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Even for Football Perspective, this is a very math-heavy post. I’ve explained all the dirty work and fine details behind this system, but if you want to skip to the results section, I’ll understand. Heck, it might even make more sense to start there and then work your way back to the top.

Background

In 2012, Neil Paine wrote a fascinating article on championship leverage in the NBA, building on Tom Tango’s work on the same topic in Major League Baseball. Championship Leverage was borne out of the desire to quantify the relative importance of any particular playoff game. Truth be told, this philosophy has more practical application in sports where each playoff round consists of a series of games. But Neil applied this system to the NFL playoffs and crunched all the data for every playoff game since 1965. Then he was kind enough to send it my way, and I thought this data would make for a good post.

The best way to explain Championship Leverage is through an example. For purposes of this exercise, we assume that every game is a 50/50 proposition. At the start of the playoffs, the four teams playing on Wild Card weekend all have a 1-in-16 chance of winning the Super Bowl (assuming a 50% chance of winning each of four games). This means after the regular season ended, the Colts had a 6.25% chance of winning the Super Bowl. After beating Kansas City, Indianapolis’ win probability doubled to 12.5%. Win or lose, the Colts’ Super Bowl probability was going to move by 6.25%, a number known as the Expected Delta.

New England, by virtue of a first round bye, began the playoffs with a 12.5% chance of winning the Lombardi. With a win over Indianapolis, the Patriots’ probability of winning the Super Bowl jumped 12.5% to 25%; had New England lost, the odds would have moved from 12.5% to zero. Therefore, the Expected Delta in a Division round game is 12.5%.

By beating Indianapolis, New England set up a crucial showdown with Denver. A win would again double the Patriots’ Super Bowl odds, this time from 25% to 50%, while a loss would drop it to zero. In the conference championship round, the Expected Delta is always 25%.

Denver also started the playoffs with a 12.5% chance of winning the Super Bowl, since the Broncos don’t get any extra credit for rostering Peyton Manning. Those odds jumped to 25% after beating San Diego and up to 50% after beating the Patriots. The Super Bowl, of course, has an Expected Delta of 50%. After the game, Denver’s odds of being Super Bowl champs will have moved 50% to either 100% or 0%.

There are 11 games (or 22 if you look at each game as one game for each team) in every NFL postseason, at least since 1990. The final game has an Expected Delta of 50%; the previous two each have an Expected Delta of 25%; the four before that each have an Expected Delta of 12.5%; and the first four each have an Expected Delta of 6.25%. This means, on average, each playoff game in the NFL has an average Expected Delta of 15.91%.

[math]( 4 * .0625 + 4 * .0125 + 2 * .25 + 1 * .50 )/11 = .1591[/math]

This means that the Super Bowl — with an Expected Delta of .50 — is 3.14 times as “important” as the average playoff game. That importance is what we call the Leverage Index, and at least since 1990, each Super Bowl has had a Leverage Index of 3.14. Peyton Manning’s performance against Seattle comes with a Leverage four times as great as Manning’s game against San Diego, because the stakes are four times as high. I’m reticent to ever type the word clutch, but using this method, we can at least quantify the stakes for each game.

Calculating a Quarterback’s Leverage-Adjusted Postseason Value

We can use this metric to grade each individual postseason by a quarterback after accounting for Leverage. For each game in the Super Bowl era, Neil calculated the Adjusted Net Yards per Attempt average allowed by each defense during the regular season, and then gave each quarterback credit (or blame) for his ANY/A average relative to that particular defense. By using this method, we have both an era and SOS adjustment all in one. Then, each quarterback’s production is adjusted for leverage. Let’s work through an example.

Warner was dominant in the 2008 postseason

Warner was dominant in the 2008 postseason.

In the first round of the 2008 playoffs, Kurt Warner faced the Atlanta Falcons, who allowed an average of 5.96 ANY/A during the regular season. Warner produced a 19/32-271-2-1 (0-0) sack line, meaning he completed 19 of 32 passes for 271 yards, threw two touchdowns and one interception, and was not sacked. That gave Warner an ANY/A average of 8.31, 2.35 ANY/A better than we would expect (based on the Atlanta defense). Of course, this was not a particularly significant game: the leverage was only 0.39.

