Predicting Over/Under Lines

Although a lot of my previous posts have focused on using statistical analysis to find patterns in the way Vegas sets the spread for NBA games, recently I’ve begun to think about using similar techniques to analyze over/under lines as well. My first step in starting to look at ways to analyze over/under lines was to think about how bookies might arrive at the lines they set. There wasn’t a whole lot of info on the internet, so instead I came up with my own theory: The seemingly logical answer to this question was that they would find the mean of the home team’s points per game average and the away team’s points allowed per game average, then add it to the mean of the away team’s points per game average and the home team’s points allowed per game average:

For example, say the Knicks are scoring 95 points per game, and are giving up an average of 105 points per game. Next, imagine that the Knicks are playing the Celtics, who are scoring 110 points per game and are allowing an average of 100 points per game. To find what I expect the over/under line should be for this matchup, I would simply take the amount I think the Celtics will score, and add it to the amount I think the Knicks will score. I would arrive at the presumed Celtics total by taking the average of the Celtics points per game and the Knicks points allowed per game ((110+105) / 2 = 107.5), and would arrive at the Knicks presumed total by averaging the Knicks points per game total and the Celtics points allowed per game total ((95+100) / 2 = 97.5). The above calculation really just boils down to adding together the 4 averages I mentioned and dividing by two, but I thought it would be helpful to explain my thought process a little. Of course, this is a pretty basic way to arrive at projected scoring totals, and doesn’t include things like style of play that theoretically would play a factor.

My next step was to come up with predictions for what the over/under line should be for each game, based on the above-mentioned averages heading into the contest. Although I wasn’t taking into account injuries for these games, which I’m assuming would actually play a big factor in establishing these lines, I nevertheless felt that using points per game and points allowed per game averages was a good way to estimate over/under lines.

After coming up with what I expected over/under lines for each game should be, I formed a hypothesis that the over would hit a majority of the time when my prediction was greater than the actual o/u line, and that conversely, the under would hit a majority of the time when my prediction was less than the actual o/u line. Although I didn’t really have a theory on why the Vegas line might be different from my predicted line in these cases, I felt that this more general analysis might provide some insights.

 

Results

I discovered that for almost every team (the two exceptions being Oklahoma City and Philadelphia), the average difference between my predicted o/u line and the actual o/u line was higher in games when the over hit, and lower in games when the under hit. Put another way, when my predicted line was higher than the actual line, the over tended to hit and vice versa. However, the difference in these two averages was only significant (with 95% confidence) for 11 of the teams (starred in the graph below).

Taking all the games into account, I found that the average difference between my prediction and the actual line in games when the over hit was .7, and the average difference between my prediction and the actual line in games when the under hit was -.79. These results were found to be significant, although almost any discrepancy when you have a sample size of 1,230 (the number of total games played in an NBA season) would be found to have significance. Using these averages, I decided to see what the outcome would be if one were to bet the over any time my o/u prediction was .7 points or more above the actual line, and to bet the under any time my o/u prediction was .79 points or more below the actual line.

Using this betting tactic, I found that you would expect to hit 54.1% of your over bets and 58.3% of your under bets. Although this looks like a profitable strategy, keep in mind that you would have to place a very high volume of bets (606 times on the over, and 387 times on the under to make this work.

 

Analysis

Overall, I was very encouraged by these results. It seems as though through the simple process of taking into account both teams’ points per game averages and points allowed per game averages, one can come up with an effective strategy for evaluating how to bet the over/under for a given NBA matchup. Although I most likely wouldn’t base my entire over/under model on the analysis described above, I think this is a great starting point for adding in more variables. More specifically, I would definitely want to add in data about injuries and referee assignments when creating a more robust model.

  2 comments for “Predicting Over/Under Lines

  1. Marver
    June 3, 2016 at 1:59 pm

    Great post. Almost no betting blog I see is talking about statistics and that’s what I like.

    Well, my two cents: injuries only plays a considerable factor when good players are included. Otherwise, you can ignore it. You can even split the data in this way: instead taking into account ppg and points allowed of each team, you can have 1) expected points made per game and points allowed per game with all players and 2) expected points made per game and points allowed per game without the great players of the team.

    Breaking the data down, you can predict the game better in my opinion.

  2. Alex Goldstein
    March 21, 2017 at 4:57 pm

    Amazing work! I would like to talk further if possible…reach out to agold2727gmail.com when you have a chance! I’ve been tracking this season including referee averages…

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