1. #1
    Ganchrow
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    An introduction to betting lines and percentages

    (I realize that this is going to be very basic for many readers, but the idea is to start off slowly.)

    Key to quantitatively analyzing a set of betting lines is determining the win probability implied by those lines. This is a simple task to accomplish mathematically but understanding the underlying concepts behind it can be quite valuable.

    If a money line is offered at -200, then this of course means that for every $200 risked $300 is returned to the bettor if the wager is successful. In other words the amount risked is 2/3 of the total amount returned. Not at all coincidentally, 2/3 is also the implied probability of the -200 line. (By “implied probability” we’re referring to the frequency with which the wager would need to win for the profit/loss expectation to be zero.)

    Using the same logic, were a line offered at -110 then for every $110 risked, $210 would be returned. $110 is 52.38% of $210, meaning that the implied probability of a -110 line is 52.38%. As such, if your bets at -110 win with frequency greater than 52.38% you’ll be making money, and conversely if your bets at -110 win less 52.38% of the time you’ll be losing money.

    So in general, for a favorite offered at a line of F (F < -100), the implied probability of a win is given by -F/(100-F). (This is just the ratio of dollar value risked to dollar value returned. Remember that F is a negative number.)

    The thought process is exactly the same for dogs. A dog offered at +200 corresponds to $300 being returned for every $100 risked, meaning that the dog’s implied probability is just $100/$300 = 1/3.

    So in general, for a dog offered at line of D (D > +100), the implied probability of a win is given by 100/(100+D). (Once again -- the ratio of dollar value risked to dollar value returned.)

    So up until now we’ve strictly been dealing with the zero-vig case, where (in the two-outcome scenario) a dog is offered at the negative of where the corresponding favorite is offered. Unfortunately, unless you’re either betting with friends or a “crossed-market” situation exists across multiple sportsbooks (or, I suppose, you’re still insane enough to play at No-Juice Sportsbook), this is an uncommon occurrence.

    Actually, given a line set there isn’t really a way to determine a single implied probability on the outcome of the event. This is because there’s no way that both sides of a vigged bet can simultaneously be zero expectation (the vig has to come from somewhere). Therefore, to come up with meaningful results one typically makes the assumption that a player’s expected losses from betting on either side of the event are equivalent. (To be sure this can at times be a rather specious assumption. One might well argue that in most sports one could comfortably expect the loss on favorites to be significantly greater than the loss on dogs. Of course this is an issue of preferences rather than of probability theory, and were bettors’ preferences ever to shift towards underdogs, one would have to draw different conclusions.)

    So let’s look at a line set of -120/+100. From the equations above we see that the zero-vig implied probability of the -120 line is just 120/(100+120) ≈ 54.55% and that the implied probability of the zero-vig +100 line is 100/(100+100) = 50%. Each of these individually represent what would be the implied probability were the line offered without vig. Because we’re assuming an equal expectation on both sides, we know that the relative probability levels are going to remain constant. The total of the zero vig lines, 54.55%+50% equals 104.55% and so we divide each zero-vig line by 104.55% to give us the appropriate implied probability of either side of the composite line set:

    Favorite probability = 54.55%/104.55% ≈ 52.17%
    Dog probability = 50%/104.55% ≈ 47.83%

    And of course, almost as if by magic, 52.17% + 47.83% = 100% total probability.

    So in general, to determine the implied probability of a two-outcome line set, one first determines the zero-vig implied probability of each line:

    Code:
    Favorite zero-vig implied probability
    = P(f) = -F/(100-F)
    
    Dog zero-vig implied probability
    = P(d) = 100/(100+D)
    And then divides each probability by the total of the probabilities to determine the proper line set probability:

    Code:
    Line set favorite probability
          P(f)
    = -----------
       P(f)+P(d)
    
    Line set dog probability
         P(d)
    = -----------
       P(f)+P(d)
    It's probably a good idea to note that this is NOT the same as just taking the implied probability of the average of the two absolute values of the constituent lines. In other words, using the -120/+100 example, it's NOT correct to say that the implied line set probability is just the implied probability of -110/+110. Determining implied line set probabilities using this method will overestimate the win probability of favorites. This becomes particularly apparent in the case of large favorites.

