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Yet another Kelly question
I'm hitting 63% of my bets this year. I bet Kelly at 55% expected win percentage. My question is am I losing a lot of money by not estimating my win % to be higher than 55%? My stakes are about 1/4 of kelly at 63%. For the sake of this discussion let's forget the fact that most people believe 63% to be an unattainable long term win % in sports gambling. This is a theoretical question only. Thanks.
Yes, ex post you could have always done by better utility-wise by having more accurately judged your edge.
Unfortunately, however, we don't have the benefit of hindsight when making our staking decision.
Ok, is there a way to figure out like per 100 bets or so how much are you losing by using 1/4 kelly opposed to 1/2 kelly??
Sure.Originally Posted by roasthawg
Put the relevant numbers in the Kelly calculator (you can use the one at http://crazyl.mysbrforum.com/), set "Consecutive Series" to 100 and compare the differences in median and expected bankrolls with Kelly multipliers of 0.5 and 0.25.
I'm putting the number in the calculator but I'm getting negative expected profit numbers...any idea why? This would be great if I could get it to work...thanks for your help!
The calculator linked from SBR Odds has some compatibility issues with a recently added JavaScript library.
Try using the calculator on Crazyl's mySBR page, or the popup version here.
Great, thanks for the link! So let me get this right...at 63% winning percentage you can expect to roughly triple your roll after 100 bets at 1/4 kelly, almost 10x it at 1/2 kelly, and multiply your roll 80 times over at full kelly?!? If that is the case then my conservative betting is costing me A TON of money indeed.
And at double Kelly your expected bankroll would be almost 3,700 times higher, while at decuple-Kelly (10x Kelly) your expected bankroll would be over 69 thousand times higher.
The problem is that you're looking at this in very much the wrong way. There are two major problems with your analysis:
- The entire point of Kelly is that it defines one's utility function differently from the simple risk-neutral (i.e., "linear") function that would inspire a bettor to maximize expected utility. As such, it's unfair to compare fractional-Kelly strategies on the basis of expectation alone. The value of an expected bankroll needs to be tempered by the inherent riskiness of that expectation. The higher the Kelly fraction the necessarily higher the expected bankroll, but also the more risky the outcome distribution.
- Your 63% figure is an ex post figure (a Latin phrase loosely translated as "after the fact"). Bet sizing decisions, however, need to be made ex ante ("before the fact", the opposite of ex post). A 50% bettor who somehow magically knew ex ante over which stretches of 10 games he was going to win 60% or more (a feat that would occur roughly 37.7% of all discrete 10 game stretches) could make lots of money even while picking at only 50% over the long term. The problem with this, of course, is that such information is only available to nonprescient bettors ex post, and so can't be used directly in bet sizing decisions. Now that isn't to say that frequent out-of-sample stretches of 63% success rates shouldn't influence one's estimates of long-term success, but such evidence (like all additional evidence, whether tending to refute or confirm), should be carefully considered from the standpoint of Bayesian Inference and taken in light of one's prior hypotheses.
In general, for straightforward models, one's expected win percentage should be estimated from careful study and in-sample refinement of one's hypothesis, further refined by realized out-of-sample performance.
One's Kelly multiplier, on the other hand, should, for a given model, be taken as a measure of the inherent level of relative risk aversion at play when trading that model.
If people are interested I'll try to throw together an Excel spreadsheet that attempts to back out a Kelly multiplier in response to a users' answers to several questions.
Last edited by ivanator; 10-08-09 at 10:31 AM. Reason: bad url
An excel spreadsheet would be great! I understand the concept of risk tolerance as well as the fact that 63% is probably on the high end of what I could ever expect to hit. Yet I've been hitting between 59%-60% of my bets for some time now so I low balled Kelly to play it safe and estimated it at 55%. But if I'm costing myself a ton of money by lowballing my expected win % I think it might be time to up it to 58% maybe. Tough call.
Ganchow - Point 2 is always the problem. I had multiple winning seasons, minimum 200 bets per and than ran into a real clunker of a season last season. My system didn't change between seasons and this year it's winning again. This is why after studying kelly extensively over the past few seasons, I narrowed bet size to 1/40 of my original bankroll with no changes. I know the risk is loss of the entire bankroll but I'd rather risk that than the excruciating climb up through the use of smaller bets after a losing streak.
Would absolutely love to see this if you have time!!! And thanks for everything else you have shared on this site while I'm at it, not sure if that gets said enough!!If people are interested I'll try to throw together an Excel spreadsheet that attempts to back out a Kelly multiplier in response to a users' answers to several questions.
And by the way, where is the HG (your handicapping general)? He also shares a lot of insight, especially on individual baseball games and basketball totals, that I enjoy reading and learning from.
Why not go to 1/2 or full kelly instead? Whats the difference?(as opposed to est edge at higher#)
The idea of "leaving money on the table" is a bunch of crap.
There's really no difference...two different ways to do the same thing is all- raise bet sizes.
I just pulled up this thread to find the link to the kelly calculator and noticed something...if I have multiple bets in the same day my bet size actually should be smaller than full kelly? This doesn't make sense to me intuitively...can anyone explain this mathematically or otherwise? Thanks.
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