Kelly-Criterion weenies...can you chek this out?

[fitguy67]

this is from Dr. Bob's excellent site: http://www.drbobsports.com/essays.cfm?p=16

(this is one of an integrated set of really well-presented articles on fundamental topics...check them all out by clicking "essays" at the top of the linked page)

Anyhow here's what's been driving me nuts for the last hour:

-->Marquette has been given a 2% chance to win (paying out 50 to 1), but you believe that their true chance is 3%.
-->North Carolina has been given an 28% chance to win an NCAA Basketball National Title (paying out 3.57 to 1), but you believe that their true chance is 35%.

Which of these is a more attractive bet?

yada yada yada... then...

If we do a Kelly calculation, we find that we should optimally wager (50*.03-.97)/50 = 1.06% of our bankroll on Marquette. We should optimally wager (3.57*.35-.65)/3.57 = 16.79% of our bankroll on UNC.

I have done and re-done this particular example repeatedly (using my approach, which i long ago determined was equivalent mathematically to the standard "formula", but much more intuitively satisfying)...and would swear that both of these answers are incorrect...but this article has been posted on this site for years. I agree with the Kelly bet-sizes calculated in every other example in the other articles in this set, just not this one.

I think it should be "to risk 1.02% of our bankroll (to win our expected value of 50%=(3%/2%)-1 of the roll at odds of +4900 or 50.00...by my logic) on Marquette...and to risk 9.72% (to win our expected value of 25%=(35%/28%)-1 at odds of +257 or 3.57...by my reasoning) on UNC".

Either there's a "fossilized" error in the logic i've always employed to do these calculations exposed by this particular example...or a rather blatant error in this article on a prominent site.

If I am wrong, and the article's correct...i'll have to go back to the drawing board on something i long ago decided was fine.

[Nick Papageorgio]

He is gunshards father .

[TheCentaur]

this is from Dr. Bob's excellent site: http://www.drbobsports.com/essays.cfm?p=16

(this is one of an integrated set of really well-presented articles on fundamental topics...check them all out by clicking "essays" at the top of the linked page)

Anyhow here's what's been driving me nuts for the last hour:

-->Marquette has been given a 2% chance to win (paying out 50 to 1), but you believe that their true chance is 3%.
-->North Carolina has been given an 28% chance to win an NCAA Basketball National Title (paying out 3.57 to 1), but you believe that their true chance is 35%.

Which of these is a more attractive bet?

yada yada yada... then...

If we do a Kelly calculation, we find that we should optimally wager (50*.03-.97)/50 = 1.06% of our bankroll on Marquette. We should optimally wager (3.57*.35-.65)/3.57 = 16.79% of our bankroll on UNC.

I have done and re-done this particular example repeatedly (using my approach, which i long ago determined was equivalent mathematically to the standard "formula", but much more intuitively satisfying)...and would swear that both of these answers are incorrect...but this article has been posted on this site for years. I agree with the Kelly bet-sizes calculated in every other example in the other articles in this set, just not this one.

I think it should be "to risk 1.02% of our bankroll (to win our expected value of 50%=(3%/2%)-1 of the roll at odds of +4900 or 50.00...by my logic) on Marquette...and to risk 9.72% (to win our expected value of 25%=(35%/28%)-1 at odds of +257 or 3.57...by my reasoning) on UNC".

Either there's a "fossilized" error in the logic i've always employed to do these calculations exposed by this particular example...or a rather blatant error in this article on a prominent site.

If I am wrong, and the article's correct...i'll have to go back to the drawing board on something i long ago decided was fine.

So you're diversifying which makes sense.

I've never liked Kelly criterion in sports because it's a bunch of exact numbers assigned according to very inexact info. This isn't video poker or blackjack. Just because we determine through some Plinko board of factors that team x has a y % chance of winning doesn't make it so. I would rather trust my overall ability and keep the betting units stable, increasing the unit size at a set time increment of a year.

