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The Dungy Index: Version 2.0

Each coach is given bonus points for mustaches.

Each coach is given bonus points for mustaches.

Back in 2006, Doug Drinen came up with the Dungy Index, a way to measure a coach’s performance in the regular season relative to expectations. Because Doug understands regression to the mean, he was impressed by Tony Dungy’s ability to continue to string together 12-win seasons year after year.1 But Doug didn’t want to just use winning percentage to rate coaches: expectations are lower when a coach inherits a bad team, and that needs to be taken into account.

Defining “expectations” is challenging. I don’t have a perfect way, but I do have a simple one: use a linear regression based off of last year’s Pythagorean winning percentage to predict the number of games a team should be expected to win this year.2 I did just that, and the best-fit formula was:

Year N+1 Wins = 4.23 + 0.472 * Year N Wins

So a 3-win team should be expected to win 5.6 games in Year N+1, a 10-win team is projected at 9.0 wins, and a 13-win team drops down to 10.4 expected wins. If you subtract the number of expected wins from the number of actual wins by the coach in a season, you are left with his number of wins over expectation. You’ll see pretty quickly why this is called the Dungy Index: he fares very, very well in it.

There are many drawbacks to this system. I’ve listed some of them at the end of the post. But as a first pass, this feels like an improvement over looking at raw wins or winning percentage. The table below shows all head coaches who coached 50+ games in the last 80 years. It is sorted by the “Wins over Exp” column. Dungy ranks 3rd on the list, and here is how his line reads: He first was a head coach in 1996 and last in 2008. He coached the Bucs and then the Colts. Dungy coached 208 games, winning 139 of them, for a 0.668 winning percentage. Dungy’s teams won 26.4 more games than you would have expected based on the regression formula. And since someone in the comments would have asked to see a list of wins over expectation per season, I added that to the end of the table, too. The table is fully sortable and searchable, and you can read some fine print at this footnote.3

