that's a different story. Then you would have to consider bankroll and probable longest losing streak.

[RXB]

ROI is everything, assuming you have been doing it long enough to call it a realistic ROI.

No, it isn't. Two people can have the same positive ROI rate, while one of them makes a whole lot more money than the other because he can bet a lot more money than the other guy. Which might have to do with win %, or the ability to play a lot more races, or a bigger bankroll, or able to bet a lot more without affecting pools by playing at tracks with bigger handles.

[podonne]

I always thought Kelly was for fixed odds wagering, or at least where the bet is small enough not to make a difference.
Would this answer differ based on the amount of the bankroll and, consequently the amount of the bet? In parimutuel wagering the expected payoff is different before and after the bet is made (albiet a small difference for small bets.)

[podonne]

Oh, and it's even more different after the race ends, give what, 40-50% of the money comes in after post time?

[Wizard of Odds]

Let me put this another way:


A Genie appears to you today with two separate mechanical systems. The Genie tells you that you can have only one of the systems. Each system gives exactly 50 bets (assume the pool size is the same for each bet) a day for the rest of your life (it's not necessary that it is even horse racing). Which one do you take:

System I: yielding +35% ROI with a 40% win rate or

System II: yielding +20% ROI with a 65% win rate.

Hence the question, "Which is better?" (i.e., which is more valuable to you)

I dream of Genie:)

[raybo]

No, it isn't. Two people can have the same positive ROI rate, while one of them makes a whole lot more money than the other because he can bet a lot more money than the other guy. Which might have to do with win %, or the ability to play a lot more races, or a bigger bankroll, or able to bet a lot more without affecting pools by playing at tracks with bigger handles.

I believe you have ROI confused. Typically, ROI refers to the profit earned per dollar bet.

[raybo]

Let me put this another way:


A Genie appears to you today with two separate mechanical systems. The Genie tells you that you can have only one of the systems. Each system gives exactly 50 bets (assume the pool size is the same for each bet) a day for the rest of your life (it's not necessary that it is even horse racing). Which one do you take:

System I: yielding +35% ROI with a 40% win rate or

System II: yielding +20% ROI with a 65% win rate.

Hence the question, "Which is better?" (i.e., which is more valuable to you)

I dream of Genie:)

Win % wouldn't make any difference in your example, assuming your wagers are static and the same in both cases. 50 wagers per day at $2 each yields $35 per day at 35% ROI, and $20 per day at 20% ROI.

[Wizard of Odds]

Win % wouldn't make any difference in your example, assuming your wagers are static and the same in both cases. 50 wagers per day at $2 each yields $35 per day at 35% ROI, and $20 per day at 20% ROI.

Raybo- you have assumed flat betting- this is not optimal! You have also not considered the probability of ruin.

In order to make the most money in the long-run, I would grab System II in a second!:cool:

[RXB]

I believe you have ROI confused. Typically, ROI refers to the profit earned per dollar bet.

No, I don't have it confused. The fact that it is "per dollar bet" is the exact point why it isn't "everything" as was suggested in your previous post. If two players have the same positive ROI but one of them, for any of the reasons that I listed earlier, can bet a lot more money without risking tapout or pool destabilization, then he's going to make more money than the other guy.

[robert99]

Raybo- you have assumed flat betting- this is not optimal! You have also not considered the probability of ruin.

In order to make the most money in the long-run, I would grab System II in a second!:cool:


In theory, risk of ruin for a 65% win rate gives only a 1.76% chance of 10 consecutive losing bets in a 1000 series. A 40% win rate gives a 91.12% chance of that happening, and is expected to occur twice in 1000 bets. Is that the cryptic point you are wishing to make?

A strong pointer to reality but not an exact science as win rate and ROI is varying all the time (not the presumed fixed number from the past) and your Kelly edge varies for each race and is actually unknown - so the math proof assuming a constant known edge falls down. Past results for a system are no guarantee of future results. Flat betting has often proven to be optimal in a real life forward live test, rather than the theoretical optimising, with hindsight, of a series of past results - you can also get the bets placed.

[ranchwest]

My question would be which fist full of dollars should you cram through the window first?

[raybo]

Raybo- you have assumed flat betting- this is not optimal! You have also not considered the probability of ruin.

In order to make the most money in the long-run, I would grab System II in a second!:cool:

You are the one that stated the rules in this thing. Of course I assumed flat betting, at a 45% ROI I would almost have to assume that. However, if you want to change the rules as people respond to your scenario, why waste our time?

And, btw, what the heck is System II? Was this thread only a prelude to some push by you to solicit the buying of a program? If so, I believe it's time for PA to step in.

[K9Pup]

In theory, risk of ruin for a 65% win rate gives only a 1.76% chance of 10 consecutive losing bets in a 1000 series. A 40% win rate gives a 91.12% chance of that happening, and is expected to occur twice in 1000 bets. Is that the cryptic point you are wishing to make?



How do you come up with these numbers? If I have a 40% hit rate that means I have a 60% miss rate. The probability of missing 2 in a row is .60 * .60 = 36%. 10 in a row would less than 1% ?????

In the case of 65%, 10 in a row would be almost 0%. You obviously calculate this differently. Please explain.

[facorsig]

With the possible exception of SMOO, I think the respondants so far, with all due respect, may have missed the subtleties.

I am growing tired of PA topics with an agenda. If you know the answer, why are you asking the freaking question? This applies to several people on PA.

Fred

[Wizard of Odds]

Sell the system? Are you kidding?

No agenda, just the Truth

I strongly suggest Dick Mitchell's "Winning Thoroughbred Stategies":)