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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.

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

### 1Re: Pythagoras Grades the Coaches

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.

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### 2Re: Pythagoras Grades the Coaches

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.

### 3Re: Pythagoras Grades the Coaches

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.

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