The following week, Warner went 21/32-220-2-1 (1-5) against the Panthers. Carolina allowed 5.43 ANY/A during the regular season, and Warner averaged 6.36 ANY/A in this game, giving him 0.93 ANY/A over expectation. The leverage was 0.79.

In the conference championship game, Warner faced an Eagles defense that allowed only 4.57 ANY/A during the regular season, but he went 21/28-279-4-0 (2-12); that works out to an 11.57 ANY/A average, giving him an incredible 7.00 ANY/A better than average in a game with a leverage of 1.57.

Then, in the Super Bowl, Warner was again outstanding. The Steelers defense allowed only 3.17 ANY/A to opposing quarterbacks during the regular season but Warner (31-43-377-3 (2-3), an 8.64 ANY/A average) was 5.47 ANY/A better than that against Pittsburgh. The Super Bowl, of course, has a leverage of 3.14.

All told, Warner had 140 attempts (including sacks). On average, each pass attempt came in a game with a Leverage of 1.62 (Warner’s four games, by definition, had Leverages of 0.39, 0.79, 1.57, and 3.14; that would give him a simple average of 1.47, but since he threw 12 more passes in the Super Bowl than in any other game, his weighted average leverage is a bit higher.) If you multiply his attempts by his ANY/A over expectation by the leverage for each of the four games, and then divided that total by 1.62 (the average leverage for each attempt), you get 714, the amount of (leverage-adjusted) adjusted net yards over expectation Warner produced. That’s the most by any quarterback in a single post-season.

Here’s another way to think about it. Based on the defenses Warner faced, he would have been expected to produce a weighted average ANY/A (weighted for both SOS and Leverage) of 3.87; in reality, he produced a weighted ANY/A (again, weighted for Leverage) of 8.97. Therefore, Warner exceeded expectations by 5.10 ANY/A. Since he had 140 dropbacks, that gives him 714 adjusted net yards of value over average. The table below shows the top 100 postseasons by a quarterback (looking at only passing numbers) using this method:

