1. #1
    Ganchrow
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    Correlated Parlays

    In another thread I noted that a player who is able to consistently pick winners with better than 52.38% frequency can increase his expected return (and assumed risk) by betting parlays. I also referred to the fact that even a player who is unable to pick winners at better than 52.38% could theoretically increase his expected return by betting correlated parlays.

    Now before you coin-flippers get your hopes up, let me state that in practice you probably canít expect to find any correlations sufficiently strong so as to overcome the inherent disadvantage of blindly betting parlays. In fact, in the situations where the strongest correlations do exist, most books wonít even allow you to parlay such bets. Nevertheless, understanding the value of parlaying even slightly correlated bets can be instructive.

    One might well ask just what exactly correlation is. Well, Webster defines it as, ďa relation existing between phenomena which tend to vary, be associated, or occur together in a way not expected on the basis of chance alone.Ē In other words, two events are correlated if when one event occurs, the other event is more likely to occur. For example thereís a correlation between smoking and lung cancer.

    One rather silly example of correlation exists when flipping a coin. One can say that a coin landing heads is positively correlated with tails being on the bottom side of the coin. There is positive correlation because when one event occurs (the coin landing heads) the other event (tails on the bottom) is more likely to occur than usual (negative correlation would mean less likely than usual -- the usual being 50%). Because when the coin lands heads thereís actually a 100% chance (neglecting the possibility of a phony coin) that the bottom side is tails, this is known as perfect correlation. Of course this is silly because as we all know that heads and tails are just different sides of the same coin and so by course one must always imply the other. Still this is illustrative of a degenerate case of correlation.

    So letís look at the math behind parlaying two bets with perfect correlation at 13/5 versus betting each one straight at -110. Well, if we bet each bet straight at -110, then we know that our expected return is -4.545%. However, due to the perfect positive correlation we know that with 50% likelihood weíll win both bets and with 50% likelihood weíll lose both bets. Therefore, if we parlay the two then our expected return:
    Code:
    = 50% x 13/5 + 50% x -1
    = 80%
    Now admittedly, this is the most extreme possible example of a correlated 2-team parlay and of course one would never find a book willing to allow the parlay of two perfectly correlated events (for instance one could never parlay Team A winning and Team Aís opponent losing). However, I hope that this simple example shows that with a correlated parlay itís possible to turn two negative expectation bets into one positive expectation bet.

    So letís step it up a bit and look at a (very) slightly more realistic example of a pair of correlated bets. Imagine a hypothetical college football game between a very strong team and a very weak team. Letís say that the very strong team is favored by 41 Ĺ points and the total is 45 Ĺ points. Now itís my claim that a correlation exists between the very strong team covering and the total going over. This is because for the strong team to cover we know that at least 42 points must be scored and if that occurs then anything more than a field goal past that and the total will go over as well. Hence, thereís a very small range of possible scores where the strong team can cover AND the under can hit (only 42-0, 43-0, 44-0, 45-0, 42-2, 43-2, or 42-3). Now note, that while the chance of the strong team covering is only 50% and the chance of hitting the over is also only 50%, the chance of hitting the over given that the strong team has covered is almost certainly considerably higher than 50%. Hence, this situation would be likely to present a profitable opportunity.

    Now a total of 45 Ĺ and side of 41 Ĺ clearly present a highly unrealistic circumstance to say the least, but nevertheless for the same reasons such a correlation also holds in more typical situations (although to a lesser extent). Ceteris paribus, when dealing with spreads one can expect some degree of correlation between the favorite covering and the total going over and also between the dog covering and the total going under.

    Because the spreads are typically such a large percentage of the total, this is especially true with hockey puck lines and baseball run lines. While itís typically difficult to find a book which will allow you to parlay run/puck lines with totals (and of course no book would let you parlay a run/puck line with a money line Ė the correlation on that would simply be way too high), such books nevertheless do exist.

