Just say no to PED (speculation)

Since 2010, five Seahawks have been suspended for PED use. That's the most in the NFL. It's bad because losing Brandon Browner or Bruce Irvin is not something the Seahawks can afford. It's bad because it distracts fans and possibly players from the actual football. And it's bad because five is a large enough number that people see a pattern.

A British political theorist named Isaiah Berlin once (or, more likely, multiple times) said,

To understand is to perceive patterns.

That's stupid.

We are brilliant at finding patterns. Constellations are my favorite example. Cassiopeia, the bright W in the northern sky, was a queen who boasted that her daughter Andromeda was more beautiful than a god's daughters. As punishment she was put on a throne in the sky where she has to spend half of her time clinging onto it during it's rotation around the North Star.

The point I'm making isn't that the story is wrong. The point I'm making is that the reason for the story - explaining the pattern of stars - isn't even real. Today we know that the some of the stars of Cassiopeia are farther from the others than they are from Earth. From another perspective they would not be a W.

When an unexplained pattern is found it is natural to try to explain it. That's fine but the first step should be to ask if the pattern even needs explaining.

Since the start of the 2010 season there have been 50 PED suspensions in the NFL (thank you Mike Sando, without whom I would be eternally lost). Intuitively it seems like 1 out of every 10 suspended player being a Seahawk confirms a pattern, but humor me and walk through the math.

Our null hypothesis will be that the probability of a player for the Seahawks testing positive for PEDs is equal to the league average probability.

If I can show with 95% confidence that playing for the Seahawks makes a PED suspension more likely then we can reject the null - then, maybe, we can start wringing our hands about the Hawks.

Analysis

If each team had the same 53 man roster for each season since 2010 this would be easy. Given that the null hypothesis is true, the probability of any given player being suspended should be .029

Under the null hypothesis (I'm going to stop prefacing with that now) each team should represent a random sample of 53 players. If the 95% confidence of any sample does not include the population probability (which we'll approximate with .029) then we can reject the null.

In other words, given that the Seahawks had 5 positive PED tests in a sample of 53 players what interval am I 95% confident that the actual rate of PED suspensions is for the Seahawks players? If it does not encompass .029 then I can reject the null (not really since I'm assuming that each team had the same 53 players but play along for a moment.)

Quickly doing a binomial confidence test (Clopper-Pearson), the Seahawks 95% confidence interval is .031-.207

The Seahawks lower bound of .031 is .002 greater than the population probability. In this approximation the null can be rejected.

We know it's too naive to say that each team had the same 53 man roster each year. Some teams have more turnover than others and more turnover means more PED tests. It is the number of PED tests conducted per team that matters.

By my understanding each player must take a test when reporting to a team and ten players are randomly tested per team each week. Players are also tested during the off season up to six times but we don't know how many players from any given team are tested or how much. Although it's probably not correct to assume that offseason testing washes out evenly across teams (it would depend on the number of contracted players as well as NFL testing decisions) without any info it's what I'll have to do.

Teams with greater turnover in their 53 man roster during a season will have more chances for a player to test positive. Teams that reach the playoffs will have more chances for a player to test positive. Each team will have a baseline of 263 tests per season. The average team will have less than a week of playoffs for around another 7 tests. Make it an average (before turnover) of 270 tests per team. Right off the bat we know that the Seahawks have played in four playoff weeks since 2010. That means that they've had a average (before turnover) of 276 tests per season.

Using these numbers the population probability of a positive drug test is .00198 the lower bound of the Seahawks confidence interval is .00196

Just the extra tests in the playoffs were enough to make the difference between the Seahawks and league at large insignificant.

But think back to 2010 and 2011. The Seahawks roster churn was famous. Through cursory searching I can't figure out an easy way to compare actual 53 man roster churn but if you think the Seahawks have had more 53 man roster churn than league average then the null cannot be rejected at even lower significance levels.

Conclusion

There is no reason to suspect that Seahawks are any more likely than other teams' players to get caught doing PEDs. To me that means that that there is no reason to suspect that Seahawks are any more likely to be doing PEDs. Out of 32 teams it's not really all that unlikely that one should have 5 players test positive in the past 3 seasons. Given that the Seahawks have had a lot of roster churn, it is even less unexpected for them.

Creating narratives around the culture brought in by Pete Carroll or how complicated play books encourage adderall use is like explaining the constellations as whims of the gods. You may like your story. Other people might too. But in the end you're explaining a pattern that probably doesn't exist.

That's irresponsible if people trust your judgement and at least a waste of your time otherwise.