Just how accurate are the oddsmakers as point spreads change and grow? Most people would predict that as spreads increase in size, the accuracy of the oddsmakers at predicting the final score should fall. What we’ve done is examined the standard deviation on the ATS (against the spread) margin of thousands of games in all of the major sports to see if there is any relationship between the size of the spread and how close oddsmakers are able to predict the final margin of victory. Knowing how accurate the oddsmakers are can help in all sorts of situations, but especially when considering teasers. If oddsmakers aren’t as accurate with bigger lines, we can reduce the risk of teasers by only taking games with smaller lines. It’s a sound theory, but results of our research will tell us whether or not that theory is true.

### Explanation of Terms

The ATS margin from which we gather the standard deviation is taken from hundreds of games at each spread. For example, a game with a line of -2 that ends with a final score of 88-76, assuming the favorite won, would be 10 (if the underdog won, the ATS margin would be 14). This basically tells us how far off the oddsmakers were at predicting the final score.

The standard deviation in the tables below has been run on the ATS margins of thousands of individual games at each spread for each sport. The final standard deviation number represents about how much variation can be expected between the actual final ATS margin and each posted spread (the expected ATS margin). The lower the variation, the more accurate oddsmakers are at predicting games with that spread.

You may find this explanation of standard deviation easier to understand:

As a slightly more complicated real-life example, the average height for adult men in the United States is about 70 inches, with a standard deviation of around 3 inches. This means that most men (about 68 percent, assuming anormal distribution) have a height within 3 inches of the mean (67–73 inches) – one standard deviation – and almost all men (about 95%) have a height within 6 inches of the mean (64–76 inches) – two standard deviations. If the standard deviation were zero, then all men would be exactly 70 inches tall. If the standard deviation were 20 inches, then men would have much more variable heights, with a typical range of about 50–90 inches. Three standard deviations account for 99.7 percent of the sample population being studied, assuming the distribution is normal (bell-shaped).Wikipedia – Standard Deviation

At the bottom of each table you will see a correlation number. The correlation basically tells us how effective the spread is at determining the standard deviation. A correlation is expressed as a number between -1 and 1 (correlation coefficient). The closer the number is to 1, the stronger (more accurate) the positive correlation, the closer the number to -1, the stronger the negative relationship. As a correlation draw closer to zero, it shows a lack of causation in the data. In our samples we expect a negative correlation (as spreads get lower (-1, -2, -3…), the standard deviation should get bigger). Note: Something to keep in mind is that because we are looking at spreads from a favorite’s perspective – meaning using negative numbers – “lower” spread numbers (-14, -15, -16…) represent “bigger” spreads, while higher numbers mean “smaller” spreads (-3, -2, -1…). Now let’s see the results for each league and find out if our theory holds any water.

We are displaying the results of our research in the form of scatter charts in order to help you visualize the data. In terms of a strong correlation, you would want to see the data points clustered in a falling line. The more spread out the data points, the weaker the correlation.

### Standard Deviation in NBA Games

Correlation: 0.60

The relationship between the spread and standard deviation of ATS margin is stronger in the NBA than it is in any other league we examined (though it’s still not really that strong in statistical terms), however, it’s the opposite of what we expected it to be. As the spreads get lower in the NBA, the variance in ATS margin actually gets lower as well (a positive correlation). This means that oddmakers predict the scores of NBA games with large spreads better than they do in games with small spreads.

As you’ll soon find out, this is not the case in every sport, but our theory for why this does happen in the NBA has to do with the predictability of a team winning the game outright. Once you get to a line of -8 in the NBA, you start seeing a high percentage (79% to be exact) of teams winning outright, in comparison to spreads of -4 where just 61.6% of those teams end up winning outright. If you are more certain that a team will win the game, it makes it a lot easier to land your estimated final score near the actual final score. With that being said, this phenomenon doesn’t seem to happen in any other sport, so it’s difficult to pinpoint the exact cause.

### Standard Deviation in College Basketball Games

Correlation: -0.33

With college basketball we get more of a the result we were expecting. We get a small negative relationship, meaning as spreads get lower, so does the standard deviation. There is a bit of a catch here. With spreads up to about -15.5, we see the same thing we saw in the NBA (a positive correlation) where the accuracy of oddsmakers goes up with the lower spreads. Once we get to spreads of -16 or more, however, we start to see that negative correlation we expected. This is likely because once spreads get over 16 points, you are most likely looking at a huge blowout (which is fairly common in college basketball) or you end up with a game that is closer than expected, making for a wider range of variance than games with bigger (closer) spreads. The reason we don’t see this in the NBA is because there simply aren’t spreads that large on a regular basis.

### Standard Deviation in NFL Games

Correlation: -0.06

There is no relevant association between the size of the spread and accuracy the oddsmaker has at predicting the final score. Lines are tight enough and talent gaps small enough in the NFL that this makes a lot of sense.

### Standard Deviation in College Football Games

Correlation: 0.09

While I’m not surprised that the standard deviation for college football games is higher on average than it is in the NFL (simply meaning it’s less predictable), I am surprised that there is no significant relationship bewteen the size of the spread versus the actual final ATS margin.

### Conclusions

There are a few things we can take away from this data. The first is that oddsmakers are very good at what they do. Although there is a lot of variance in how far the spreads they set are off of the final score, they are, in large part, very consistent with the amount of that variance.

We can also safely say that our theory on the relationship between the size of the spread and amount of variance in the final ATS margin was completely wrong – and that’s great! Proving a theory wrong is just as effective as proving one right. While there may be certain sample situations where you can expect a higher volatility in ATS margins, by and large there is no reason to expect a game with a bigger point spread to be more “off” the final ATS margin than a game with a smaller spread.

### More on Standard Deviation in Football & Basketball

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