    The same methodology can also be used when looking at multi-way propositions: Namely, determine each individual zero-vig probability, and then divide each by the total to get the implied probability for each outcome in the line set.
    Points Awarded:

    bigbank gave ganchrow 1 SBR Point(s) for this post.

    Dave Head gave ganchrow 5 SBR Point(s) for this post.

    Nomination(s):
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  2. #2
    Uncle Joe
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    Good thing you gave out the basic course and not the advanced course! Can you use a game from today maybe tonights' NBA game to show some real numbers and lines for that formula?

  3. #3
    Baphomet
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    Thx Ganchrow, very useful for me.

  4. #4
    David
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    If you only bet underdogs at a line that is better than the implied probability at Pinnacle will you be profitable long term?

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  5. #5
    SBR_John
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    Man, I'd hate to be booking Ganchrow's action!

    I'm going to need my note pad when I read his posts.

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  6. #6
    FairlySquarely
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    ganchow, why weren't you teaching my engineering statistics classes in college? i would've actually went to class!

  7. #7
    RickySteve
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    Quote Originally Posted by David
    If you only bet underdogs at a line that is better than the implied probability at Pinnacle will you be profitable long term?
    If you believe Pinnacle is an efficient market and/or possesses a crystal ball, then yes (and not just for underdogs.)

  8. #8
    Ganchrow
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    Quote Originally Posted by Uncle Joe
    Good thing you gave out the basic course and not the advanced course! Can you use a game from today maybe tonights' NBA game to show some real numbers and lines for that formula?
    Sure.

    Tonight's NBA game at Pinnacle is currently:
    Miami +210
    Dallas -230

    This means that Miami's zero-vig implied probability would be:
    100/(100+210) ≈ 32.26%

    and Dallas's would be:
    230 / (100 + 230) ≈ 69.70%

    The total of the implied zero-vig probabilities (also known as the bookie's overround) is 32.26% + 69.70% ≈ 101.96%.

    This means that the implied line set probability for Miami is 32.26%/101.96% ≈ 31.64% and for Dallas is 69.70%/101.96% ≈ 68.36%.

    Make sense?
    Points Awarded:

    dj_destroyer gave ganchrow 1 SBR Point(s) for this post.

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  9. #9
    isetcap
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    So if I handicap this game and my numbers show that Miami has a 35% chance of winning, then my money should be on them at Pinnacle, right?

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  10. #10
    Ganchrow
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    Quote Originally Posted by David
    If you only bet underdogs at a line that is better than the implied probability at Pinnacle will you be profitable long term?
    Quote Originally Posted by RickySteve
    If you believe Pinnacle is an efficient market and/or possesses a crystal ball, then yes (and not just for underdogs.)
    Ricky pretty much hits the nail on the head. It all comes down to down to how good a predictor you believe Pinnacle to be. Under the assumption of efficient markets (probably a good juimping off point) it shouldn't matter on the average whether you bet a dog or favorite, just so long as you can get in at better than the prevailing market price.

    That said, in the real world it's reasonable to say that if you can consistently beat Pinnacle's dog number you can expect to make money long-term.

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  11. #11
    Dark Horse
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    Quote Originally Posted by ganchrow
    Sure.

    Tonight's NBA game at Pinnacle is currently:
    Miami +210
    Dallas -230

    This means that Miami's zero-vig implied probability would be:
    100/(100+210) ≈ 32.26%

    and Dallas's would be:
    230 / (100 + 230) ≈ 69.70%

    The total of the implied zero-vig probabilities (also known as the bookie's overround) is 32.26% + 69.70% ≈ 101.96%.

    This means that the implied line set probability for Miami is 32.26%/101.96% ≈ 31.64% and for Dallas is 69.70%/101.96% ≈ 68.36%.

    Make sense?
    I think the lines at Tradesports give the 0-100 values. lol. (with odds converter elsewhere on the page)
    But the lecture is interesting...

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  12. #12
    Ganchrow
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    Quote Originally Posted by Dark Horse
    I think the lines at Tradesports give the 0-100 values. lol. (with odds converter elsewhere on the page)
    But the lecture is interesting...
    Analytical tools like that are certainly great to have, but its only by understanding the methodology that you can perform your own quantitative analysis.

