Written by: Yusuf Mehkri
In correspondence with Sam Ventura’s class: 36-144 – Winning with Statistics in Sports
At the start of every NFL game, the team that wins the coin toss has the ability to decide which half they want to start the ball with. Some coaches decide to start the game with the ball, so that they can get points on the board early on, which can motivate the players to continue playing with the same level of intensity and passion. On the other hand, a majority of coaches believe that starting with the ball in the second half is more advantageous, because it is the only time in the game (except for turnovers) when a team can end up with the ball two possessions in a row. How is this possible? A team could end the second quarter with possession of the ball and then start the third quarter with the ball again following the second half kickoff. However, both of these viewpoints are based solely off of years of experience as opposed to statistics and analytics.
Therefore, I set off to find out two things:
- Does it make a difference whether a team starts off a half with the ball?
- Does this effect change in the first vs. second half?
In order to investigate this issue, I relied heavily on the nflscrapR package, which aggregated game data from seven NFL seasons. With the package, the game data was broken down into scores, which were then used to calculate the score differentials (away team scores subtracted from the home team scores) at the end of every half.
Table 1: Average Score Differentials at the End of Every Half
|Mean Score Differential||Standard Error|
|Home Team Starts the Half||1.703 Points||0.231|
|Away Team Starts the Half||0.486 Points||0.227|
Visually, the frequency distribution graph doesn’t seem to show much of a difference in the score differentials of the two different situations. However, the two mean score differentials are relatively far apart and further analysis brings us to a clearer conclusion. After running a t-test (with the null being no difference and the alternative being a difference greater than zero), I got a p-value of near zero (at 9.852*e-05), which means that there is a statistically significant difference. Although both the home and away teams score more points on average when they start the half with the ball, the effect is significantly better for the home team, which likely reflects a home-field advantage.
Furthermore, I organized the data by separating it into first and second half score differentials to see if there is any significant difference in the score differentials in that way. Just like before, the score differentials were calculated by subtracting the away team’s score from the home team’s score (Home – Away). The differentials were then further divided into separate groups depending on whether the home or away team had started with the ball in that half. Thus, the data I was left to work with included the score differentials and points scored by the home teams and away teams in the halves in which they started with the ball and in those in which they did not.
Table 2: Average Score Differential for Home and Away Teams by Half
|First Half||Second Half|
|Score Differential||Standard Error||Score Differential||Standard Error|
|Home Team Starts||1.9421||.329||1.4204||.322|
|Away Team Starts||1.1177||.356||-0.0792||.290|
Interpreting the table: Score differentials are calculated with the respect to the home team by subtracting the away team’s score from the home team’s score. Thus, the score differential of 1.9421 corresponds to the home team scoring 1.9421 more points, on average, than the away team when it starts the first half with the ball. Likewise, the score differential of -0.0792 corresponds to the away team scoring .0792 more points, on average, than the home team when it starts with the football in the second half.
The data shows an alarming difference in the score differentials between the first and second halves for the away teams, and so I ran a t-test (with the same hypotheses as before) to check for statistical significance. Running it twice for both the home and away teams, I found some very interesting results. The p-value for the difference in the first and second half score differentials for home teams was a 0.13 and for the away teams was .005. With a .5% likelihood of getting data as extreme as seen here (for the away teams) with a sample of this size and assuming the null hypothesis to be true, the results are statistically significant. Therefore, it is more advantageous for the away team to start with the football in the second half. For the home team, although a p value of .13 is not statistically significant, it does provide mild evidence that suggests that this should be explored further.
From this analysis, we can conclude two things. First, that the team that receives the football at the start of a half will score more points on average than the opposing team. Although this doesn’t have much of an impact on the outcome of an NFL football game where both teams have a chance to start a half with the ball, it does confirm the fact that there is a clear benefit to having first possession of the football. Moreover, the second half of the analysis has far greater implications and brings us to the second conclusion. By separating the data into first and second half score differentials, we found that it does make a difference whether the team is a home or an away team. Since there was no significant difference between the score differentials of the first and second halves for the home teams, it shouldn’t matter which half they choose to start the ball with. Although many coaches have their own preferences based off of experience and instinct, there seems to be no real difference in the score differentials for either half from a statistical perspective.
On the other hand, the findings from this data seem to suggest that the away team should always choose to defer when they win the coin toss (to receive the ball in the second half). According to Sports Illustrated, this is already what most teams are doing since about 80% of the teams that won the coin toss in the 2015 NFL season chose to receive the ball in the second half.
Although there isn’t enough evidence to say why there’s such a clear benefit for the away teams to start with the football in the second half, there certainly is a benefit. I believe that a great follow-up analysis could look into how many times there have been double possessions of the football (playing the last offensive drive of the first half and then receiving the ball to start the second half) and if there is any correlation between those and the final outcome of the game. Until then, we can only continue to speculate.