[Smoke]

The article is correct

Go back to the drawing board

[fitguy67]

hmmm...this is the very first time I've seen that the Kelly Bet proposed does not aim at winning the expected value of the bet...
...so i just went to a Kelly-Bet calculator (Proline Tools)...and entered the NC example...to confirm that i might have had it wrong all this time
__________________

...entered the following

win/loss probabilities: 35 in 100

payout odds: 100 to win 257.14 (equivalent to implicit break-even odds of 28% as stated in the example=3.5714 decimal)

player's bankroll: 10,000
____________

then i hit "calculate", fully expecting to see the $1,679 that would agree with the article (and Smoke)...

instead I see:

Kelly%9.72

Kelly Bet $972

...seems a popular Kelly-calculator has to come along with me to the drawing board
____________

I'm going to look for another calculator to verify what I thought was not only an easier way to figure out a kelly bet...but also an easy way to check them as well...namely that

a full-Kelly bet is the one that aims to win a % of the bankroll exactly equal to the perceived edge
(the "formula" is just a systematic way of figuring the risk-amount of that bet out...but applying it without checking the result for this characteristic...is not a good idea, as we see in this example it would result in a large overbet on a long-odds play)

risking 1679 at book odds with implied 28% probability (ie. +257.14) aims at winning 4,317...far more than the 25% edge that the capper perceives)...

the 972 that i put out there hits it bang on....it's the amount you'd risk to win the full-amount of the perceived 25% edge, 2,500
________
I just whacked the same NC example into another online Kelly calculator (Bettify Tools)...it RE-confirmed my suspicion that this article did indeed have the wrong results,apparently for a long time (but it's still a damn good article...all of them on that site are worth a good look)...and that proposed full-kelly bets should always be checked to make sure they target the same % as the edge you perceive

[durito]

You are right.

He has made a mistake converting % to us odds. 28% = +257 as you said, but he is using +357

[mathdotcom]

Tout loser

[MonkeyF0cker]

So you're diversifying which makes sense.

I've never liked Kelly criterion in sports because it's a bunch of exact numbers assigned according to very inexact info. This isn't video poker or blackjack. Just because we determine through some Plinko board of factors that team x has a y % chance of winning doesn't make it so. I would rather trust my overall ability and keep the betting units stable, increasing the unit size at a set time increment of a year.

http://forum.sbrforum.com/handicapper-think-tank/1571755-estimated-edge-error-simulation-kelly-conundrum.html

[cyberbabble]

Conventional wisdom seems to be that sports bettors wanting to use Kelly end up using fractional Kelly betting.
Do you think this is true?
If so, why. They can't handle the frequent big swings in bankroll?

[MonkeyF0cker]

Conventional wisdom seems to be that sports bettors wanting to use Kelly end up using fractional Kelly betting.
Do you think this is true?
If so, why. They can't handle the frequent big swings in bankroll?

http://forum.sbrforum.com/handicapper-think-tank/1571755-estimated-edge-error-simulation-kelly-conundrum.html

Run sims. Find out for yourself.

[thom321]

or take a look at the results I got from running some sims with an adjusted version of Monkey's simulator.

http://forum.sbrforum.com/handicapper-think-tank/1571755-estimated-edge-error-simulation-kelly-conundrum-p2.html#post13827307

[mathdotcom]

Boring

Half you Kelly master debaters can't find EV so it is moot, let alone EV in markets with long odds where it actually matters

For spread and totals bettors you can figure it out on the fly

[cyberbabble]

I'll accept that, in some sense, Kelly is the best bet sizing method.

As general rule, if one wants to be successful in a given endeavor, one should learn about what the successful people do. This doesn't mean blindly trying to copy what the other person does. It means trying to understand what the successful person does. Then decide whether to try to copy what the successful person does.

In your experience/opinion do successful sports bettors use full Kelly?

[fitguy67]

only the boring get bored

[fitguy67]

I'll accept that, in some sense, Kelly is the best bet sizing method.