CoachFirst YearLast YearTeamsGWinsWin %Win Over ExpWin Over Exp/S
Don Shula19631995clt-mia4903310.67650.71.54
George Halas19201967chi3632400.66132.61.09
Tony Dungy19962008tam-clt2081390.66826.42.03
Paul Brown19461975cle-cin298202.50.6826.31.14
Bill Belichick19912012cle-nwe2881870.64926.21.46
Marty Schottenheimer19842006cle-kan-was-sdg327200.50.61325.51.22
Tom Landry19601988dal406252.50.62225.30.9
Bill Parcells19832006nyg-nwe-nyj-dal303172.50.56922.31.18
John Madden19691978rai142106.50.7520.72.07
Vince Lombardi19591969gnb-was136990.72820.62.06
George Allen19661977ram-was168118.50.70520.61.71
Joe Gibbs19812007was2481540.62120.41.28
Bud Grant19671985min259160.50.62191.06
Bill Cowher19922006pit240149.50.62317.61.18
Chuck Knox19731994ram-buf-sea334186.50.55815.40.7
Tom Coughlin19952012jax-nyg2561470.57415.10.94
Mike Smith20082012atl80560.714.32.86
Ray Flaherty19361949was-naa-cra108720.66714.21.42
Mike Holmgren19922008gnb-sea2721610.59213.70.8
Mike Shanahan19882012rai-den-was2921670.57213.50.71
Blanton Collier19631970cle112770.68813.31.67
Dan Reeves19812003den-nyg-atl3571910.53512.50.54
Steve Owen19311953nyg2421470.60711.70.56
Sean Payton20062011nor96620.64611.51.92
Mike McCarthy20062012gnb112740.66111.51.64
Marv Levy19781997kan-buf2551430.56111.50.67
George Seifert19892001sfo-car1761140.64810.30.94
Jeff Fisher19942012oti-ram2781490.53610.20.57
Bill Walsh19791988sfo15292.50.6099.50.95
John Fox20022012car-den176940.5349.40.86
Don Coryell19731986crd-sdg195111.50.5729.10.65
Buck Shaw19461960sfo-phi13683.50.61490.82
John Harbaugh20082012rav80540.6758.91.78
Andy Reid19992012phi224130.50.5838.80.63
Chuck Noll19691991pit342193.50.5668.80.38
Jimmy Johnson19891999dal-mia144800.5568.40.93
Buddy Parker19491964crd-det-pit188108.50.57780.53
Jim Lee Howell19541960nyg84550.65581.14
Dennis Green19922006min-crd2071130.5467.90.61
Lovie Smith20042012chi144810.5637.70.86
Mike Ditka19821999chi-nor2161210.567.70.55
Lou Saban19601976nwe-buf-den18793.
Bum Phillips19751985oti-nor159820.5166.90.63
Mike Tomlin20072012pit96630.6566.61.1
Jimmy Conzelman19211948rii-mil-dpn-prv-crd6835.50.5226.61.09
Ted Marchibroda19751998clt-rav17083.50.4916.50.59
Wade Phillips19852010nor-den-buf-atl-dal143820.5736.30.57
John Rauch19661970rai-buf70410.5866.21.23
Greasy Neale19411950phi11165.50.595.60.56
Gary Kubiak20062012htx112590.5275.20.74
Jim Mora19862001nor-clt2311250.54150.33
Dick Vermeil19762005phi-ram-kan2291200.5244.40.3
Bobby Ross19922000sdg-det137740.544.40.49
Chuck Fairbanks19731978nwe85460.5414.40.73
Sid Gillman19551974ram-sdg-oti214115.50.544.20.25
Mike Martz20002005ram85530.6244.20.69
Ron Meyer19821991nwe-clt104540.5193.90.44
Mike Sherman20002005gnb96570.5943.60.6
Jon Gruden19982008rai-tam176950.543.40.31
Marvin Lewis20032012cin16079.50.4973.30.33
Art Shell19892006rai108560.5193.10.45
Tom Flores19791994rai-sea184970.5272.90.25
Allie Sherman19611968nyg112590.5272.90.36
Red Miller19771980den62400.6452.90.72
Jack Pardee19751994chi-was-oti164870.532.80.25
Joe Schmidt19671972det8446.50.5542.70.46
Weeb Ewbank19541973clt-nyj266133.50.5022.70.13
Hank Stram19601977kan-nor2241280.5712.60.16
Raymond Berry19841989nwe87480.5522.30.39
Jim Fassel19972003nyg11258.50.5222.30.33
Potsy Clark19311940det-bkn92510.55420.26
Charley Winner19661975crd-nyj9346.50.520.28
John Ralston19721976den7035.50.5071.90.38
Walt Michaels19771982nyj8739.50.4541.80.29
Steve Mariucci19972005sfo-det139720.5181.70.18
Jim Mora20042009atl-sea64310.4841.60.4
Pete Carroll19942012nyj-nwe-sea112580.5181.60.23
Brian Billick19992007rav144800.5561.40.16
Wayne Fontes19881996det133660.4961.40.16
Barry Switzer19941997dal64400.6251.40.34
Tony Sparano20082011mia61290.4751.30.31
Mike Holovak19611976nwe-nyj10856.50.5231.20.14
John Robinson19831991ram143750.5241.20.13
Brad Childress20062010min74390.5270.70.14
Dan Devine19711974gnb56270.4820.70.17
Mike Tice20012005min65320.4920.50.09
Jerry Glanville19851993oti-atl129600.4650.40.05
Sam Rutigliano19781984cle97470.485-0.2-0.03
Forrest Gregg19751987cle-cin-gnb16175.50.469-0.3-0.03
Walt Kiesling19391956pit-phi-crd9032.50.361-0.4-0.04
Red Hickey19591963sfo5527.50.5-0.4-0.08
Buddy Ryan19861995phi-crd11155.50.5-0.4-0.06
Ken Whisenhunt20072012crd96450.469-0.5-0.09
Jerry Burns19861991min95520.547-0.7-0.12
Eric Mangini20062010nyj-cle80330.413-0.8-0.15
Wally Lemm19611970oti-crd13567.50.5-0.9-0.09
Butch Davis20012004cle58240.414-1-0.26
Curly Lambeau19211953gnb-crd-was239136.50.571-1.2-0.06
John Mackovic19831986kan64300.469-1.3-0.33
Gene Stallings19861989crd5823.50.405-1.4-0.34
Rex Ryan20092012nyj64340.531-1.4-0.35
Gus Dorais19431947det53210.396-1.5-0.3
Vince Tobin19962000crd71280.394-1.6-0.31
Jack Patera19761982sea80330.413-1.9-0.32
Jack Del Rio20032011jax139680.489-2-0.22
Jack Christiansen19631967sfo6727.50.41-2.1-0.41
Red Strader19481955naa-nyy-sfo58260.448-2.3-0.46
Dutch Clark19371942det-ram66310.47-2.5-0.41
Mike Nolan20052008sfo55180.327-2.5-0.63
Nick Skorich19611974phi-cle9847.50.485-2.9-0.42
Ray Rhodes19951999phi-gnb8037.50.469-2.9-0.59
Dave Wannstedt19932004chi-mia169820.485-3-0.27
Ray Malavasi19661982den-ram85440.518-3.1-0.51
Jim Haslett20002008nor-ram108470.435-3.1-0.44
George Wilson19571969det-mia146690.473-3.1-0.29
Neill Armstrong19781981chi64300.469-3.3-0.83
Chan Gailey19982012dal-buf80340.425-3.8-0.76
Jim Hanifan19801989crd-atl9339.50.425-3.9-0.56
Dick Jauron19992009chi-det-buf142600.423-4.1-0.41
June Jones19941998atl-sdg58220.379-4.2-1.04
Joe Walton19831989nyj11153.50.482-4.5-0.64
Tommy Prothro19711978ram-sdg88360.409-4.5-0.64
Alex Webster19691973nyg7029.50.421-4.5-0.9
Norm Van Brocklin19611974min-atl15966.50.418-4.7-0.39
Dave McGinnis20002003crd57170.298-5-1.26
Jim Dooley19681971chi56200.357-5.4-1.36
Bart Starr19751983gnb13153.50.408-5.4-0.61
Bill McPeak19611965was7022.50.321-5.8-1.17
Jim Schwartz20092012det64220.344-5.8-1.46
Joe Kuharich19521968crd-was-phi14259.50.419-5.9-0.53
Mike McCormack19731982phi-clt-sea8129.50.364-5.9-0.99
Dick Nolan19681980sfo-nor15671.50.458-6-0.55
Bill Austin19661970pit-was5618.50.33-6.2-1.55
Pop Ivy19581963crd-oti76330.434-6.2-1.03
Monte Clark19761984sfo-det11951.50.433-6.4-0.8
John McKay19761984tam11944.50.374-6.5-0.81
Norv Turner19942012was-rai-sdg237114.50.483-6.6-0.44
Leeman Bennett19771986atl-tam119500.42-6.7-0.84
Darryl Rogers19851988det58180.31-6.8-1.7
Ray Perkins19791990nyg-tam117420.359-6.9-0.87
Sam Wyche19841995cin-tam191840.44-7.1-0.59
Romeo Crennel20052012cle-kan83280.337-7.4-1.24
Dennis Erickson19952004sea-sfo96400.417-7.5-1.26
Dom Capers19952005car-htx96370.385-7.6-1.26
Bruce Coslet19902000nyj-cin124470.379-7.7-0.86
Harland Svare19621973ram-sdg7423.50.318-8-1.14
Rich Kotite19911996phi-nyj96400.417-8.4-1.39
Bert Bell19361941phi-pit58110.19-8.9-1.48
Lindy Infante19881997gnb-clt96360.375-9-1.5
David Shula19921996cin71190.268-9.1-1.82
Joe Bugel19901997crd-rai80240.3-9.7-1.94
Herman Edwards20012008nyj-kan128540.422-11-1.37
Dan Henning19831991atl-sdg11238.50.344-12.1-1.73
Marion Campbell19741989atl-phi11534.50.3-14.9-1.66