The Best Single-Postseason Passing Performances From 1965 to 2012

RkQuarterbackTmYrGAttLevExp ANY/AAct ANY/AANY/A OvExValue
1Kurt WarnerARI200841401.623.878.975.1714
2Jim PlunkettOAK198041041.24.0610.596.54680
3Joe MontanaSFO19893851.684.4212.187.76658
4Jake DelhommeCAR200341101.573.739.345.61616
5Daryle LamonicaOAK19682890.852.819.146.33564
6Joe MontanaSFO19883961.754.039.785.75552
7Joe FlaccoBAL201241321.575.379.374528
8Troy AikmanDAL19923961.864.6410.135.49527
9Terry BradshawPIT19783821.713.379.225.85479
10Doug WilliamsWAS19873871.644.089.355.27458
11Aaron RodgersGNB201041401.594.67.813.21449
12Steve YoungSFO19943912.054.929.624.7426
13Joe MontanaSFO198431161.564.297.93.6418
14Peyton ManningIND200931321.834.427.473.04402
15Terry BradshawPIT19793861.473.658.244.59394
16Jim KellyBUF19903831.884.138.864.74393
17Jim McMahonCHI19853721.623.799.295.5393
18Phil SimmsNYG19863611.754.711.066.36388
19Kurt WarnerSTL199931241.935.118.213.1384
20Ken StablerOAK19763751.212.577.434.86364
21Bart StarrGNB19662591.083.229.356.13361
22Mark RypienWAS19913791.944.859.284.42350
23Jeff GeorgeMIN19992820.654.18.134.02330
24Jeff HostetlerRAI19932430.595.0112.637.62328
25John ElwayDEN19983901.874.718.343.63327
26Troy AikmanDAL19953841.814.918.663.75315
27Bernie KosarCLE19872741.093.878.094.22312
28Terry BradshawPIT19753621.412.487.374.89303
29Drew BreesNOR200931041.935.258.162.91303
30Drew BreesNOR201121120.625.027.692.67299
31Matt RyanATL20122781.224.798.613.82298
32Joe NamathNYJ19682811.492.335.973.64295
33Bart StarrGNB19673841.192.716.123.41286
34Colin KaepernickSFO20123851.855.578.923.34284
35Dan MarinoMIA198431201.814.096.432.34281
36Warren MoonHOU19912800.574.387.823.44275
37Roger StaubachDAL19753911.351.924.872.95269
38Kurt WarnerARI20092610.574.568.854.29262
39Ken StablerOAK19772780.852.736.073.34261
40Randall CunninghamMIN19972790.63.676.953.28259
41Brett FavreGNB19963782.054.677.993.31258
42Mark SanchezNYJ20103920.954.837.582.75253
43Tom BradyNWE20043881.934.747.612.87252
44Brett FavreGNB199531080.974.97.212.31250
45Tom BradyNWE200331261.914.936.911.98250
46Len DawsonKAN19693671.261.985.73.73250
47Dan FoutsSDG19802861.073.486.342.85245
48Ken AndersonCIN19813861.814.156.792.63226
49Joe TheismannWAS19824951.832.544.922.38226
50Brett FavreGNB199731031.984.26.382.18225
51John BrodieSFO19702750.911.894.832.94221
52Eli ManningNYG200741281.644.86.531.72220
53Erik KramerDET19912761.174.27.042.84216
54Dan MarinoMIA19942690.615.478.533.06211
55Daryle LamonicaOAK19672621.61.715.093.39210
56Kelly HolcombCLE20021450.394.799.424.63208
57Joe MontanaSFO19813951.474.436.622.19208
58Ken StablerOAK19742700.92.45.362.96207
59Aaron RodgersGNB20091470.395.089.344.26200
60Drew BreesNOR20062871.264.026.292.27198
61Joe MontanaSFO19902621.154.067.193.13193
62Philip RiversSDG20082790.593.726.142.42191
63Tom BradyNWE20052670.64.877.682.81188
64Troy AikmanDAL19933891.724.626.722.1188
65Roger StaubachDAL19773691.543.15.82.71188
66Peyton ManningIND200641591.514.095.261.17186
67Fran TarkentonMIN19733841.382.084.292.21185
68Terry BradshawPIT19743521.313.156.663.51183
69Ken StablerOAK19752680.961.934.612.68182
70Russell WilsonSEA20122690.615.818.432.62181
71Danny WhiteDAL198231020.854.065.781.72176
72Doug FlutieBUF19981390.393.578.054.48175
73Ken StablerOAK19732420.91.035.184.16175
74Peyton ManningIND20071480.794.127.753.63174
75Jim KellyBUF19891550.694.017.163.15173
76Neil O'DonnellPIT19942771.345.117.362.25173
77Joe MontanaSFO19832811.14.776.882.11171
78Mark MalonePIT19842661.074.386.922.54167
79Peyton ManningIND20042770.615.017.162.15166
80Lynn DickeyGNB19822630.774.427.052.63166
81Scott BrunnerNYG19812540.63.496.553.05165
82Bill NelsenCLE19692630.911.824.442.62165
83Joe FergusonBUF19741260.581.597.856.26163
84Ken AndersonCIN19751320.581.216.285.07162
85Jeff HostetlerNYG19903842.024.546.451.9160
86Matt HasselbeckSEA20102840.624.986.861.87157
87Rich GannonOAK20012620.64.647.162.52156
88Mark SanchezNYJ20093691.045.117.362.25155
89Kurt WarnerSTL2001311324.625.991.37155
90Ron JaworskiPHI19792670.563.545.822.29153
91Brad JohnsonTAM20023991.864.846.371.53151
92Eli ManningNYG201141741.585.776.640.87151
93Rodney PeetePHI19952320.465.039.774.74151
94Johnny UnitasBAL19703611.163.796.242.45149
95Dan MarinoMIA19902810.634.676.451.78144
96Steve YoungSFO19922701.214.176.212.05143
97Don MeredithDAL19661330.751.926.244.32143
98Donovan McNabbPHI20022831.272.924.631.72142
99Roger StaubachDAL19783801.842.844.61.76142
100John ElwayDEN198631141.684.525.751.23140