As general rule, if one wants to be successful in a given endeavor, one should learn about what the successful people do. This doesn't mean blindly trying to copy what the other person does. It means trying to understand what the successful person does. Then decide whether to try to copy what the successful person does.

Many successful bettors take Kelly into strong account...but no-one that wants to survive uses FULL kelly cuz the risk of ruin is too high...divide the full-Kelly bet by anywhere from 2 (still very aggressive=unnervingly hi-probability of crashing account before doubling it) to 8 (very conservative=negligible probability of crashing before doubling account)

In your experience/opinion do successful sports bettors use full Kelly?

Many successful investors/traders/bettors take Kelly into strong account...but no-one that wants to survive uses FULL kelly cuz the risk of ruin is too high...divide the full-Kelly bet by anywhere from 2 (still very aggressive=with a still-unnervingly hi-probability of crashing an account before doubling it) to 8 (very conservative=negligible probability of crashing before doubling account)....1/3, 1/4, and 1/5 kelly are the most commonly-employed levels used in the financial world (including seriously-managed sports-betting operations)

[mathdotcom]

I see

Take the result from a maximization problem (BR growth), a mathematically rigorous result, and then divide it by an arbitrary number.

Rigorous + Arbitrary = Arbitrary

[mathdotcom]

Reminds me of Justin7's use of 'FUDGE FACTORS' in his book

It's the classic move of squares trying to masquerade as sharp

[GunShard]

He is gunshards father .

Nope. More like Justin7's father.

[MonkeyF0cker]

I see

Take the result from a maximization problem (BR growth), a mathematically rigorous result, and then divide it by an arbitrary number.

Rigorous + Arbitrary = Arbitrary

One could look at fractional Kelly as an arbitrary number, but that's not accurate in all cases.

It can and should be considered in a utility function of risk aversion.

[mathdotcom]

Arbitrary in the sense of post #15 in the thread. In his case Kelly is only providing an upper bound and he is arbitrarily choosing to bet somewhere below what Kelly recommends. Give me a utility function and I'll give you a precise Kelly fraction, but I don't see how coming up with your utility function can't be arbitrary. Not to mention that people define their BRs differently. So again Kelly amounts to simply telling you "don't bet more than this".

Other reasons:
- precisely calculating Kelly during 2H is a waste of time (again, just use it as a guide to see around where you should be betting, and bet more on games with higher EV). Decide before hand what you'll bet on games with an x edge, x+1 edge, x+2 edge, etc.
- for derivative markets, you're probably constrained by the book limit than Kelly.
- Kelly staking is well above what you're comfortable with for sanity reasons.

This is why I've always argued that Kelly is wildly overrated as an important gambling principle, and all too often discussed by people who clearly have no edge (If you start a thread titled "Flat betting is better than any form of Kelly", then you fall in this category). The main exception to me is when you have a large set N of low probability parlayable games which you could theoretically risk hundreds of thousands on. In this case you might not have a good intuitive feel for whether you should be betting $5 or $500.

DrBob is a prime example of someone stroking himself with Kelly even though his EV seems to be quickly declining from miniscule to 0.

[MonkeyF0cker]

Arbitrary in the sense of post #15 in the thread. In his case Kelly is only providing an upper bound and he is arbitrarily choosing to bet somewhere below what Kelly recommends. Give me a utility function and I'll give you a precise Kelly fraction, but I don't see how coming up with your utility function can't be arbitrary. Not to mention that people define their BRs differently. So again Kelly amounts to simply telling you "don't bet more than this".

Other reasons:
- precisely calculating Kelly during 2H is a waste of time (again, just use it as a guide to see around where you should be betting, and bet more on games with higher EV). Decide before hand what you'll bet on games with an x edge, x+1 edge, x+2 edge, etc.
- for derivative markets, you're probably constrained by the book limit than Kelly.
- Kelly staking is well above what you're comfortable with for sanity reasons.

