1. #1
    Bsims
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    My experience using the Kelly criteria

    In 2012 I was between major health problems and had the opportunity to use the Kelly criteria to size my wagers for an entire MLB season. One of the major techniques I used was simulation. I would simulate each game one batter at a time to get a final score. Then I repeated this 5000 times to get the probability of each team winning. I used this probability, the game odds, and the Kelly formula to size my wager.

    I ran simulations early in the morning using typical lineups and made wagers. Later when I had the actual lineups I repeated the simulations and wagers. Following is a table of my actual results. Also included are the results if I had made $100 unit wagers on those games ($100 bet on dogs and to win $100 on favorites).

    Morning Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 999 $104,344 -$1,440 0.986 $104.45
    Kelly 999 $94,800 $27 1.000 $94.90
    Actual LU Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 1097 $117,062 $2,005 1.017 $106.71
    Kelly 1097 $154,734 -$752 0.995 $141.05

    The morning wagers performed poorly, dropping $1,440 on unit wagers. But actually using Kelly they showed a $27 profit. Note that Kelly resulted in smaller wagers.

    The wagers based on actual lineups lost $752 using Kelly, but would have won $2,005 on unit wagers. Here the average Kelly wager was $141 versus $107 on unit wagers.

    Combined I actually lost $725 using Kelly, but would have made $565 on flat unit bets. I also would have bet less. My return per dollar bet was $0.995 with Kelly and would have been $1.017 on flat bets. In other words, using Kelly turned a winning season into a losing season.

    I wondered about this, and ultimately figured it out. I had averaged larger wagers on losing bets with Kelly than on winning bets. That makes sense. With Kelly your bets increase when you win and decrease when you lose. (If you are familiar with dollar cost averaging in investing, Kelly produces a kind of dollar cost averaging in reverse.)
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  2. #2
    Bsims
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    There's more to the story from 2012, parlays (I know some say parlays are for suckers). But in 2012, Kelly parlays showed a profit of $11,618 for me and flat wagers would have returned $9,292. Clearly Kelly was a good choice, but it was mainly due to larger average bets, $120 to $100. Here is the table and the total for all 3 types of bets.

    Parlays Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 984 $98,400 $9,292 1.094 $100.00
    Kelly 984 $118,909 $11,618 1.098 $120.84
    Total Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 3080 $319,806 $9,857 1.031 $103.83
    Kelly 3080 $368,443 $10,894 1.030 $119.62
    For the season, Kelly or not was pretty much of a toss up. I'll look at 2013 tomorrow.

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  3. #3
    evo34
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    I may have misunderstood the end of your post, but unless your bets are somehow negatively correlated, Kelly should not make you bet larger on losing bets. I.e., your current bet doesn't know whether you just won 10 out of 12 or lost 10 out of 12.

  4. #4
    KVB
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    Eventually, that will happen with Kelly betting.

    Whether it's a specific streak or a more general one over time, winning will lead to larger bets for the eventual losing play and losing will lead to smaller bet sizing for the eventual winning play. Unless somehow the better can avoid that common, natural win loss variance.

    Kelly is dangerous this way and these examples can help illustrate one of the problems with Kelly betting in the sports markets. That is that changing your bet size changes your break even point.

    Kelly is essentially a progressive betting system in which you bet more right away simply because you've won more or perceive a noticeably increased edge on a bet, or vice versa.

    I'm not trying to argue for or against Kelly but it does point out on of the hidden pitfalls that many bettors will miss.

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  5. #5
    gdon44
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    Kelly gives you a percentage of your bankroll to bet. So when you win the bankroll goes up hence the higher bet you play for future bets in this case. But what if you didn't adjust your bankroll after every bet? I think keeping your bankroll (or whatever term you want to call it) the same for a week or even a month takes away that variance and the appearance of a progressive betting system that you discovered. You are then not betting higher amounts the more you win.

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  6. #6
    evo34
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    The bottom line is that Kelly is only optimal if your bankroll is truly finite and if you know your precise edge. And no one knows his precise edge in sports betting.

  7. #7
    Bsims
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    Very good points gentlemen. KVB provided an excellent explanation of the pitfalls of Kelly in sports betting. evo34 is correct, Kelly does have a good place if your bankroll is finite. It puts a money management discipline on your wagers that is sadly lacking in most of us. gdon44 has an excellent suggestion. One could use Kelly only to size bets relative to one another by fixing the balance at the beginning of the season and not move it.

    Fortunately with my record keeping I'll be able to simulate doing precisely this in the 2012 and 2013 season. By the way, when I post the 2013 season you'll see what a terrible season looks like.

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  8. #8
    rkelly110
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    Glad you made it through your health problems, Bsims.

    This Kelly criteria is to bet the ML fav of the day with a min of -222 and lower odds. I use decimal odds to pinpoint the true fav.

