# Relationship between Total Over/Under scores and actual total scores in sports

I have a data set of actual scores from sporting games, matched with the bookmaker's Total Over/Under Score (O/U Score) and the odds the bookmaker was offering that the game's total score would fall Over the O/U Score, or Under the O/U Score.

The head of my data table looks like this:

Thus for the first game, the bookmaker was offering decimal odds of 1.884 ($$\frac{1}{1.884}$$ ≈ an implied probability of 0.531) that over 179.5 points in total would be scored, and decimal odds of 1.97 ($$\frac{1}{1.97}$$ ≈ an implied probability of 0.508) that under 179.5 points in total would be scored. In fact 176 points were scored in total in that game.

The full data is viewable here, and there are 1033 games in total for which I've collected this data.

In the second tab of that spreadsheet I have deleted all rows in which the odds the bookmaker was offered were unequal for each side of the Over/Under line. The head of that data table looks like this:

In these particular rows the bookmaker has offered decimal odds of 1.925 for each side of the Over/Under line. In some later rows the odds equal some other values, e.g. 1.9 for each side of the Over/Under Line.

Considering only the 318 games with "equal odds", the total score was Over the line in 46.54% ($$\frac{148}{318}$$) games, and Under the line in 53.46% ($$\frac{170}{318}$$) games. I would have expected it to be closer to 50%.

A graph of the 318 games with equal odds is displayed below. The Pearson correlation between the Over/Under Score and the actual total score is 0.3934.

Ultimately I want to use the odds and the Total Over/Under score (both provided by the bookmaker) to a "best guess" about what the total score will be. Reflecting a bit on that, it seemed I'd need to

1. Quantify how good the bookmaker's line is as a predictor of the total game score.

2. Query whether there is any bias in the over/under score listed by the bookmaker, and if so to quantify that bias.

3. To work out how to get from the uneven odds to generate a "best guess" about what the total score of a game will be. For instance, in the very top row of the table it seems that due to the uneven odds the true expected total score should be expected to be more than 179.5, but I'm unsure how much more.

It seems a rather simple research scenario, but I'm unsure of how to proceed, and googling this site didn't reveal any similar-seeming scenarios.

• Dabbling around - am not a maths person but this is my area of interest which is why I lurk. Bottom line admittedly it was based on margin of victory (ATS) but see the Steven Levitt paper of 2004 re: Bookmakers skewing lines to maximise profits from the clients. People historically want to bet an over (e.g. who wants to see a low scoring game) so totals lines will be higher than a predicted score typically. As most bookmakers game lines run largely through algorithms (see the Cantor Fitzgerald and in play markets) they have to be careful though not to skew related markets though. – user8812 Nov 1 '18 at 12:29
• When I first saw the data it occurred to me that the desire by punters to see a high-scoring game might produce a bias in the bookmaker's Over/Under line - that's fascinating! I'm reading the Levitt paper right now and it is relevant, but are there any papers that attest to people historically wanting to bet an over? – user1205901 - Reinstate Monica Nov 1 '18 at 12:51
• Will have a dig through stuff I have and see if I can find something. I'm sure I read it somewhere but I think it is more anecdotal than empirical evidence. Have mucked about with modelling sports a little and my gut reaction is total lines are high. Can't prove it but I think it would make sense. – user8812 Nov 1 '18 at 12:55
• football-data.co.uk/blog/unwise_points_spread.php everything seems to refer to the favourite long shot bias and favourites in a game unfortunately. Don't think a lot of work has been put in on totals. Think they are 100% beatable though especially when you start modelling them and then factoring in players and the weather. – user8812 Nov 1 '18 at 13:05