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I am trying to compare betting lines on NFL across different sportsbooks to find the optimal one to bet. Here is an example:

  • Sportsbook 1 offers: team A spread: -6 odds:-116
  • Sportsbook 2 offers: team A spread: -6.5 odds:-110

How do I compute which one is better.

#My attempt:# If team A loses or wins by less than 6 points I lose my bet regardless if I chose sportsbook 1 or 2. Therefore I ask the following question: If we assume team A wins by at least 6 points, what is my expected return?

  • Using Sportsbook 1: $E_1 = p_{>6} \times a \times \frac{216}{116}$
  • Using Sportsbook 2: $E_2 = p_{>6} \times a \times \frac{210}{110} - p_{=6} \times a$

Here $a$ is the amount bet, $p_{>6}$ is the probability of an NFL game finishing with a point differential greater than 6 and $p_{=6}$ is the probability of an NFL game finishing with a point differential of exactly 6. I can compute $p_{>6}$ and $p_{=6}$ using historical data. I find $p_{>6} \sim 0.61$ and $p_{=6} \sim 0.066$. Using these probabilities I find $E_1 \ sim 1.13 \times a$ and $E_2 \sim 1.09 \times a$ implying that I should bet at sportsbook 1 to maximize returns.

Is this analysis correct?

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    Welcome to Sports Stack Exchange. We do not have MathJax enabled, so your equations are unfortunately not readable here. Can you include an alternative version of them to provide answerers with the necessary information?
    – Nij
    Sep 7, 2023 at 4:27
  • I dont know MathJax but wouldnt you want your calculation for Sportsbook 1 to be >5 instead of >6? Does sportsbook 2 have a spread for 5.5, that would be the comparison. Sep 7, 2023 at 10:39
  • Sorry about this MathJax issue. I will try to update the quesiton.
    – pphili
    Sep 7, 2023 at 12:53
  • The expectation values are computed assuming team A wins by 6 or more. Otherwise, the bet loses in both cases. For sportsbook 1, if team A wins by more than 6 we win the bet and profit the bet, a, multiplied by the payout 216/116. If team A wins by exactly 6, we profit 0. That's how I computed the expectation value.
    – pphili
    Sep 7, 2023 at 12:55

1 Answer 1

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I think you are right that sportsbook 1 has better value. I calculate the profitability of a bet by pretending I am making this bet 100 or a 1000 times on seperate matches and seeing what the hypothetical returns are. The below calculations are based on 1000 bets of $1 and I have converted the odds to european style.

If I am understanding p_{>6} correctly, according to you the probabilities are as follows

  • 0.610 that it is great than 6 -- ($p_{>6})
  • 0.390 that it is 6 or less
  • 0.066 that it is 6 exactly -- ($p_{=6})
  • 0.324 that it is less than 6

Sportsbook 1 offers: team A spread: -6 odds:-116 (1.86)

  • If it is less than 6 you lose -- (324 * 0) = $0
  • If it is 6 exactly you get your stake returned -- (66 * 1) = $66
  • If it is more than 6 you get your stake returned plus winnings -- (610 * 1) + (610 * (1 * (1.86 - 1))) = $1134.6

So after 1000 bets your account will have $1200.6

Sportsbook 2 offers: team A spread: -6.5 odds:-110 (1.91)

  • If it is less than 6.5 you lose -- (390 * 0) = $0
  • If it is more than 6.5 you get your stake returned plus winnings -- (610 * 1) + (610 * (1 * (1.91 - 1))) = $1165.1

So after 1000 bets your account will have $1165.1

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