    On a related note, I suspect that SBR is going to have tools such as this in the very near future. So if anyone has any ideas on what they'd to see, there's never a bad time to speak up about it...

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  13. #13
    dj80d
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    is there a tool on this and what is it

  14. #14
    mathdotcom
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    Quote Originally Posted by dj80d View Post
    is there a tool on this and what is it
    It's called an excel spreadsheet.

    But welcome to the forum.

  15. #15
    dj80d
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    thanks im hella new just lookin for some help

  16. #16
    sycoogtit
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    Holy crap, that's good stuff. That should be stickied.

  17. #17
    Joe Dogs
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    Very Interesting......Thanks for info

  18. #18
    SlickFazzer
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    good to review from time to time.

  19. #19
    bigbank
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    Ganchrow is the man. Ganchrow gets a point.

  20. #20
    whatsgood5
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    Very nice write-up Ganchrow!

  21. #21
    LT Profits
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    RIP Ganchrow.

  22. #22
    THEGREAT30
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    Quote Originally Posted by LT Profits View Post
    RIP Ganchrow.
    In reality or just from the forum? Good day

  23. #23
    LT Profits
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    Sorry, forum.

    Threads like this make me miss him more.

  24. #24
    FishFace5
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    Damn.
    Thanx LT.
    What happened to this guy??

  25. #25
    LT Profits
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    First he was promoted to run SBR office in Costa Rica, then he was let go for some reason. Nobody knows the details.

  26. #26
    suicidekings
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    Quote Originally Posted by LT Profits View Post
    First he was promoted to run SBR office in Costa Rica, then he was let go for some reason. Nobody knows the details.
    I feel fairly confident he's either hurting the books badly by now or working for one of them (ie: getting paid not to hurt them). He's got a scary amount of knowledge on the fundamentals of how to succeed at sports betting.

  27. #27
    Flying Dutchman
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    LT, has he washed up anywhere else?

    ...damn fine mathematician...

  28. #28
    JohnAnthony
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    I've heard some talks about a "secret project", was that terminated?

  29. #29
    Flying Dutchman
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    Quote Originally Posted by suicidekings View Post
    I feel fairly confident he's either hurting the books badly by now or working for one of them (ie: getting paid not to hurt them). He's got a scary amount of knowledge on the fundamentals of how to succeed at sports betting.
    If he's hurting them it's happening quietly...

  30. #30
    Peregrine Stoop
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    Quote Originally Posted by sycoogtit View Post
    Holy crap, that's good stuff. That should be stickied.
    no stickies

    it sounds stupid, but forcing lurkers to use search functions and figure out the best stuff is a pretty decent firewall from everything getting much, much harder for all of us

  31. #31
    suicidekings
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    Quote Originally Posted by Peregrine Stoop View Post
    no stickies

    it sounds stupid, but forcing lurkers to use search functions and figure out the best stuff is a pretty decent firewall from everything getting much, much harder for all of us
    Even reading the basics isn't enough though. For anyone to actually profit from it they need to put a lot of effort in, and I feel like the casual lurkers firewall themselves off through a lack of follow through. I'd rather see a stickied & locked thread at the top with links to quality threads from the past outlining the basics than see the same questions get addressed over and over again, cluttering the Thinktank up.

  32. #32
    Patrick McIrish
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    This was very basic material but Ganchrow had enough to keep everyone on their toes. Hate to sound like a pussy but it breaks my heart he's not here any longer.

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  33. #33
    Brock Landers
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    if he were able to pound out this formula into a more user friendly format, and its proven to be accurate, players would be killing the books
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  34. #34
    Jive
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    Quote Originally Posted by suicidekings View Post
    I'd rather see a stickied & locked thread at the top with links to quality threads from the past outlining the basics than see the same questions get addressed over and over again, cluttering the Thinktank up.
    I was just going to suggest this as I read through this thread. Have a locked post (or subforum if there are enough threads) saying, "Beginners start here" or "Sports Investing 101." I second your idea, SK.

  35. #35
    Mini19
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    He was way to smart to be posting at forums

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