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Quarterback wins over Pythagoras

by Chase Stuart on July 18, 2012

in Passing, Statistics

No, this article isn’t an article about quarterbacks squaring off against ancient Greek mathematicians. Today, we’re going to look at quarterback win-loss records and see how they compare to their Pythagorean win-loss records.

Over 30 years ago, Bill James wrote that, on average, baseball teams’ true strengths could be measured more accurately by looking at runs scored and runs allowed than by looking at wins and losses. Since then, sports statisticians have applied the same thinking to all sports. The formula to calculate a team’s Pythagorean winning percentage is always some variation of:

(Points Scored^2) / (Points Scored ^2 + Points Allowed^2)

With the exponent changing from 2 to whatever number best fits the data for the particular sport. In football, that number is 2.53. We can look, for example, at the Pythagorean records for each team in the league last season, and line it up against their actual record:

Year
Tm
Record
Win%
PF
PA
Pyth Wins
Diff
2011KAN7-90.4382123383.763.24
2011GNB15-10.93856035912.082.92
2011DEN8-80.5003093905.712.29
2011OAK8-80.5003594336.141.86
2011NWE13-30.81351334211.781.22
2011NYG9-70.5633944007.851.15
2011ARI8-80.5003123486.91.1
2011TAM4-120.2502874943.230.77
2011TEN9-70.5633253178.250.75
2011NOR13-30.81354733912.330.67
2011BAL12-40.75037826611.340.66
2011ATL10-60.6254023509.390.61
2011SFO13-30.81338022912.520.48
2011CIN9-70.5633443238.640.36
2011PIT12-40.75032522711.40.6
2011MIA6-100.3753293138.5-2.5
2011MIN3-130.1883404495.3-2.3
2011PHI8-80.5003963289.87-1.87
2011CAR6-100.3754064297.44-1.44
2011SEA7-90.4383213158.19-1.19
2011IND2-140.1252434303.05-1.05
2011HOU10-60.62538127811.03-1.03
2011SDG8-80.5004063778.75-0.75
2011CLE4-120.2502183074.74-0.74
2011WAS5-110.3132883675.62-0.62
2011DAL8-80.5003693478.62-0.62
2011BUF6-100.3753724346.46-0.46
2011NYJ8-80.5003773638.38-0.38
2011CHI8-80.5003533418.35-0.35
2011STL2-140.1251934072.1-0.1
2011JAX5-110.3132433295.08-0.08
2011DET10-60.62547438710.01-0.01


Pythagorean records aren’t perfect predictors of the future, and no one claims that they are. To the contrary, it is established that there are better models one could use to predict a team’s future record. That said, for predictive purposes, Pythagorean records certainly have one benefit: they are more predictive than actual win-loss records.

Brett Keisel

But as is apt to happen when new statistics are introduced, certain other conclusions tend to be drawn. Consider the underlying features of the Pythagorean record: it says that wins and losses are irrelevant. A team that goes 1-2 while winning 30-0 and losing 17-16 and 17-14 will have a better Pythagorean record than a team that goes 3-0 while winning each game 20-17. What’s happened in recent years is “stats” guys tend to cite certain teams (think the Eagles and Chargers) as being “better than their record” because of their underlying statistics. Other might respond by simply saying that those teams tend to “choke” and don’t play up to their talent level.

As a result, in some corners, overachieving relative to your Pythagorean record is almost considered synonymous with being clutch, while underachievers are chokers. But, of course, arguments go both ways: Yes, one could argue that by winning frequently in close games, a team or quarterback is a winner and clutch and all that jazz. Alternatively, one could argue that by frequently losing in close games, a quarterback is unlucky, and underrated by those whom emphasize win-loss records for quarterbacks.

That said, we can at least add to the discussion. Presented below is the Pythagorean record for every quarterback with at least 100 games started (post-season, included) since 1950. As always, quarterbacks who played before 1950 may be included, but only their stats from since 1950 will be presented below. The list is sorted by quarterbacks with the most wins over Pythagoras.

