NFL Coaches Salary

Recently in the local news I saw that our beloved Seattle Seahawks coach, Pete Carroll (or "Uncle Pete" as he's known at our house) is up for a contract negotiation soon. He's been the heart and soul behind turning the Seahawks from a national "meh" to one of the top teams in the NFL, including back to back Super Bowl appearances, and one of the best records in the league. Naturally, he'll be asking for more money.

So I was wondering: Does the Win/Loss record indicate Pete Carroll deserves more money?

For reference, I toyed with this idea a few years ago for NCAA coaches

I searched Google and quickly gathered some data on NFL Coaches Salaries, as well as their age. I then grabbed a few years of Win/Loss standings from ESPN (again, top hit on Google). Averaging together the results from the past 3 years of NFL play, let's see how they look! Of course I've highlighted the Seahawks with a bright green star.

The line of best fit was simply calculated using a least squares regression in Python. There's a lot of scatter (much more than in my NCAA analysis previously), but I'm only averaging 3 years of play instead of 10 this time. Here's how to read this graph: points above the line are winning more than average given their level of pay, and points below are winning less.

Right away you can see two interesting (or just obvious) things:

1. Uncle Pete is already one of the top paid NFL coaches
2. The Seahawks are one of the best performing teams in the NFL over this time period

So he might have a good case for being paid more! Let's see just how undervalued he might be. By subtracting the model from the data, we can compute the coaches "value":

This is a pretty noisy distribution, and not a great discriminant of "value", but thats ok... this is definitely not my most absurd football related article to date...

So, teams with the best value coaches by this metric are:
1 - Denver Broncos
2 - Carolina Panthers
3 - Cincinnati Bengals

and Seattle's Pete Carroll is a respectable 8th. Given that he's one of the oldest coaches in the NFL, I don't know how much room he'll have to negotiate. However, if the salary data I've grabbed is accurate, this year's NFL champions, the Denver Broncos, are getting a hell of a deal with Gary Kubiak.


Of course we have to talk about the other end of the distribution. The team with the "worst valued" coach in the NFL currently is:
32 - Tampa Bay Buccaneers

Look, don't put too much stock in what I'm saying based on random numbers from the internet. As I understand it the coach's salary doesn't count towards the team's salary cap, but still, it doesn't look great Tampa....


The data and Python code to make these figures is of course available for use on GitHub!

Football Statistics: the Impact of Smiling

If you've ever watched a professional football game (and this is probably true for most professional sports) then you have seen these little portraits of players that appear at the bottom of the screen. On some TV networks they are actually short video clips where the players announce their alma mater, on some networks they are animations where the players each raise their heads and occasionally blink (these creep me out), and for other networks these head-shots are just still photos. Some players smile in their photos, some do not.

Key & Peele have a recurring bit about this player introduction phenomenon.

While watching a Seahawks game this past year, my mother in law posed an amusing question: Do players who smile in their photos play better football?

The question is simple and whimsical, in other words perfect. I don't know anything about how often these photos are taken, what the player's mindset is when they're shot, or if there is any prior expectation about attitude/persona and player record. I set out to find some answers...

For this study I am only focusing on Quarter Backs (QBs) in American professional footbal (NFL), though it would be easy to extend to all positions if anyone can help me get the data! Right away I know I'll need a few ingredients: photos of each player, some classification of their smiles, and some real stats on their records in the NFL.

NFL Replacement Referee Bias

Today I'm happy to feature the first guest post on If We Assume, written by fellow astronomer Peter Yoachim! He's discussing the now-famous debacle by the replacement referees (see also here) that occurred in last night's Seattle Seahawks game (Some are calling it the "worst call in NFL history"). Take it away Peter...

Getty Images

After watching the refs botch Monday Night Football (Go Seahawks!?), I was wondering if there's a way to quantify just how bad the NFL replacement referees are.

One thing that stood out in the game was how many calls went the Seahawks' way on the final drive--which reminded me of the discussion of home-field advantage in Scorcasting.  They concluded that referee bias is the primary driver in home-field advantage across sports.  They even note that in the NFL from 1985-1998, the home team won 58.5% of the time, but after instant replay was introduced, the home team only won 56% of the games (1999-2008).