    One other structural example of correlation exists in baseball between the money line and the total. Because if the home team is winning after 8 Ĺ innings the game ends, there is less of an opportunity for the game to go over. Hence, there tends to be a correlation between the home team covering and the under and conversely between the away team covering and the over. This correlation is not very large (batting in the bottom of the ninth tends to add less than ľ of a run on average), but it is nevertheless undeniably present and the parlay opportunity is readily available at most books. Now this doesnít mean that one should go out and blindly bet this, but if an advantaged bettor tends to like the over and the away team anyway (or the under and the home team) a parlay can make these bets extra attractive.

    Thereís one last example of correlation Iíd like to briefly mention. Successfully handicapping a game is typically about making predictions as to how each team is likely to perform. Now if one is able to isolate those factors that are most likely to affect the outcome and use the exact same set of predictions about those exact same factors to predict the winner ATS and the total, then one is likely to have a correlation. This is true insofar as if that prediction set turns out accurately, both bets become more likely to win. For example, letís assume that one feels a particular quarterback to be vastly overrated and letís further assume that one believes this is by far the most important factor in determining both the total and the winner ATS. Now if this prediction turn out to be true, then itís more likely that the game will go under (less production than expected by the odds makers from the quarterback) and also that the team with the underrated quarterback will lose (again less production from the quarterback than expected). In other words a correlation exists.

    Now this isnít to say that one can take any harebrained set of predictions one likes and use them to impute correlation, but if one often find that when oneís predictions prove true both the total and the spread (or the total and the money line) tend to win, then it certainly may make sense to explore using parlays to leverage larger returns in these types of situations.

    In short, betting a correlated parlay consisting of two events of given likelihood clearly gives one an advantage over betting an uncorrelated parlay consisting of two events of similar likelihood. Correlation, however, is not a panacea. This is to no small extent due to the fact that the most highly correlated events are simply not parlayable. Hence, its not recommended for an unadvantaged player to seek correlated bets to parlay. Even with the correlation heís not likely to decrease his disadvantage to even the level of a straight bet (although his disadvantage would certainly be less than for an uncorrelated parlay). That being said, if an advantaged bettor tends to like two slightly correlated bets anyway, then thereís even more reason to parlay them than if the bets were independent. The added risk is of course always a factor with parlays, but the additional expected return of a correlated parlay might just be enough to change the mind of the advantaged bettor who avoids parlays from a risk managment perspective.

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  2. #2
    pags11
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    unbelievable knowledge here...

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  3. #3
    raiders72001
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  4. #4
    rm18
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    good info, but do you actually know places that let you parlay LSU and the over?

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  5. #5
    raiders72001
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    There are books that allow this type of parlay. They may not on this LSU game but they have been for some of the Tex and USC games. Don't take this the wrong way but I don't want to reveal which books do this.

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  6. #6
    JoshW
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    Good stuff Ganchrow, enjoyed reading.

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  7. #7
    Max Levine
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    Excellent article, Ganchrow.

    Not sure what the odds are on correlated parlays in hockey. I tried it once, expecting a lot of goals from one side. Got the run line but lost the Over as all the scoring came from one team. Wouldn't you say the odds are better in football?

    Max

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  8. #8
    Ganchrow
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    Quote Originally Posted by Max Levine
    Not sure what the odds are on correlated parlays in hockey. I tried it once, expecting a lot of goals from one side. Got the run line but lost the Over as all the scoring came from one team. Wouldn't you say the odds are better in football?
    Fiirstly, let me state that I personally bet neither hockey nor football, I have never myself embarked on a statistical study of either hockey or football correlations. Hence, I'm only speaking based on second hand knowledge when I claim that the general consensus seems to be that hockey pl - total correlations are greater than most (bettable) football spread - total correlations. Now this certainly makes logical sense. The greater the percentage of the total that the spread is, the closer you'd find yourself to going over if the favorite covers.

    Also note that the higer the money adjustment factor for the favorite, the lower the correlation. In other words, given a total of 6.5 -110, then ceteris paribus you'd expect greater correlation between that and a puck line of -1.5 -110 then with that and a puck line of -1.5 -260.