We can take a closer look at Dungy’s career. While he did well in Tampa Bay, and he receives a significant amount of credit for his work with the Buccaneers in 1997, the majority of Dungy’s value comes from keeping the Colts among the elite teams in the league for seven straight years.

YearTeamExp. WinsWWin Over Exp

As a reminder, this is just another tool to examine head coaches, not the tool to measure them. There are many flaws with this study: I’ll start with six, but I’m sure you guys can think of some more.

  • I should probably use a different regression formula for different eras. Presumably, team winning percentages are “less sticky” now than they used to be, which would imply that a regression formula for the ’70s would differ from what we would use now. It’s worth keeping in mind that doing this would only serve to make Dungy look better, I imagine.
  • I should use a different exponent to come up with Pythagorean records for different eras. I used 2.5 as the exponent for all years because I’m lazy.
  • I excluded all seasons when a coach was taking over an expansion team. Since different expansion teams were given different benefits, I decided to punt on this issue instead of thinking about a thoughtful answer.
  • I created career rankings by summing the values for each season. That’s probably not the best way to do things, although again, a method that focuses more on peak production will likely only serve to benefit Dungy.
  • “Wins over projected wins” is a flawed way to measure coaches. It should also go without saying that projecting team wins based solely on Pythagorean record in Year N-1 is not a perfect way to measure projected wins, even if that wasn’t a flawed method to measure a coach.
  • Playoff wins are obviously way more important than everything else, and are currently ignored in this system. But in case you forgot, I already looked at playoff wins over expectations when I used the Vegas lines (or the SRS) to come up with expectations. Dungy graded out as below average in that system.

