## Under the Hood - NFL Home vs Away Scores Posted on 09/29/17 : 0 comments

### The Call on the Field

In NFL sports betting, we commonly hear that Vegas odds makers give the home team an automatic 3-point advantage. It would be nice to know whether there is any truth to that statement. In this analysis, we will use historical NFL game data and test this myth to determine if statistics can back the claim.

### Approach & Data

We are going to compare the home and visitor scores of NFL games and perform statistical tests to see if there is a basis for the 3-point advantage. First we need to get some game data. At Hooded Rhino, we have a data set of all NFL games since the 2000 season. We have a total of 3989 games to use for this analysis.

In the data, the average home teams score is 22.99 and the average score of visitor teams is 20.36 points. Perhaps, the difference of 2.63 points is the reason the 3-point rule of thumb was created. Also, it is interesting to see that the median home spread is exactly -3 points.

### Distribution of Home Team Lines

First we can look at the distribution of the spreads given to the home teams. In the histogram below we can see that a -3 point spread is the most common by far. While this may lead us to believe that home teams get an automatic 3 points, it isn’t statistically backed. We need to look into the data a little more.

### Home vs. Visitors Scores

It may help to visualize the actual home and visitor scores. In the plot below, we can see that home and visitor scores are evenly spread but on average, the home scores are slightly higher than the visitor scores.

### Distribution of Scores

Now, we can look at the distributions of the home and visitor NFL scores. In the plot below, we see some interesting results.
1. The away teams score zero (0) points more often.
2. The distribution of visitor scores has two peaks while the home distribution of home scores has one distinct peak. We should investigate this in a future analysis.
3. There ranges of scores are almost even; however there is a distinct shift in the two distributions.

### Statistical Test of Means

Next, we want to see if there is a statistical difference between the means of the distributions. For this we will look at a two-tail t-test.

#### Null and Alternate Hypotheses

H0: There is not a difference between home and visitor scores in the NFL
(μhome = μvisitor)

H1: There is a significant difference between home and visitor scores in the NFL
(μhome <> μvisitor)

#### 95% T-Test

With a 95% confidence interval, we can see that there is a significant difference between the two means (p-value = 1.073832910^{-29}). We reject the null hypothesis, accept the alternate hypothesis, and conclude there is a difference between the home and visitor scores. Interesting, the 95% confidence level for the difference of average scores is in the range of 2.172-3.077 points. Perhaps that is why sports bettors state that Vegas sports books give home teams the 3-point spread.

#### 99% T-Test

Next, let’s check the 99% confidence t-test.

With a 99% confidence interval, the p-value is still very low (1.073832910^{-29}), and the range of difference is between 2.03 and 3.22 points.

#### 99% Paired T-Test

Lastly, we want to check two see if there is a relationship between the two distributions with a paired T-Test.

As we see, the 99% confidence intervals change slightly, but still in the range of 3 points.

### Conclusion

After further review, the call on the field is confirmed, and the 3-Point home advantage is UPHELD.
From this analysis, it appears that the 3-point rule of thumb in NFL sports betting has statistical roots. This statistical fact is begging to be taken advantage of in terms of sports wagers. In future articles, we will look at more sportsbook “myths” and see how they stack up.