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07 Aug 2003

Pythagoras Grades the Coaches

By Aaron Schatz

In Pythagoras on the Gridiron, 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
 

Year Team W L T PCT PF PA PYTH PYTH WIN LUCK
1983
New York Giants
3
12
1
0.219
267
347
0.350
6
-0.131
1984
New York Giants
9
7
0
0.563
299
301
0.496
8
0.066
1985
New York Giants
10
6
0
0.625
399
283
0.693
11
-0.068
1986
New York Giants
14
2
0
0.875
371
236
0.745
12
0.130
1987
New York Giants
6
9
0
0.400
280
312
0.436
7
-0.036
1988
New York Giants
10
6
0
0.625
359
304
0.597
10
0.028
1989
New York Giants
12
4
0
0.750
348
252
0.682
11
0.068
1990
New York Giants
13
3
0
0.813
335
211
0.749
12
0.063
1993
New England Patriots
5
11
0
0.313
238
286
0.393
6
-0.080
1994
New England Patriots
10
6
0
0.625
351
312
0.569
9
0.056
1995
New England Patriots
6
10
0
0.375
294
377
0.357
6
0.018
1996
New England Patriots
11
5
0
0.688
418
313
0.665
11
0.023
1997
New York Jets
9
7
0
0.563
348
287
0.612
10
-0.050
1998
New York Jets
12
4
0
0.750
416
266
0.743
12
0.007
1999
New York Jets
8
8
0
0.500
308
309
0.498
8
0.002
  AVERAGE
9.2
6.7
 
0.579
   
0.572
9.1
0.006

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
 

Year Team W L T PCT PF PA PYTH PYTH WIN LUCK
1996
Tampa Bay Buccaneers
6
10
0
0.375
221
293
0.339
5
0.036
1997
Tampa Bay Buccaneers
10
6
0
0.625
299
263
0.575
9
0.050
1998
Tampa Bay Buccaneers
8
8
0
0.500
314
295
0.537
9
-0.037
1999
Tampa Bay Buccaneers
11
5
0
0.688
270
235
0.582
9
0.106
2000
Tampa Bay Buccaneers
10
6
0
0.625
388
269
0.704
11
-0.079
2001
Tampa Bay Buccaneers
9
7
0
0.563
324
280
0.586
9
-0.023
2002
Indianapolis Colts
10
6
0
0.625
349
313
0.564
9
0.061
  AVERAGE
9.1
6.9
 
0.571
   
0.555
8.9
0.016

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
 

COACH
WINS
LOSSES
PCT
YEARS
PYTH
PYTH WINS
LUCK
>1 OVER
>1 UNDER
STDEV LUCK
Shell, Art
9.4
6.6
0.587
5.8
0.502
8.0
0.085
3
0
0.055
Rhodes, Ray
7.5
8.5
0.469
5.0
0.415
6.6
0.053
2
0
0.074
Green, Dennis
9.7
6.3
0.606
10.0
0.556
8.9
0.050
5
0
0.066
Meyer, Ron
8.5
7.3
0.538
5.5
0.487
7.7
0.050
2
0
0.097
Fassel, Jim
9.1
6.9
0.568
6.0
0.522
8.3
0.046
2
0
0.033
Gibbs, Joe
10.8
5.1
0.680
10.0
0.636
10.1
0.044
4
0
0.066
Reeves, Dan
8.8
7.2
0.552
20.0
0.515
8.2
0.037
9
3
0.079
Mariucci, Steve
9.5
6.5
0.594
6.0
0.559
8.9
0.035
2
1
0.072
Schottenheimer, Marty
9.7
6.2
0.611
16.5
0.577
9.2
0.034
6
1
0.060
Shula, Don
9.8
6.2
0.613
13.0
0.583
9.3
0.030
6
0
0.049
(APPENDIX: ACTIVE, 3-5 YEARS)
Sherman, Mike
11.0
5.0
0.688
3.0
0.626
10.0
0.062
1
0
0.067
Martz, Mike
10.3
5.7
0.646
3.0
0.600
9.6
0.046
1
0
0.018
Haslett, Jim
8.7
7.3
0.542
3.0
0.510
8.2
0.031
0
0
0.029