This is why I've always argued that Kelly is wildly overrated as an important gambling principle, and all too often discussed by people who clearly have no edge (If you start a thread titled "Flat betting is better than any form of Kelly", then you fall in this category). The main exception to me is when you have a large set N of low probability parlayable games which you could theoretically risk hundreds of thousands on. In this case you might not have a good intuitive feel for whether you should be betting $5 or $500.

DrBob is a prime example of someone stroking himself with Kelly even though his EV seems to be quickly declining from miniscule to 0.

Ahh. But you're proposing an arbitrary solution as well.

As far as utility, when I first started I was willing to be fairly aggressive. As my bankroll has grown, I've become more conservative and subsequently the Kelly fraction that I use has changed. I don't think there's anything wrong with ensuring that you're betting a Kelly amount correlational to edge and risk aversion. As far as time goes, unless you're basing your EV off of eyeballing the market, it would be a trivial step to include a calculation for any type of Kelly wager and would take less than a nanosecond longer than merely evaluating your EV.

Incorporating Kelly staking in any fraction will not make you rich alone. However, the concept that bets should be scaled according to edge and the gain in EG for doing so is important for bettors to understand.

[fitguy67]

the kelly divisor is to the kelly%...

what z-score is to standard deviation..

in either case, far from arbitrary...select a different value...and specific frequency/probability implications are locked in (in fact, in each case, you can read them right off STANDARD tables or graphs or find them embedded in your software)

choosing how much to dilute your full-kelly% to match your risk/reward situation is entirely akin to a medical school deciding at what percentile (based directly on z-score) to "draw the line" on intake quality...

in either case, choice (aka. careful selection) is involved...but the mathematical/probability implications of each and every value are crystal clear...and far far from arbitrary

[mathdotcom]

Ahh. But you're proposing an arbitrary solution as well.

Exactly the point sir! Making the argument that Kelly in practice is often arbitrary so may as well admit it and just be arbitrary.

If you have a 500K BR and you've just created an NBA spread model, what exactly is your BR? Are you willing to state it as 500K and potentially go down with the ship? I think defining your BR once you have a significant one is the most arbitrary part of Kelly. For this question I would say somewhere between 50K and 100K. For a tried and true model earning consistent returns year after year I probably still wouldn't define my BR as any more than 300K.

I believe Stanford Wong said your definition of BR should be 'the amount lost that would cause you to stop betting', and I agree.

As for your change in aggression, it is probably because when you started with a smaller BR you went after low hanging fruit with high EV. As it grows you have to settle for lower EV in exchange for more volume, which increases risk substantially. More $$ at stake and less certain edge.

[MonkeyF0cker]

Exactly the point sir! Making the argument that Kelly in practice is often arbitrary so may as well admit it and just be arbitrary.

If you have a 500K BR and you've just created an NBA spread model, what exactly is your BR? Are you willing to state it as 500K and potentially go down with the ship? I think defining your BR once you have a significant one is the most arbitrary part of Kelly. For this question I would say somewhere between 50K and 100K. For a tried and true model earning consistent returns year after year I probably still wouldn't define my BR as any more than 300K.

I believe Stanford Wong said your definition of BR should be 'the amount lost that would cause you to stop betting', and I agree.

As for your change in aggression, it is probably because when you started with a smaller BR you went after low hanging fruit with high EV. As it grows you have to settle for lower EV in exchange for more volume, which increases risk substantially. More $$ at stake and less certain edge.

That is where I would simply use a smaller Kelly multiplier with my bankroll remaining at $500k.

[milwaukee mike]

good discussion here.
more interesting than the normal babble, I would interject that gambling (whether you have to justify it with a model or not) is about finding good opportunities and having the balls to bet big on them.

people with a high intellect and a positive attitude will never need someone else's mathematical model to be successful

[mathdotcom]

That is where I would simply use a smaller Kelly multiplier with my bankroll remaining at $500k.

