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There are no fewer than four problems with passer rating.

1. It does not adjust for era.

2. It only includes four variables — completion percentage, yards per attempt, touchdown rate, and interception rate — which means valuable information like sacks, first downs, and rushing are excluded.

3. The variables it does include are improperly weighted: a completion is worth 20 yards (too much), a touchdown is worth 80 yards (also too much), and an interception is worth -100 ways (again, too much).

4. Like nearly all non-proprietary formulas, it does not provide any situational context: an interception on 1st-and-goal from the 1 is the same as an interception on a Hail Mary, a 10-yard catch on 4th-and-9 is the same as a 10-yard catch on 3rd-and-30, etc.

These are just some of the reasons why passer rating is stupid. For reasons I can’t quite articulate, I only want to focus on solving the issue presented by problem number one. Yes, it may be silly to artificially tie one hand behind my back, but my goal here is not to come up with a new formula, but just to fix one specific issue with passer rating that everyone can acknowledge.

The past two days, I have been writing about passer rating. If you ignore the upper and lower limits in the formula, passer rating’s four variables can be re-written like this: [click to continue…]


Playing like cowards

When athletes lose to inferior opponents, the excuses quickly follow. That’s a pretty good rule of thumb, and it applies to women’s soccer, too. Here’s what Hope Solo said after the U.S. lost to Sweden in the Olympics:

“I thought that we played a courageous game,” Solo said. “I thought that we had many opportunities on goal. I think we showed a lot of heart. We came back from a goal down; I’m very proud of this team.

“I also think we played a bunch of cowards. But, you know, the best team did not win today; I strongly, firmly believe that. I think you saw America’s heart. You saw us give everything that we had today. Unfortunately the better team didn’t win.”

The U.S. outshot Sweden 27-2, but the game ended 1-1 after 120 minutes plus stoppage time. The unique thing about soccer is that its tiebreaker is a shootout, which is kind of like playing an NFL game and then having a field goal kicking contest. In other words, once you go to a shootout, the better team suddenly doesn’t have much (any?) of an edge.

Asked to elaborate on what she meant by cowards, Solo referenced Pia Sundhage, the Swedish coach who formerly coached the United States and won two Olympic gold medals.

“Sweden dropped off, didn’t want to open play,” Solo said. “They didn’t want to pass the ball around. They didn’t want to play great soccer, entertaining soccer. It was a combative game, a physical game. Exactly what they wanted and exactly what their game plan was. They dropped into a 50. They didn’t try and press, they didn’t want to open the game and they tried to counter with long balls. We had that style of play when Pia was our coach.

“I don’t think they’re going to make it far in the tournament. I think it was very cowardly. But they won. They’re moving on, and we’re going home.”

[click to continue…]


Thoughts on Thresholds Models of Collective Behavior

I would like to recommend Revisionist History, a new podcast from Malcolm Gladwell. His third podcast, The Big Man Can’t Shoot, nominally covered Wilt Chamberlain and his struggles at the free throw line. But, as is often the case with Gladwell’s work, it’s about so much more than that.

Of particular interest to me was the academic paper Gladwell cited, which formed the meat of the podcast. It was written by Mark Granovetter, back in 1978, and is titled Threshold Models of Collective Behavior. Here’s a link to the paper, which I recommend reading if you have the time.   But a couple of Granovetter’s examples resonated with me as being particularly relevant o us, and I would like to reproduce them here using a football analogy.

[Note: You may wonder why am I copying his work here? I find the application of this idea of threshold models of collective behavior to be worthwhile for our broader discussion, and I think the best way to encourage discussion of it here is to reproduce it in our world, rather than just telling you to go read a link.  Full credit, of course, belongs to the author.]

Many analysts, myself included, think that NFL teams are way too conservative when it comes to going for it on 4th down. In general, coaches do not call plays in an optimal way, and we have long understood that part of the problem is no coach wants to take the heat for failing unconventionally. So we just assume that “the NFL” is overly conservative on this point.

