Pythagoras Grades the Coaches

By Aaron Schatz

In Pythagoras on the Gridiron [1], one of the first articles we posted here on FootballOutsiders.com, we noted that an NFL team's season record can usually be predicted based on points scored and allowed, a system known to baseball fans as the Pythagorean Theorem.  When a team finishes with more or less wins than their performance would otherwise indicate, a large part of that is luck.  But is it luck only?  What about coaching?

In football, the rules of the game change late in each half.  All of a sudden, time is limited, and 60 yards just don't cut it when you need to get 80 in three minutes.  So it would make sense that poor clock management is probably a frequent problem with teams that under-perform their predictions, and vice versa.  And if this is the case, then some coaches would have a pattern of outperforming their teams' projections, while others would have a pattern of underperforming.

When I first pondered this theory, the first man to come to mind was the man who may be the best coach in the history of the NFL: The Tuna, Bill Parcells.  One sign of Parcells' greatness might be a pattern of teams that win more games than projected, which is an indication of good clock management and the ability to take the close ones.

So I ran Parcells coaching record, starting with the 1983 New York Giants:

BILL PARCELLS
 

The standard deviation of luck for all NFL teams over the past 20 years is .0617, and conveniently that is almost exactly the same as the difference of one win in a 16 game season, which is .0625.  You'll notice that seasons where the team finished at least a game over projection are highlighted blue, while seasons where the team finished at least a game under projection are highlighted red.

As we might expect, Parcells' teams, on average, finish with a better record than their Pythagorean projection would indicate.  You'll notice an interesting pattern, though, that doesn't demonstrate confidence in anyone picking the "over" on the 2003 Cowboys.  Parcells' teams each underperformed in his first year with a new club.  Even the 1997 Jets, who we consider massive overachievers due to their 1-15 record the previous year, actually won one less game than they should have given their 348 points scored and 287 points allowed.

How good is Parcells compared to other coaches?  Actually, he's not that great.  Parcells' average of +.006 is pretty insignificant.  He doesn't finish among the top 25 coaches with five or more years in the since the 1982 strike.  Here's a coach who looks a little better.  Thanks to the interest of our resident Bucs fan, Ian, I looked next at Tony Dungy:

TONY DUNGY
 

OK, that looks a little better, but Dungy's record still presents a mix of teams that had "positive luck" and teams that had "negative luck."  The records of most coaches look like this, and most of the numbers here are not large.  With only 16 games on the schedule, it is easy for a team to miss projection by a fraction of a game, and that doesn't really mean anything.  Even if adding together a coach's entire record shows a trend towards beating the yearly Pythagorean projection -- or falling short of it -- coaches tend to move back and forth between overachieving and underachieving years.

But some don't.  Some coaches demonstrate very clear trends, leading team after team to a record better (or worse) than the Pythagorean projection. And the very best coaches by this measurement are a bit surprising.

I took every NFL team in every season since 1983 and compared the Pythagorean projection for each team to its actual record.  Then I listed every coach with at least five seasons running a team since 1983, and also created an additional chart of any coach with only three or four seasons who is active as of 2003.  Any season where a coach ran the team for less than six games was not counted.

Here are the top 10 coaches with at least five seasons, ranked by average "luck" -- or how much their teams exceeded the projection in an average year.  The chart also includes the number of seasons where the team exceeded its projection by more than one win, and the number of seasons where the team missed its projection by more than one loss.  STDEV LUCK is the standard deviation of luck for that coach over the seasons represented -- the lower this number, the more consistent the coach was in exceeding (or in a later chart, missing) the team's projection. 

You'll notice something similar about the top three guys.  In fact, I would like to now take the opportunity to point Jesse Jackson towards the donation button on the lower right-hand portion of the screen.

TOP 10 COACHES, 1983-2002
 

Yes, that's right, Art Shell.  Art Shell took over the Los Angeles Raiders four games into the 1989 season and coached them through 1994, and never finished below the Pythagorean projection.  He is the only coach over the past 20 years to beat the standard deviation over his entire career average.  Here is Shell's full record:

ART SHELL
 

So here we have a coach who made the playoffs four times in six years.  His team won at least one more game than its Pythagorean projection three times, including the 1993 team which ranks among the top 10 overachievers of the last 20 years.  And yet it has been a decade since anyone gave him a head coaching job.

Now, I know that this method measures only one small part of a coach's ability.  It doesn't reflect general game planning, or motivation, or roster construction, or how well you get your team into shape in those August two-a-days.  But don't you think there should be a job for Art Shell in a league that runs guys like Dennis Erickson out there over and over?

I also think that, after looking at this chart, you have to have a lot of respect for Dan Reeves.  Here's a guy who has consistently won more games than the Pythagorean projection over 20 years with three different franchises.  2002 was actually one of his rare underachieving years.

OK, so those are the top overachieving coaches.  What about the top underachievers, the guys who consistently win fewer games than their teams' projections year after year?  Well, the man at the bottom is really going to shock you.  Let's see if you can recognize this guy:

COACH X
 

Yes, that is two-time Super Bowl champion Dick Vermeil.  Since his 1997 comeback, Vermeil has endured five straight seasons below the Pythagorean projection, and in four of those seasons his teams were more than a whole win worse.

OK, so you may be thinking, maybe this is a hazard of playing that up-tempo St. Louis offensive game.  After all, defense wins championships, right?  Well, look above.  Yes, while Dick Vermeil is at the very bottom of the list, Mike Martz would be in the top ten if he had two more seasons under his belt.  Here are the two coaches combined for the last six years of Rams football:

ST. LOUIS RAMS, 1997-2002
 

So, three underachieving years under Vermeil, followed by three overachieving years under Martz, playing basically the same style.  That doesn't look good for Vermeil.  If you want to find a Dick Vermeil team that had a better record than its Pythagorean projection, you have to go back to 1979, the year before the Eagles won the Super Bowl.

DICK VERMEIL (INCLUDES PRE-1982, SEASONS WEIGHTED TO 16 GAMES IN AVERAGE)
 

Dick Vermeil isn't the only well-regarded Super Bowl champion coach who doesn't come out very well according to Pythagoras.  I was pretty shocked about this:

BILL BELICHICK
 

In case it isn't obvious from the pro-Patriots slant of my articles, I worship the ground Bill Belichick walks on.  At least I can take some solace in the fact that the only two Belichick teams that haven't underachieved have been the last two.  Both Belichick and Vermeil appear on the list of the 10 most underperforming coaches of the past 20 years.  I lowered the threshold to four seasons here because two of the lowest-ranking coaches couldn't quite finish that fifth year.

BOTTOM 10 COACHES, 1983-2002
 

Hey, Crimson Tide fans, this is why younger brother Mike now coaches your team while David runs the family steakhouse business.  Finally, for fun, here are the top five and bottom five coaches based on standard deviation -- the most and least consistent coaches when it comes to the Pythagorean Theorem.  Five year minimum is required for this table.

TOP 5 AND BOTTOM 5 COACHES, STANDARD DEVIATION OF LUCK
 

Yes, not only does Dick Vermeil suck, he sucks with amazing consistency.

Looking for your favorite coach?  This page [2] is the chart of all coaches with at least five years between 1983-2002 (plus active coaches with three or four years).  This page [3] is a year-by-year look at some of the more significant coaches of the past two decades.