Originally Posted by GameTheory

Consider what we were talking about earlier in terms of the way the public bets. The ROI on favorites is much much higher than the ROI on longshots (when betting randomly) -- so it is quite normal for the lower odds horses to perform better as a group. It also makes it quite likely you are seeing an anomaly -- in some samples just betting the favorite makes a flat-bet profit. How does the favorite fare in your sample?

Originally Posted by singunner

I have absolutely no idea what you just said. I've read it 4 or 5 times now and it continues to not make sense. Are you asking about the shape of the distribution? Perhaps it will be skewed?

If you have an average, unless it is purely theoretical, there's usually a probability that it will be skewed (not symmetrical). Until you encounter a large enough sampe, this will almost always be the case. However, as it is an average, there will be equality on both sides of the mean. There's no way for one side of the average to have more than the other; hence, it's an "average".

Are you saying to eliminate the lower-odds instances? Because I was under the impression that most people considered that the basics of handicapping.

Originally Posted by speculus

Favs: avg odds 1.38 @ 0.5 ROI 19%.

Originally Posted by speculus

By asking these questions, I am trying to drive home the point that to judge the performance of a person who varies the bet size on the premise of FLAT-BET ROI is, like GT said somewhere on this thread, comparing oranges to apples.

Because the FLAT-BET ROI (say, with avg odds = x) can give TRUE PICTURE for those who VARY THEIR BET SIZE if and only if there is PERFECTLY SYMMETRICAL distribution of odds around the figure x, NOT otherwise. And the probability of this happening even for a player who makes finite number of bets is very low, perhaps close to zero, if not zero.

Now imagine there is an "adjustible" formula that is sensitive to odds in such a way that it brings in loads of money on all winners @ greater than the avg odds and takes care of a good part of losing bets on either side of avg odds (this is an important condition because your bet size is going to be determined based on odds too as one of the factors and while making bet, especially at longer odds, you don't know whether it's going to be an eventual winner).

If you believe (for whatever reason, maybe on account of your performance history, general strike rate etc) that your profile is skewed in favour of the left side (for odds less than the avg odds), the "adjustible" nature of the formula should give you the freedom to shift the focus in such a way that now, bet size should change in such a way that more profits should come in from the favs and winners below the avg odds.

The asymmetrical nature of actual winning odds with reference to the flat bet avg odds offers a chink (or maybe a window?) through which one can attack this problem. This is precisely what I want to state.

Originally Posted by speculus

To give you a concrete example, let's go back to flat betting. If the "average odds" on winners is say 2-1, it is not even necessary that there will be at least one or more winners at the odds 2-1.

As an example, in a small sample (say a week's bets?) suppose there are only 5 winners with the odds averaging to 2-1, technically the actual odds could be:

0.8 1.7 1.2 2.3 4 (without a single actual 2-1)

Or there could be an actual 2-1 among them like

1.8 2 3.2 0.9 2.1

Question 1: WHAT IS THE PROBABILITY that the sample will be "perfectly" distributed around 2 ?

Or in other words, WHAT IS THE PROBABILITY that for each figure (2+x) in the sample, there WILL BE a corresponding figure (2-x) also in the same set?

If not the exact probability in terms of a sample of n figures, can you give your opinion whether you feel it will be:

a. High?
b. Very high?
c. Close to infinity?
d. Low?
e. Very low?
f. Close to zero?

Question 2: If n (number of specimens in the sample) is too high (say tends to infinity), then how would you describe the same probability? Again

a. High?
b. Very high?
c. Close to infinity?
d. Low?
e. Very low?
f. Close to zero?

Originally Posted by GameTheory

It is getting hard to talk about this with theory only -- it sounds like maybe you are holding the probability of winning each bet as a constant based on the whole group? Imagine that your "formula" only allowed 2 possible bet amounts -- $10 (or any positive amount) and $0. Then you "adjusted" so that you bet $0 on the crappy bets and $10 on the good bets. (i.e. you flat bet on those propositions you actually end up betting) That's not "money management", that is just filtering out the negative expectation wagers. Once you do that, NOW money mangement comes into play. You should be able to assign an expectation, positive or negative, based on:

a) the probability of winning THAT wager
b) the estimated odds you are going to get on THAT wager



-----------------

It sounds like you are attempting to do something like this:

You have some selection method for picking horses.