Seeing Warner’s 2008 as the top postseason performance isn’t too surprising. What about Jim Plunkett’s 1980 season? Over four games, he had a 96.2 passer rating and averaged 9.1 yards per attempt while throwing for 7 touchdowns. Remember, this was 1980, not 2013: that year, Brian Sipe won the passer rating crown with a 91.4 rating. More importantly, Plunkett gets extra credit for being at his best in the biggest games. In the AFC Championship Game, he was 14/18 for 261 yards and 2 touchdowns. In the Super Bowl, he threw for 261 yards and 3 touchdowns on 21 passes. If the goal is to reward quarterbacks for being at their best in the most critical games, then Plunkett’s position at number two is legitimate.

Joe Montana’s magical 1989 is number three, and the only reason he’s behind Plunkett is because he had fewer attempts. Montana’s leverage-adjusted 7.76 ANY/A over expectation is the best performance in a postseason since 1965. Jake Delhomme’s presence at #4 might be surprising, but that’s a function of his production in a high-leverage situation against a great opponent. Forget the name, and consider that a quarterback ten years ago faced the #1 pass defense in the league (by ANY/A) and threw for 323 yards and 3 touchdowns with no interceptions on 33 pass attempts in the Super Bowl. Had Carolina won that game (and, perhaps, had Delhomme not subsequently imploded five years later), we might remember his 2003 playoffs the way we think of Joe Flacco’s 2012 postseason.

Working Through Another Example

Speaking of Flacco, I was a bit surprised he wasn’t in the top 3, but that’s essentially a function of the built-in era adjustment. Let’s go through this method using Flacco’s 2012 season, but using another method to get to the same result.

ELITE

ELITE.

Flacco’s first game was against the Colts, who allowed 6.54 ANY/A during the regular season. If we multiply that number by the leverage (0.39) and his number of dropbacks (24), we get 61.66. In Denver, Flacco faced a team that allowed 4.87 ANY/A during the regular season. Multiply that number by the leverage (0.79) and dropbacks (35), and you get 133.85. In the AFC Championship Game, Flacco had 38 dropbacks against a team that allowed 6.31 ANY/A during the regular season; multiply those two numbers by the leverage (1.57) and you get 376.83. Finally, he faced the 49ers in the Super Bowl, and San Francisco allowed 4.88 ANY/A during the regular season. Flacco had 35 dropbacks in a game with massive leverage (3.14); the product of those three numbers is 536.91.

If you add up those four numbers – 61.66, 133.85, 376.83, and 536.91 — you get 1,109.26. Next, we divide that number by Flacco’s total number of dropbacks (132) to get 8.40. The last step is to divide that number by the average leverage of each pass Flacco attempted. Do the math, and that number is 1.57. Once you divide 8.40 by 1.57, you get the Expected (leverage-adjusted) ANY/A for Flacco during the post-season, which is 5.37. That’s a really high number, at least historically speaking, which simply reflects the fact that putting up good passing numbers was a lot easier in 2012 than it was in 1972. Flacco is essentially getting dinged for an era adjustment, but that’s appropriate.

How did Flacco actually do? He had an ANY/A of 12.88 against Indianapolis, 10.97 against Denver, 7.76 in New England, and 9.54 in the Super Bowl. Adjust for his number of attempts and leverage, and Flacco produced a leverage-adjusted ANY/A of 9.37. That’s also a hair lower than his non-leverage adjusted ANY/A of 10.02, which makes sense: his best game was against Indianapolis, the lowest-stakes game in which he played. Flacco was still great, but the leverage and the era combine to put him at “only” 4.00 ANY/A better than expectation.

You might be surprised that Tom Brady doesn’t fare all that well in this metric. In fact, he only has three top-100 seasons, and none in the top 40. Well, Brady’s never had one dominant postseason. His best year was in 2004, but even then, his numbers there look merely “very good” as opposed to historically great. Is his playoff reputation overrated? Perhaps. In Part II, I’ll show you the career playoff ratings.

I won’t pretend that the math involved isn’t overly complicated. But hey, Neil and I already did all the work for you. So what do you think of the list?

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