QB
G
W
L
T
WIN%
PF
PA
Pyth W
Diff
Peyton Manning2271507700.66158624848140.39.7
Jake Plummer142717100.52803311661.59.5
Dan Marino25815510300.601594553541469
Dan Pastorini122596300.4842229257050.18.9
John Elway2521628910.64558644896154.38.2
Tom Brady1811404100.773488533031328
Jay Schroeder104644000.6152097196256.47.6
Jeff George127478000.372231299740.86.2
Eli Manning130775300.5923102287471.35.7
Ken Stabler1581035410.6553557291098.64.9
Brian Sipe113575600.5042248239052.14.9
Fran Tarkenton25013011460.53253505235128.44.6
Steve McNair163966700.5893541321091.64.4
Neil Lomax102475320.4712110235843.94.1
Jim Zorn106446200.4152120255740.73.3
Jim Plunkett154807400.51931433143773
Y.A. Tittle139785650.5793390308777.72.8
Jake Delhomme104614300.5872260205758.22.8
Babe Parilli104504770.5142308234950.82.7
Sonny Jurgensen149697370.4873210336969.92.6
Matt Hasselbeck158837500.5253513346180.52.5
Joe Namath132646440.52960304963.52.5
John Brodie164768080.4883548369877.72.3
Joe Theismann132834900.6292899242580.72.3
Jeff Blake100396100.392000248236.72.3
Phil Simms1691016800.5983430299698.82.2
Ben Roethlisberger127903700.7092964215587.82.2
Trent Dilfer119635600.5292121208560.82.2
Neil O'Donnell107584900.5422126204656.11.9
Bobby Layne139835240.6123298281483.31.7
Tommy Kramer114565800.4912343243154.31.7
Joe Ferguson175809500.4573287355778.81.2
Daunte Culpepper104436100.4132234261641.81.2
Jim Hart182879050.4923830391288.60.9
Charley Johnson124595780.5082756275162.10.9
Chris Chandler155698600.4453056336168.20.8
Archie Manning1393510130.2632212336535.70.8
Earl Morrall108673830.6342258184067.70.8
Jim McMahon103703300.682137160669.30.7
Joe Montana1871335400.71146053245132.40.6
Jim Kelly1771106700.62141073394109.40.6
Norm Van Brocklin105633840.6192808234064.40.6
Danny White102673500.6572573201266.40.6
Jim Harbaugh145687700.4692708285367.70.3
Billy Kilmer121635710.5252441235763.20.3
Dave Krieg1841018300.54939263631101.1-0.1
Richard Todd112506110.4512251242950.6-0.1
Jon Kitna125507500.42611305750.2-0.2
Tobin Rote119516440.4452722295953.2-0.2
Jack Kemp111674130.6172586213268.8-0.3
Bobby Hebert103564700.5442190202756.5-0.5
Craig Morton154866710.5622948265787.1-0.6
Lynn Dickey113466430.422226249748.3-0.8
Kerry Collins1878410300.4493671394984.9-0.9
Ken O'Brien112506110.4512261240351.7-1.2
Randall Cunningham144855810.5943320281686.8-1.3
Brett Favre32219912300.61877516361200.4-1.4
Brad Johnson132765600.5762806244477.4-1.4
Carson Palmer108505800.4632389246751.8-1.8
Jeff Garcia122606200.4922751270462.3-2.3
Bernie Kosar115565810.4912397234959-2.5
Kurt Warner129765300.5893440288578.6-2.6
Vinny Testaverde2199212610.4224271473495.3-2.8
Drew Brees162976500.5994335359699.8-2.8
Roger Staubach131963500.7333121200598.8-2.8
Milt Plum103564160.5732243190961.9-2.9
Dan Fouts178898810.5034231410092.5-3
Philip Rivers103663700.6412783209769.2-3.2
Johnny Unitas1941246640.64947253594129.3-3.3
George Blanda108555210.5142707251958.9-3.4
Steve Bartkowski131607100.4582670272763.8-3.8
Norm Snead158529970.3513096378459.4-3.9
Boomer Esiason178839500.4663893396087.1-4.1
Warren Moon21310510800.49346654568109.3-4.3
Jim Everett158669200.4183190347770.4-4.4
Steve Grogan138756300.5433089274179.4-4.4
Steve Beuerlein104485600.4622106209052.5-4.5
Bob Griese162986130.61434272717104.1-4.6
Roman Gabriel159866670.5633386292394.1-4.6
Steve DeBerg144548910.3782822324559.4-4.9
Mark Brunell161837800.5163480323388-5
John Hadl169827890.5123712347091.7-5.2
Donovan McNabb1771076910.60740563235113.2-5.7
Trent Green115565900.4872883271261.9-5.9
Drew Bledsoe1991019800.50841283889107-6
Steve Young1571025500.6540452958108.1-6.1
Terry Bradshaw1771215600.68440452776127.7-6.7
Troy Aikman1801057500.58339503241112.1-7.1
Ron Jaworski151777310.5132878261684.6-7.1
Ken Anderson178938500.52237943433100.2-7.2
Rich Gannon139805900.5763352270687.9-7.9
Len Dawson167996080.61739272972111.8-8.8
Bart Starr1671035860.63538402786115.6-9.6