If the replacement refs are much worse than the regulars, we might expect the home-field advantage to grow.  My logic being, if the refs are botching more calls, those botched calls will tend to be in favor of the home team, that gives them an advantage, so they should win more.

How have home teams fared so far?  After 48 games this NFL season, the home teams have a record of 31 wins and 17 losses, for a whopping 64.6% win rate!  But is that significantly more than 56%?  31 wins is actually only 4 more wins than we would have expected with the regular refs.  As always happens when I try to calculate the statistical significance of something, I got bogged down in an arcane wikipedia page, when it told me to look up some value from a table.  Whenever a statistician tells me to look something up in a table, I reply, "Fuck that, I can Monte Carlo this in 5 lines of Python."  So I did:


#play 10,000 seasons of football with 48 games each
hg = np.random.rand(10000,48) 
#home team wins 56% of the time
hg[np.where(hg <= 0.56)]=1 
#the rest are losses
hg[np.where(hg < 1)]=0 
#total up the wins per season
ack = np.sum(hg, axis=1) 
print 'probability of home team winning 31 or more games with 1999-2008 refs = %.2f'%(np.size(np.where(ack >= 31)) /10000.*100)+'%' 

If you run that, you find out that we would expect  31 (or more) home team wins only 15% of the time.  To turn it around: 85% of the time the home teams have fewer wins at this point in the season.  We normally say something is significant when we reach the 5% level, so we're not there yet.  If the home teams keep winning at a 65% rate (or higher) for 3-4 more weeks we should make it to significance!  That's about the only reason I've found to root for the replacement refs sticking around--damned, scabs!

NCAA Football Coach Salary vs. Wins

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A question was posed to me the other day: "Is Steve Sarkisian (head coach for UW's football team) worth the money we're paying him?". For the record, his salary is currently around $2.25 million, though he's not paid by tax payer money.

The question of an employee's worth intrigues me. No doubt people have strong opinions/feelings on the matter. How do we quantify this to answer it objectively?

In the case of a factory worker, we might say that the number of gizmos he/she produces per hour without error determines their value. I don't think this kind of metric works for things like teachers...

Still, football coaches are often judged based on their team's performance. So I decided that the best way to answer the question was to compare the salaries and win/loss records for NCAA FBS (aka Division I-A) coaches.

Detailed data on coach salaries wasn't super easy to find, I would have liked to find a neat & tidy table with salary broken down by year for each coach, alas. I did find this nice compilation by USA Today. I grabbed win/loss stats here. Note: for my analysis I have not followed up on any of these stats/teams individually, so no doubt there have been hires/fires and raises/cuts which will affect the specific details.

The correlation between higher pay and better winning percentage is promising. The median salary is $1.46 million. Texas is doing well, but boy they're paying for it! I then subtracted a linear fit (dashed line) from the winning percentages to determine the typical scatter.

The standard deviation in winning percentage at a given salary is +/- 12%. All the coaches that fall within this "region of acceptable performance" are highlighted in purple. I believe these coaches are "worth it". Twice the standard deviation is gold/yellow. Coaches in this region should either be asking for a raise, or watching for the hammer to fall.

There are a few major outliers that bear mention. Boise State is getting a whopper of a deal (as noted in Fig 1), as well as Ohio State. On the unfortunate side, Duke is very far below par; the sole outcast in the negative 3rd standard deviation. This doesn't bode well for an athletics program under scrutiny to dial back costs.

So this has all been in good fun, and I certainly hope no one is actually fired on my account! Looking at Washington in particular, Sark seems to be just below the standard deviation, but in fairness he's only been coach since 2009. After our victory over Portland State this weekend, I'm hopeful he'll make up some lost ground this year!

The full table of data is below the fold...
Update: due to demand from the wise folks on Reddit, I have updated the table to be sorted by School name and added helmet thumbnails. (I took them down, it seemed to be causing havoc with his website)