ESPN recently reported that the NFL ejections record (since 2001) is on pace to fall during the 2016 season. That is significant because the NFL implemented rules this off-season that changed how ejections are determined. So it’s a natural question to wonder if the rule is having an unwanted effect on the overall game and continue the No Fun League. Fortunately, we can apply some neat statistics to put some numbers around the current state of the NFL ejections record. Here’s what we know:
- Through Week 9 of the 2016 season, there have been 10 ejections
- Available data sets the season record at 13 ejections, back in 2001
- ESPN has provided a table with rejections for each season, going back 7 seasons. That table is shown below
Courtesy ESPN
We can apply something known as the Poisson Distribution to these numbers. In a nutshell, if you provide an average of independent, singular events – which ejections are – we can assign a probability of the value being higher or lower than a given value. By summing up the values for the years 2010 – 2015, we get an average of 7.17 ejections per NFL season. That’s a good start for our study.
The next part is to take our average and plug it into the Poisson Distribution and figure out the likelihood (probability) of breaking the record of 13 ejections in any given season. By doing this we can come up with the probability of having 13 or more ejections in any given season at 3.18%. Note that this also includes tying the record. If we are looking at strictly breaking the record (i.e. more than 13 ejections), the probability drops to 1.5%
In any given season, the probably of breaking the 13 ejections in a season record is 1.5% or something that should only happen about 1 in 67 full NFL seasons
NFL Ejections Record: 9 Weeks Into The Season
But we are 9 weeks into the 2016 NFL season and can work with the information we’ve gained to this point in time. We know that we have 10 ejections so far and that puts us on pace to reach about 18.88 ejections in 2016. We can assume that there will be some referee and player bias now that we are now aware of the record, so let’s round down to 18 ejections. By plugging in these numbers, we can see that the probability of reaching 18 or more ejections in a year drops down to 0.0476% or about 1-in-2100 seasons!
If the 2016 NFL season reaches 18 ejections, that has a probability of 0.0476%, or something that should only happen about 1 in 2,100 full NFL seasons!
While the NFL remains a sport with many variables, at some point there must be a quantitative threshold where rules and changes need to be re-examined. Is a 1-in-2,100 event near that threshold for the NFL ejections record? I don’t know, I am not privy to those conversations, but perhaps it should be. To go from an average of 7 ejections to 18 is alarming in itself; realizing that it should happen less than once in two millenniums should raise someone’s concern at the NFL.
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