How do you compare NFL betting lines?

Question

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?

Answer 1

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