Is a 0.5 multiplier on a 500K BR any different than a 0.25 multiplier on a $1million BR?

[statnerds]

This is why I've always argued that Kelly is wildly overrated as an important gambling principle, and all too often discussed by people who clearly have no edge (If you start a thread titled "Flat betting is better than any form of Kelly", then you fall in this category). The main exception to me is when you have a large set N of low probability parlayable games which you could theoretically risk hundreds of thousands on. In this case you might not have a good intuitive feel for whether you should be betting $5 or $500.

DrBob is a prime example of someone stroking himself with Kelly even though his EV seems to be quickly declining from miniscule to 0.

Sometime like, sometimes no like your posts...love this one.

And I know you don't give a fukk either way, but well done sir.

[durito]

Tout loser

He didn't even write that part of his site, that loser stiff at 2p2 that interned for him did. Bob touts a ridiculous money mgmt system where your unit is constant across the whole season, which led him to wipe out 100% of anyone's bankroll who followed exactly his advice in 2007.

[GETMONEYKID]

no-one that wants to survive uses FULL kelly cuz the risk of ruin is too high

risk of ruin betting full kelly is 0%

[fitguy67]

http://www.bjmath.com/bjmath/proport/riskpaper1.pdf

Kid,
Risk of ruin does not always imply bringing the account down to absolute zero. With kelly bet-resizing and strictly sequential betting it would of course take infinity to approach zero even with 100% losing bets (assuming you could find a book to keep taking your microscopic-sized bets). So in the Kelly context the idea of "ruin" has been modified to the event of "losing a sufficiently large % the account to consider the betting project a failure". So the "risk of ruin" probabilities i refer to emerge basically as "races" to double vs. being cut in half, to triple before having account cut to a third of its initial value, etc. etc...basically to have your account hit a fraction "a" (eg. 0.33x)before hitting it's reciprocal multiple "1/a" (eg. 3x). I'm simplifying greatly but it's basically hitting a pre-defined "uncle" point.

If you are really interested in how the concept of "ruin" is modified in the Kelly context...check out page five and forward on the link above.

You'll notice that i'm assuming you're a "smart kid" who might be legitimately interested in the topic(and not just being what my dad called a "smart-assed" kid)...and am responding in a civil fashion to your "technically" correct (meaning correct if you employ the "technique" of failing to modify your definitions properly to the context of the discussion) but obviously trivial point. Considering the intellectual-weight of your point...i'll again give you the benefit of the doubt and suppose you really DID need the support of those "dancing dorks" to make it.

[GETMONEYKID]

We think of getting cut down to a fraction a as an alternate concept
of “ruin” or “unhappiness”.

This seems pretty terrible. And I get that it's a paper dedicated to risk, but where do they explain that the cost of the lower risk of ruin in fractional betting is a longer time horizon for doubling?

[fitguy67]

Kid, chek out the set of articles in the money-management section here

http://www.drbobsports.com/essays.cfm?cat=0

(they're a lot more straightforward than that risk paper)...all 7 parts won't take long to go thru...but items #3,4, and 7 seem to be most what you're after

[GETMONEYKID]

I'm not really after anything, just pointing out that the paper's missing key information one would need in order to make an intelligent decision. Explaining how to limit exposure to risk (bet less herp derp) without acknowledging the fact that this completely neuters expected growth is at best extremely negligent.

[mathdotcom]

He didn't even write that part of his site, that loser stiff at 2p2 that interned for him did. Bob touts a ridiculous money mgmt system where your unit is constant across the whole season, which led him to wipe out 100% of anyone's bankroll who followed exactly his advice in 2007.

Even worse then

[u21c3f6]

Is a 0.5 multiplier on a 500K BR any different than a 0.25 multiplier on a $1million BR?

Not for the first wager. However, as the number of wagers increase, the smaller bankroll will eventually surpass the larger bankroll.

Joe.