Now, let’s make some assumptions. “Being aggressive” is not a binary thing — there are hundreds of aggressive/conservative options/decisions that come up in a season — but to simplify things, let’s assume that coaches can either be aggressive or conservative. And, let’s assume that right now, all 32 head coaches are conservative.

However, let’s assume that all 32 coaches think being aggressive is better than being conservative, but they also have resistant to switching from being conservative to being aggressive. And these resistances are not uniformly held: these 32 coaches each have different thresholds on when to make that switch. Let’s say the Patriots would be willing to be aggressive as long as just one other team was aggressive first. This would mean New England is very eager to be aggressive, but just doesn’t want the spotlight solely on them. And let’s say the 49ers would be aggressive as long as two other teams became aggressive first. And the Ravens would be aggressive as long as three other teams were aggressive first. [click to continue…]


When an athletic but raw player is drafted, it’s common to hear that he will succeed if he can be “coached up” in the NFL. That idea relies on the assumption that there’s going to be enough individualized coaching in the NFL for that player to reach his potential. But I’m not really sure if that is true, especially when it comes to less highly-touted prospects.

This was an interesting article about offensive linemen in the NFL who believe that the time limits on practices under the CBA “have forced NFL coaches to spend most of their time installing the offense, rather than focusing on the tricks of the trade. That’s led to sloppy play.” And Ryan Riddle, a former sixth round pick who now writers at Bleacher Report, recently tweeted something similar, saying that NFL coaches focus on the macro level rather than individual technique. [click to continue…]


NBA 3-Point Attempts and Going For it On 4th Down

In overly simple terms (ignoring things like fouls, rebounds, game theory, etc.), the expected value of a 2-point field goal attempt is the 2-point field goal percentage multiplied by 2, and the expected value of a 3-point field goal attempt is the 3-point field goal percentage multiplied by 3. Here’s a look at the EV for both 2-point and 3-point attempts in every NBA season going back to 1979-1980, courtesy of basketball-reference:


The inflection point came right around 1990; after that, the 3-point shot was associated with a higher expected value, and since ’97-’98, the 3-point shot has about 12% more EV than a 2-point shot. Now, I know just about nothing about the NBA and even less about NBA analytics, but it’s easy to draw a couple of conclusions from this chart. One would be that teams should be taking more 3-pointers, even though “traditional coaches” have not been fans of the 3-point shot. It’s easy to look at this chart and dismiss it, and say that a team shouldn’t take a bunch of 3 pointers just because the math says it makes sense. On the other hand, you have the Golden State Warriors. [click to continue…]


Yesterday, the NFL approved a one-year rule to kickoffs to change the spot of the snap after a touchback to the 25-yard line. Last year, 56% of all kickoffs were not returned, and the average starting field position following kickoffs was heavily impacted by the 2011 rule change that moved kickoffs from the 30 to the 35 yard line:

kickoff fp

This change goes in the other direction, albeit with competing interests. On one hand, this provides a significant incentive for kickoff returners to take a knee. Many kickoffs are boomed several yards into the end zone; at this point, the odds are pretty low that an average return five yards deep will make it out ahead of the 25-yard line. [click to continue…]


Additional Thoughts on Sam Bradford

On Thursday, I wrote about the mediocre (and worse) statistics produced by Sam Bradford throughout his career. Today, I wanted try to present the other side of the case. I’ve written about Bradford a few times here at Football Perspective, and some of those articles are instructive:

  • A year ago, I wondered whether Bradford would break out in his first season with the Eagles, and became a quarterback with the rare age 27 breakout season. I wrote that the odds were highly against a quarterback playing like Bradford through age 26 and then turning into a very good quarterback, but number one picks stuck on bad teams were the quarterbacks most likely to buck that trend.