So if I have all of these caveats, why am I posting this? One answer is that I’m a good enougher. Another answer: most of the things I mentioned are easy enough to fix the next time around and won’t have a big impact on the results (but would have taken some time to implement). So before I spend a lot of time doing fixing those problems, I’d be curious to hear your general thoughts on this system, and any other tweaks you think I should consider implementing.

  1. Admittedly, this looks less impressive when you consider that Jim Mora, Jim Caldwell, and John Fox have won 13+ games with Peyton Manning, too. []
  2. All ties are counted as half-wins. []
  3. A. All coaches were included, but only their seasons since 1933 were counted. So George Halas’ line does not represent his career numbers, but instead his production since 1933. Why 1933? Because 1932 is a somewhat useful cut-off point, which makes it the first Year N-1 in the sample.
    B. I did not count any games where a coach was in charge of an expansion team. So Dom Capers’ line does not show his career line, either.
    C. I counted a tie as half a win. Don Shula did not win 331 games; he won 328 games and tied in six other games, but I am using 331 as a shorthand.
    D. For coaches who were fired or hired in mid-season, I used their actual number of wins but subtracted the pro-rated number of expected wins. []
  • “I should probably use a different regression formula.”

    Oh man! All I have to say is, “Stay tuned.”

    • Chase Stuart

      Yet another reason to be a good enougher: someone else can do the work for me in between versions!

  • Shattenjager

    I find it rather funny that there are Shulas in the top five and bottom five in total wins over expectation.

    Per season, Mike Smith is quite the outlier. Obviously, his career so far is rather short compared to the other top guys, but he’s .79 wins per season above second!

    How in the world did Marion Campbell keep getting jobs?

    • Chase Stuart

      Yeah, Smith is well on his way to becoming another Dungy.

      Good question about Campbell. His coaching resume is pretty unimpressive.

      • Richie

        Yeah, Smith is well on his way to becoming another Dungy.

        I think it’s quite helpful to have your coaching career coincide with the prime of a QB who is consistently good-to-very good and consistently healthy. That’s something that most of the guys at the top of the list have in common.

  • Vishal

    In the expected year n+1 wins formula what is year n wins? expected wins in year n or actual wins in year n?
    If it is the latter, why are Dungy’s expected wins in 2004, 2005 and 2007 different when the year n wins should be 12 in all cases?

    On an unrelated note, 4 of the top 10 (and 2 of the top 5) coaches in terms of wins over expected per season coached in the last decade. Similarly, 5 of the top 10 (and 11 of the top 20) coached in the last 20 years. Either we are living in an era of legendary coaching talent or this statement – ” …team winning percentages are “less sticky” now than they used to be…” – may not be as accurate as you think.

    • Chase Stuart

      Year N wins are disregarded; only Pythagorean wins from Year N are included.

      As for your other point, I suspect that if you ran this study at any point over the last 30 years, recent coaches would do best in Expected Wins per Season. That’s because the best recent coaches haven’t had their down periods yet. Had we run this in 1999, Mike Shanahan and Dennis Green would probably look great.

      • Richie

        Did you adjust for length of seasons? (14-game, 16-game, etc.)

        • Chase Stuart

          I did not. Another easy thing to add, although my thinking was old-timers already have a benefit in this sort of thing because of the summing of each season.

  • Kibbles

    One problem with grading coaches based on how much they outperform expectations is that they’re part of setting expectations. If some hypothetical coach existed whose mere presence on a team improved their scoring differential by 100 points, this system would underrated him, because it would set expectations in year N+1 off of the 100-point-improved version of the team in year N.

    Of course, this is just another factor that makes Dungy’s run look more impressive.

    • Chase Stuart

      Correct on both accounts.

      I haven’t thought through the math completely, but I don’t think this will change things much. My current rankings compress things slightly, but that’s about it. Every great coach is slightly underrated, while every bad coach is slightly overrated.

  • The Question

    Your model says that Jason Garrett exceeds expectations by stringing together 9-7 seasons.

    I know gambling is immoral, but why not use the over under line from Vegas as “expectations?”

    • Chase Stuart

      Because I don’t have historical over/under lines.