I have a Question About Bet Size/Varying Weights

I'm happy to keep this discussion going, but I'm short on time the next few days. Driving out from CA to Vegas this afternoon for a few days. I was being a little loose when I said 50% of my bets; just trying to get my point across. You are correct that if that was the case I would surely want to identify what subset was losing and eliminate it from my betting. I never bet just to have action, I bet to invest. It should be easy to see why one bet is worth several times another. A recreational 50% - 52.4% bet has no value while one with P(cover) above 53% is infinitely more valuable. A 56% bet has about a 6.9% ROI while a 53% bet has about a 1.2% ROI. Isn't that several times better? No one is saying that in order to bet 3 times as much the P(cover) has to astronomically (and unattainabably) better like 65% or something. The fact is a 56% bet is much better than a 53% or 54% bet so why not bet more. I'm not going to get into any bankroll trouble if my 10 unit bet is coming from a 300 Unit bankroll. That is 3 1/3 % for my largest bet. I think you are assuming the 1 unit bet is maybe 1% of bankroll and the 10 unit bet is irresponsibly high relative to bankroll. I'm essentially saying that if you can't identify a significant edge then you should be betting very little on "marginal" 1-2 unit bets. In your example of making 100 bets, You "outperformed" me by betting 3 units on all bets while I downsized on the 1 and 2 unit bets. Since in our example 1 and 2 unit bets are hitting above 52.4% then they are profitable, so of course you will outperform. I would turn the example around and say if you bet 900 units across the 300 plays, I would bet differently. In your example if I had 100 plays at 1, 2, and 3 weights and had 900 units to spend on them then I would bet 4.5 units on the 3 weights, 3 units on the 2 weights and 1.5 units on the 1 weights. This would yield a substantially greater profit. I have to stop for now; we can do more math later but want to hit the road.

Thanks for time and answers Happy and Cal. And Cal, have a great trip!!

I guess that I still really don't understand the value in varying weights and that might be because I don't have a good idea on how to determine how much an edge is. Cal stated that I must be talking about % of bankroll but I know that 10 Units does not equal 10%. That would be outrageous to even consider anyone doing. My example of 1, 2, and 3 Units was just an example. The results would still be higher at 1, 5, and 10 since playing 10 Weight on all would create more bankroll growth as long as your bankroll could sustain the dips and as long as All Subsets were +EV... If anyone has any added thoughts please add it here and thanks again. I at least have a better idea now as to why bettors weight their plays as they do..

If you have any background in capital budgeting to me betting is very similar. For instance a company that has a required ROI objective of 15% for projects will only invest in projects with a return at least that amount. There is a clear cutoff. And the capital will be used up presumably by investing the most amount in the projects with the highest ROI. The limited capital will go into the projects with the highest ROI so as to maximize return. Let's ignore variance for a moment although that will play a part of course in what projects get selected and assume we know the projects will pay off according to the expected cash flows. Comparing to Calsport's analysis a bet that has no advantage is similar to a project for a firm with an ROI below its required return. It shouldn't get any investment. Calsport won't make a bet that doesn't have a positive expected return and a firm won't invest in a project that doesn't return a certain level of ROI. A bettor can also raise the benchmark of course and require a return of 3% let's say before making a bet so that even bets with a positive return are not made. The return on higher return bets will presumably get the most investment just like higher return projects would get the most investment in a firm. I think Calsport's writeup and this framework make it pretty clear why bets with a higher return would get more investment than bets with lower return. The confusion I think and what BP might be getting at is that he can't understand why a handicapper would weight plays for different weights and this is a much different problem than betting. The bettor can allocate capital to strong bets based on the market. The handicapper is making selections based on whether something will win or not and by definition is making plays vs. the market. The handicapper has to make decisions on weights by the likelihood they think the play they select will win. A bettor has the advantage of being able to make bets that aren't the market price and can base their advantage vs. the market price. Back to the company comparison when ranking projects it can be assumed the projects to be invested in have certain cash flows. However, a corporation as a handicapper is looking at projects where it also has estimate cash flows on projects so the return is uncertain. It is clear the handicapper has to be more conservative depending on skill in guessing what are truly the best return projects or bets. The fact that a handicapper is losing on 5 star projects probably indicates that the handicapper isn't truly selecting bets that have a P worthy of a 5 star project or bet. I'll also use a market example but an off number bettor is like an individual trader an can bet nimbly in the market. Betting handicappers actually should not be a big part of that bettor's strategy to win. Practically this is probably bettors at 1000 maybe 2000 and under. Larger bettors are like mutual funds and unfortunately for them handicapping will likely have to be a more important strategy for them to win since they can't get their orders filled at better than market prices for the amounts they want. They have more capital to deploy and are trying to make more money their hurdle rate for a bet is much lower. The problem is they can get into some problems with this as their hurdle rate is too low or they just deploy capital because they have to. Calsport emphasizes that the estimate of P is crucial. If one can really do it. obviously they will be successful and can vary their bet sizes with confidence. I'll also comment on the BP comment that nobody would bet 10% of bankroll on a play. I agree a prudent bettor wouldn't. However, a prudent bettor isn't necessarily the smartest bettor and I believe theories in this area probably say to bet a higher percentage of your bankroll for optimum growth than one might feel comfortable with.

Thanks Skeeter. Good stuff. I am probably one of those bettors who can't clearly detect what a 5 Star Project is so probably best for me to continue to play level, or almost level. Your thoughts are appreciated..