    Finally, remember that just because two events are positively correlated, doesn't mean that they will always occur together. We're still talking about statistical phenomena here. If you're correct in your belief that one team is likely to score appreciablely more than expected, then correlation almost certainly does exist the over and the favorite puck line (and to a lesser extent in this case even over and the favorite money line). Will the correlation payoff every time? No, certainly not. But if you already have an advantage on both bets, and you can stomach the added risk, the correlation will over the long term make the parlay even more attractive than the component straight bets.

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  9. #9
    Dimaliciousss
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    Hey, let me start off by saying that this is a great post. I am a bookie in Brooklyn and I have an oversees website that I use for my customers. Now this service that I use to run my book had no idea about the fact that you are not allowed to parlay puck lines with totals in hockey. I feel very stupid saying this but neither did I. I had one customer that was winning for 2 months straight. He would bet the underdog + 1 1/2 and under. He would bet about 2000 a game and win somewhere around 2300 because the puck line would usually make the line about - 280 or so. Anyways, can you guys give me a little more detail about how exactly you know, which games would be correlated and which to stay away from. I know alot of local bookies who would allow this sort of action.

  10. #10
    Bluehorseshoe
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    Quote Originally Posted by Dimaliciousss View Post
    Hey, let me start off by saying that this is a great post. I am a bookie in Brooklyn and I have an oversees website that I use for my customers. Now this service that I use to run my book had no idea about the fact that you are not allowed to parlay puck lines with totals in hockey. I feel very stupid saying this but neither did I. I had one customer that was winning for 2 months straight. He would bet the underdog + 1 1/2 and under. He would bet about 2000 a game and win somewhere around 2300 because the puck line would usually make the line about - 280 or so. Anyways, can you guys give me a little more detail about how exactly you know, which games would be correlated and which to stay away from. I know alot of local bookies who would allow this sort of action.

    I have the same office.

    I never knew "WHEN" to the play the correlation either.

  11. #11
    RickySteve
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    Lowlife Bookie Seeks Expert Unpaid Consultants

    Must love dogs and long walks on the beach. N/S, D/D-free. BBW a plus.

  12. #12
    Wheell
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    Dimaliciousss: Short form: +1.5 and under 3.5, 5.5, or 7.5 is natually correlated (same with 9.5, and 11.5). Of course +1.5 and under 4 or under 6 isn't shabby, but the math is even more in your favor when you have a whole number for the dog to score that guarantees correlation. With an ou of 5.5 if the dog scores 2 correlation is guaranteed.

  13. #13
    RickySteve
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    Quote Originally Posted by Wheell View Post
    Dimaliciousss: Short form: +1.5 and under 3.5, 5.5, or 7.5 is natually correlated (same with 9.5, and 11.5). Of course +1.5 and under 4 or under 6 isn't shabby, but the math is even more in your favor when you have a whole number for the dog to score that guarantees correlation. With an ou of 5.5 if the dog scores 2 correlation is guaranteed.
    <>

    They must be here somewhere...

  14. #14
    raiders72002
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    RickySteve proves again why he's the asshole of SBR.

  15. #15
    RickySteve
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    Language please.

  16. #16
    tacomax
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    Quote Originally Posted by raiders72002 View Post
    RickySteve proves again why he's the asshole of SBR.
    Nope, the title is still yours.

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  17. #17
    Dimaliciousss
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    ??

    Quote Originally Posted by Wheell View Post
    Dimaliciousss: Short form: +1.5 and under 3.5, 5.5, or 7.5 is natually correlated (same with 9.5, and 11.5). Of course +1.5 and under 4 or under 6 isn't shabby, but the math is even more in your favor when you have a whole number for the dog to score that guarantees correlation. With an ou of 5.5 if the dog scores 2 correlation is guaranteed.
    Thank you for trying to explain to me. I am having a difficult time understanding though, I am a novice. Can you be clear on what you mean by 9.5 and 11.5, and what do you mean by "when you have a whole number for the dog" because all i ever see is 1 1/2 puck line i never seen a whole number.

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