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
 

Year Team W L T PCT PF PA PYTH PYTH WIN LUCK
1989
Los Angeles Raiders
7
5
0
0.583
215
204
0.531
6
0.052
1990
Los Angeles Raiders
12
4
0
0.750
337
268
0.633
10
0.117
1991
Los Angeles Raiders
9
7
0
0.563
298
297
0.502
8
0.061
1992
Los Angeles Raiders
7
9
0
0.438
249
281
0.429
7
0.009
1993
Los Angeles Raiders
10
6
0
0.625
306
326
0.463
7
0.162
1994
Los Angeles Raiders
9
7
0
0.563
303
327
0.455
7
0.108
  AVERAGE
9.4
6.6
 
0.587
   
0.502
8.0
0.085

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
 

Year Team W L T PCT PF PA PYTH PYTH WIN LUCK
1997
Guess!
5
11
0
0.313
299
359
0.393
6
-0.081
1998
Guess!
4
12
0
0.250
285
378
0.339
5
-0.089
1999
Guess!
13
3
0
0.813
526
242
0.863
14
-0.050
2001
Guess!
6
10
0
0.375
320
344
0.457
7
-0.082
2002
Guess!
8
8
0
0.500
467
399
0.592
9
-0.092
  AVERAGE
7.2
8.8
 
0.450
   
0.529
8.5
-0.079

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
 

Year Team W L T PCT PF PA PYTH PYTH WIN LUCK COACH
1997
St. Louis Rams
5
11
0
0.313
299
359
0.393
6
-0.081
Vermeil
1998
St. Louis Rams
4
12
0
0.250
285
378
0.339
5
-0.089
Vermeil
1999
St. Louis Rams
13
3
0
0.813
526
242
0.863
14
-0.050
Vermeil
2000
St. Louis Rams
10
6
0
0.625
540
471
0.580
9
0.045
Martz
2001
St. Louis Rams
14
2
0
0.875
503
273
0.810
13
0.065
Martz
2002
St. Louis Rams
7
9
0
0.438
316
369
0.409
7
0.028
Martz

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)
 

Year Team W L T PCT PF PA PYTH PYTH WIN LUCK
1976
Philadelphia Eagles
4
10
0
0.286
165
286
0.214
3
0.072
1977
Philadelphia Eagles
5
9
0
0.357
220
207
0.536
8
-0.179
1978
Philadelphia Eagles
9
7
0
0.563
270
250
0.545
9
0.017
1979
Philadelphia Eagles
11
5
0
0.688
339
282
0.607
10
0.080
1980
Philadelphia Eagles
12
4
0
0.750
384
222
0.786
13
-0.036
1981
Philadelphia Eagles
10
6
0
0.625
368
221
0.770
12
-0.145
1982
Philadelphia Eagles
3
6
0
0.333
191
195
0.488
4
-0.154
1997
St. Louis Rams
5
11
0
0.313
299
359
0.393
6
-0.081
1998
St. Louis Rams
4
12
0
0.250
285
378
0.339
5
-0.089
1999
St. Louis Rams
13
3
0
0.813
526
242
0.863
14
-0.050
2001
Kansas City Chiefs
6
10
0
0.375
320
344
0.457
7
-0.082
2002
Kansas City Chiefs
8
8
0
0.500
467
399
0.592
9
-0.092
  AVERAGE
7.802
8.2
 
0.488
   
0.549
8.8
-0.062

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
 

Year Team W L T PCT PF PA PYTH PYTH WIN LUCK
1991
Cleveland Browns
6
10
0
0.375
293
298
0.490
8
-0.115
1992
Cleveland Browns
7
9
0
0.438
272
275
0.494
8
-0.056
1993
Cleveland Browns
7
9
0
0.438
304
307
0.494
8
-0.057
1994
Cleveland Browns
11
5
0
0.688
340
204
0.770
12
-0.083
1995
Cleveland Browns
5
11
0
0.313
289
356
0.379
6
-0.066
2000
New England Patriots
5
11
0
0.313
276
338
0.382
6
-0.070
2001
New England Patriots
11
5
0
0.688
371
272
0.676
11
0.011
2002
New England Patriots
9
7
0
0.563
381
346
0.557
9
0.006
  AVERAGE
7.6
8.4
 