    Using 2% of your roll. Increasing only after losing 3 in a row. (conservative)

    Have records of over 5 years in each sport (except soccer) and consistently hit over 60% except the NFL.


    You will have people say you can't win with those low odds, but my record keeping (profit) says otherwise.
    You could use the ML fav of the day to bet on RL's or ATS for better odds and more profit if you choose.
    Win % won't be as good.

    It works for me, but might not for someone else. GL (4-0 in MLB play offs so far)

  9. #9
    Bsims
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    Following is the table of results for MLB in 2013, a terrible season all around. The first thing to notice is that the simulations, both morning and actual lineups were terrible. Kelly lost a lot less than the flat unit bets, but that was primarily because the average bet size plummeted during this losing season. The average return per dollars was slightly higher for the unit bets than the Kelly one. By the way, this is an excellent example of the points made above. Evo34ís point about its place for those with a finite bankroll. Kelly kept it from totally disappearing and would allow one to wager all season.


    Morning Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 732 $80,982 -$3,445 0.957 $110.63
    Kelly 732 $12,971 -$725 0.944 $17.72
    Actual LU Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 841 $73,511 -$3,573 0.951 $87.41
    Kelly 841 $11,818 -$786 0.933 $14.05
    Parlays Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 936 $93,600 $1,693 1.018 $100.00
    Kelly 936 $152,673 $116 1.001 $163.11
    Total Bets Amt Bet Net Ret/$ Avg Bet
    Flat $100 2509 $248,093 -$5,325 0.979 $98.88
    Kelly 2509 $177,462 -$1,395 0.992 $70.73

    The parlays had a difficult year also, but did show a profit. Again, the flat wagers performed much better than the Kelly ones. They had a larger positive net on a smaller average bet. For the combination, Kelly had a smaller loss because of the smaller bet sizes. They did have a higher return per dollar because of higher wagers on the profitable parlays and significantly lower ones on the poorly performing simulations. In a sense, Kelly was worthwhile for me since that Is what I used.

    Iím not sure what I would have done in 2014 had not a second medical disastor in five years occurred in January 2014. I spent most of 2014 and 2015 in hospitals and laid up at home. Next step is to analyze gdon44ís suggestion.

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  10. #10
    Bsims
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    I've implemented gdon44's suggestion of using the Kelly formula to size the bets, but not change the Kelly balance. I applied this to the 3 types of wagers over both seasons. I've produced a chart with the results. The value I'm reporting is the return per dollar to eliminate bet size as a factor.

    Type Season Unit Kelly Flat Kelly
    Morning 2012 $0.986 $1.000 $0.977
    Actual LU 2012 $1.017 $0.995 $1.013
    Parlays 2012 $1.094 $1.098 $1.098
    Total 2012 $1.031 $1.030 $1.018
    Morning 2013 $0.957 $0.944 $0.974
    Actual LU 2013 $0.951 $0.933 $0.963
    Parlays 2013 $1.018 $1.001 $1.017
    Total 2013 $0.979 $0.992 $0.978

    Nothing jumps out as clearly being a better or worse choice. I'll probably do a similar analysis on the 2017 season over the winter.

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  11. #11
    evo34
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    Quote Originally Posted by rkelly110 View Post
    Glad you made it through your health problems, Bsims.

    This Kelly criteria is to bet the ML fav of the day with a min of -222 and lower odds. I use decimal odds to pinpoint the true fav.

    Using 2% of your roll. Increasing only after losing 3 in a row. (conservative)

    Have records of over 5 years in each sport (except soccer) and consistently hit over 60% except the NFL.


    You will have people say you can't win with those low odds, but my record keeping (profit) says otherwise.
    You could use the ML fav of the day to bet on RL's or ATS for better odds and more profit if you choose.
    Win % won't be as good.

    It works for me, but might not for someone else. GL (4-0 in MLB play offs so far)
    Sign up at pickmonitor.com and let us know how it goes.

  12. #12
    rkelly110
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    Quote Originally Posted by evo34 View Post
    Sign up at pickmonitor.com and let us know how it goes.
    Not a tout.

  13. #13
    HeeeHAWWWW
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    OP: Do you have a log of your estimated edges for those matches? If so, try comparing with flat RoI - the reason is that Kelly kills you if you over-stake.

  14. #14
    Miz
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    nice post. thanks for sharing. I used kelly successfully for several seasons and then out of the blue had a below average season hitting 54.4% (into opening lines) and actually lost money. It just worked out that on days with fewer simultaneous events and thus larger wagers, i did worse. Just bad luck really, or variance or whatever you want to call it. The year previous to it I strongly suspect I was overbetting slightly, and variance was on my side creating unrealistically large profits. It is important to keep the variance in perspective and to not be too alarmed if you have a strong win pct and kelly underperforms what flat betting would've been. In the end, you can only estimate your edge. People like to feel safe, and so flat betting appeals to them in that regard. I use a 2/3 kelly now. It just depends on your comfort level really. This whole game is an estimate.

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