(If you want to see a the list of the 271 quarterbacks with at least 20 games started, click here.)

What conclusions can we draw from this list? To each his own, of course. But for my money, not too much. John Elway and Tom Brady have reputations for being clutch, and indeed, they rank in the top six in quarterback wins over Pythagoras. But Jeff George was 6.2 wins over Pythagoras on significantly fewer starts, and ahead of “clutch” heroes such as Eli Manning and Ken Stabler. And any list that goes “Peyton Manning-Jake Plummer-Dan Marino” just looks odd. What’s even more surprising is who is at the bottom of the list. Bart Starr is considered one of the clutchest quarterbacks in football history, but this says he underachieved to the tune of 10 wins in his career. Troy Aikman, Terry Bradshaw and Steve Young — Hall of Famers with 10 Super Bowl rings among them — are in the bottom 10. Some think Philip Rivers isn’t clutch, and he sits below average on the above list: right next to Johnny Unitas.

Looking at the data on a per-game basis — i.e., wins over Pythagoras per game — doesn’t seem any more useful. The top overachieving quarterbacks are Jay Schroeder, Dan Pastorini, Jake Plummer, Jeff George, Tom Brady, Eli Manning, Brian Sipe, Peyton Manning, Neil Lomax and Dan Marino. The worst ten? From worst to tenth to worst, the list goes: Bart Starr, Rich Gannon, Len Dawson, Trent Green, Ron Jaworski, Steve Beuerlein, Ken Anderson, Troy Aikman, Steve Young and Terry Bradshaw.

It would seem difficult to cite this in support of Eli Manning or Tom Brady being clutch on one hand, and not to follow up by calling Bart Starr and Troy Aikman, chokers. As is often the case, I think the take-away is the least sexy one. Great quarterbacks tend to play well, but who wins close games often has more to do with luck than ability. Labels like clutch are finicky, anyway. Is Matt Ryan clutch? He’s got a reputation as being both “ice” cool in the clutch and of being a playoff choker. Is Tom Brady less clutch now than he was a seven years ago? When Aaron Rodgers’ reputation as being a “choker” because of a 1-11 record in close games dispelled when his team stormed through the playoffs and won Super Bowl XLV? Or does he still carry the label since his teams never trailed in three of those games and he never lead a 4th quarter comeback during the playoff run? After all, Rodgers is only 3-18 when presented with 4th quarter comeback opportunities.

{ 2 comments… read them below or add one }

Andrew July 18, 2012 at 3:44 am

Well, I think “clutchness” (I’m nearly certain that’s not a word) is hugely subjective. That being said, some of these names aren’t that surprising. Aikman played poorly in the Superbowl, and labeling him a “choker” because of that doesn’t seem to be that unreasonable. On the flipside, what about losses accrued because you defense was terrible or because you didn’t get an opportunity due to the sudden death rule? I tend to think that wins and losses, both regular season and in big post-season games, are immensly over-valued metrics for QB skill. There are 21 other starters, and numerous others who play throughout the game. Being the most important player on the field (in the current era, that is) doesn’t mean that any success or failure is your sole responsibility. I hate that everyone is fawning over Eli Manning now that he has two SB rings, even going so far as to suggest that he’s therefore a better QB than Peyton, but no one says Justin Tuck is the best pass rusher because of his rings. Terry Bradshaw has a ton of SB rings, but I don’t think of him as an all-time great at QB. His numbers simply don’t warrant it, and those SBs weren’t won on the strength of his arm. On the flipside, would you prefer a great QB who never won a SB, a la Marino, or a pretty good one who has won multiple rings, like Bradshaw or Eli Manning? I don’t know if that question has a right answer.

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pqlqi July 19, 2012 at 11:54 pm

most reasoned response i’ve seen on the interwebs in months. kudos

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