0.477
   
0.530
8.5
-0.054

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
 

COACH
WINS
LOSSES
PCT
YEARS
PYTH
PYTH WINS
LUCK
>1 OVER
>1 UNDER
STDEV LUCK
Shula, David
4.1
11.9
0.254
4.4
0.335
5.4
-0.081
0
2
0.088
Vermeil, Dick
7.2
8.8
0.450
5.0
0.529
8.5
-0.079
0
4
0.017
Henning, Dan
5.5
10.5
0.344
7.0
0.419
6.7
-0.075
0
4
0.066
Pardee, Jack
8.7
7.3
0.545
4.6
0.618
9.9
-0.073
0
2
0.072
Burns, Jerry
8.7
7.2
0.547
6.0
0.612
9.7
-0.065
0
3
0.085
Bugel, Joe
4.8
11.2
0.300
5.0
0.356
5.7
-0.056
0
3
0.091
Gregg, Forrest
6.5
9.3
0.411
5.0
0.465
7.4
-0.054
0
2
0.081
Belichick, Bill
7.6
8.4
0.477
8.0
0.530
8.5
-0.054
0
4
0.043
Turner, Norv
7.2
8.6
0.456
6.8
0.498
8.0
-0.042
0
2
0.068
Reid, Andy
9.8
6.3
0.609
4.0
0.649
10.4
-0.039
0
1
0.028

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
 

COACH
WINS
LOSSES
PCT
YEARS
PYTH
PYTH WINS
LUCK
>1 OVER
>1 UNDER
STDEV LUCK
Infante, Lindy
6.0
10.0
0.375
6.0
0.410
6.6
-0.035
2
3
0.128
Marchibroda, Ted
6.6
9.4
0.415
7.0
0.388
6.2
0.027
2
1
0.125
Coughlin, Tom
8.5
7.5
0.531
8.0
0.549
8.8
-0.018
4
3
0.109
Flores, Tom
7.8
8.1
0.487
8.0
0.484
7.7
0.003
2
1
0.109
Seifert, George
10.4
5.6
0.648
11.0
0.677
10.8
-0.029
3
4
0.108
                     
Ryan, Buddy
7.9
7.9
0.500
7.0
0.485
7.7
0.015
1
0
0.046
Belichick, Bill
7.6
8.4
0.477
8.0
0.530
8.5
-0.054
0
4
0.043
Campbell, Marion
4.9
10.9
0.309
6.0
0.323
5.1
-0.014
0
1
0.042
Fassel, Jim
9.1
6.9
0.568
6.0
0.522
8.3
0.046
2
0
0.033
Vermeil, Dick
7.2
8.8
0.450
5.0
0.529
8.5
-0.079
0
4
0.017

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

Posted by: Aaron Schatz on 07 Aug 2003

3 comments, Last at 02 Sep 2007, 2:45am by Len

Comments

1
by empty13 (not verified) :: Sun, 03/26/2006 - 12:05am

Like something similar I have used, it is conducive to noting trends, which have some utility in guiding bets.

Being one game off over 16 can mean little, however. Most really good teams end up giving up one game late in a season in order to preserve their studs, whether they have clinched HFA positively or not. Some really bad teams end up winning a game they shouldnt late in the year because of the preceding statement, and/or because another team simply doesnt take them seriously (ne @ MIA, late 04 season).

So maybe it should only track performance in "meaningful games".

It would be interesting to see if the trends continue from 2003 on. I suspect that for Dennis Green, they do not.

It also seems that a fair number of coaches who didnt win a championship look real good if only the Pythagorean approach is considered.

Good PY coaches won 3 in 107 seasons = 2.8% (all Joe Gibbs) and likely decreasing with time.

Bad PY coaches won 2/55 = 3.6% and likely increasing with time.

/////////////

2
by Paul (not verified) :: Tue, 07/18/2006 - 3:33pm

Basing a coach's ranking on his year to year performance is far from reveiling the truth. One has to look at trends and what a coach starts and finishes with. If you look at Vermeil you will see year after year he in most cases betters his team. This is through player aquisitions, coaching, etc. IE the complete picture not just an overall win/loss record.

3
by Len (not verified) :: Sun, 09/02/2007 - 2:45am

Holy cow.

I came here because of a sidebar in an issue of ESPN slamming Norv Turner only to discover the same formula considers Belichick, Buddy Ryan and Vermeil bad coaches.

This simply doesn't work.