You look at a sample of horses picked by that method and the results are (for example) 25% winners at avg odds of 5/2 (a flat bet loss of 12.5%).

You make the assumption that those numbers will hold up -- in the future you'll also see 25% winners at avg odds of 5/2 and you'll lose 12.5% flat betting.

You assign a probability of 25% for all future wagers made with that selection method.

You wonder if you can somehow come with a money managment formula that will make a profit with this method even though it lose when flat betting.

You come up a formula that somehow favors certain bets (betting more on them) and downgrades others (betting less on those).

In the future, your assumption holds up and you do in fact get 25% winners and flat betting would have lost 12.5%, YET you make a 10% profit using your formula.

You declare, "Eureka! I have done what the mathematicians say is impossible and have made a profit where no profit should be possible!"

--------------


Am I getting warm?

If so, then you will not be comparing apples to apples, and if successful you will not accomplish anything that was previously thought impossible. You will simply be holding back information you had all along and using it in your "money management" formula to filter out the bad bets. How will your formula draw distinctions between bets to determine which should be favored and which should be downgraded? Well, either you'll:

1) Use some handicapping factor to adjust the estimated probability of winning THIS wager -- NOT MONEY MANAGEMENT

and/or

2) Use the tote board odds to adjust the estimated probability of winning for THIS wager -- NOT MONEY MANAGEMENT

and/or

3) Use the tote board odds to adjust (or determine for the first time) positive/negative expectation on THIS wager -- NOT MONEY MANAGEMENT

I get the feeling you're mostly playing around with option #3, maybe with some option #2 thrown in. Which is good -- everyone should do that to be more accurate if they are able. But that's not money management. You are adjusting your original expectation (which was based on the result of a group as a whole) to a more accurate expectation for this wager (based on the results of wagers with similar odds to what you are seeing on the board now).

Which is not money management, but simply refining information you already had to a greater level of detail. NOW, if the bet still has a positive expectation, you apply whatever money management system you are going to apply to determine how much to bet, and you're on your way.

Money management only applies to those wagers that are left over after you make all the distinctions you are able to make between them -- in other words only when you have your full information and already know your best estimate of the expectation for this wager. But as soon as you drop some wagers picked with your selection method because you've decided they have a negative expectation at some certain odds range, then you no longer can compare your final results (after dropping those wagers) with the group as whole (which included those wagers). Cause they're different groups now, aren't they?


It would be much easier to talk about this with a bet-by-bet breakdown of what you are talking about, complete with your handicapped pre-race probability estimates, estimated odds, and final results. Then we can talk about nuts & bolts instead of vague and confusing generalities.

(I'll get to your other question about probability distribution shortly.)

Originally Posted by GameTheory

Now that I look at this closely, it would appear that the answer is unknowable. You're asking what is the probability of seeing a certain distribution when we only know the average. Answer: there is no way to know without more information. For instance, if we knew were going to have a normal distribution with mean X and standard deviation Y, then we could make some good estimates of the odds we'd see and how often we'd see them.

But we are restricting our discussion to horse racing odds, so there are some practical limits as to what we might see in terms of high and low, and we can look at odds in general on winning horses to find what that distribution looks like. But will that distribution hold up for any subset of winners chosen with some arbitrary selection method? We don't know.

But I can see what you are getting at, and you'd just have to look at the sample in question to make your estimates for the future. I think I know where you are going with this (see my previous post), but it still ain't "money management"...

Originally Posted by speculus

You had your chance of coming clean on that, but you chose to hide behind this mumbo jumbo.

Originally Posted by speculus

GT, I just put forward a viewpoint why the money management concepts originating from the flat-bet roi standpoint could be useless or worthless for those who vary bet size, and you build up a whole case against me saying I "may be doing this and may be doing that." Can't you wait until the testing is over?

Originally Posted by speculus

Just for your information, I am NOT doing ANYTHING that you are speculating about. I am completely open to the idea that perhaps the loss-into-profit phenomenon (found only in one sample so far, although it has improved the performance of most negative flat-bet roi by reducing the losses) may be due to some reasons peculiar to that sample. But at the same time, I cannot overlook the fact that the formula is outperforming flat bet by a wide margin consistently.

Originally Posted by Cesario!

I simply stopped betting on horses under 8-1 (or on exacta opportunities that offered the same).