In the context of defending Bradford, it is easy to point to a revolving cast of characters, both at receiver and offensive coordinator. His first three seasons in St. Louis, he had a different leading receiver and different offensive coordinator each year. In fact, he’s now had five different leading receivers in each of his five seasons, and last year was the first time he’s had a player gain even 700 receiving yards:

YearTop ReceiverRec YdsOffensive Coordinator
2010Danny Amendola689Pat Shurmur
2011Bradon Lloyd683Josh McDaniels
2012Chris Givens698Brian Schottenheimer
2013Jared Cook671Brian Schottenheimer
2015Jordan Matthews997Pat Shurmur

As a result, no player has gained even 15% of Bradford’s career passing yards. In fact, Bradford’s career-leading weapon is Brandon Gibson, who has 11.2% of Bradford’s yards. And only Danny Amendola is also over seven percent.

Brandon Gibson226165211.2%
Danny Amendola22913989.5%
Chris Givens1199936.7%
Jordan Matthews1179186.2%
Lance Kendricks1249006.1%
Steven Jackson1458715.9%
Zach Ertz1058165.5%
Austin Pettis1206904.7%
Danario Alexander746054.1%
Daniel Fells653912.6%
Brandon Lloyd583512.4%
Laurent Robinson753442.3%
Jared Cook423342.3%
Mark Clayton463322.2%
Brian Quick453152.1%
Darren Sproles652972.0%
Brent Celek202952.0%

That’s a pretty underwhelming set of receivers. One thing that might be instructive is seeing how those players have fared without Bradford. Let’s go in descending order based on the number of targets each player has seen from Bradford. [click to continue…]


Before you can get good at projecting fantasy points, you need to understand how fantasy points are scored.  And there’s probably no better place to start than in the passing game.

I used the following scoring system to determine passing fantasy points: 1 point per 25 yards passing (this is gross passing, so if you look at team passing data, you need to add back in sack yards), 4 points per touchdown pass, and -1 point per interception.  That’s it.

The average team in 2015 scored 16.1 fantasy points per game; to make life a bit more intuitive, I am going to convert fantasy point numbers into a plus/minus average number. So the Patriots passing attack, which scored 329.5 fantasy points in 16 games, and averaged 20.6 FP/G, gets credited as +4.5. That was the best average in football. On defense, the Patriots were slightly better than average, at +0.3 points per game (here, positive is good for defense; if you forget, just check the Saints line). Using New Orleans as an example, the Saints get a +4.2 offensive grade (ranked 2nd) and a -6.5 defensive grade (32nd). I put all 32 teams into the table below with their respective offensive and defensive grades and ranks: [click to continue…]


How many interceptions will a team throw in a game?  That’s dependent on a number of things, of course, but I want to focus on three things: how interception prone the team is, how interception prone the opposing defense is, and the Game Script.

Suppose you knew what the Game Script of a game would wind up being; given that you have a general sense of the offense’s and defense’s interception rates, what weight would you put on each variable to predict a team’s interception rate?

The same is true for other statistics.  For example, what about rushing yards?  How many yards would you project Team A to run for against Team B, if you knew the rushing stats for  Team A’s offense, Team B’s defense, and the Game Script?

Or passing yards.  Or completion percentage.  The interplay between offense and defense is always interesting — some research suggests about 60% of the result is due to the offense, with 40% based on the defense — but throwing in Game Scripts adds an interesting element.

Oh, and one final thought: how would you go about trying to answer these questions.  What studies would you run?  What would you like me to do?


Grouping Players Into Attackers and Mitigators: Part I

I’ve been reading Chris Brown’s excellent new book, The Art of Smart Football. One of the passages in Brown’s book about legendary head coach Sid Gillman stood out to me:

Realizing that a football field is nothing more than a 53⅓-yard-wide geometric plane, Gillman designed his pass patterns to stretch defenses past their breaking points. His favorite method was to divide the field into five passing lanes and then allocate five receivers horizontally in each one. Against most zones, at least one receiver would be open.

Below is an example of what Gillman was referring to:1 you can see that, horizontally, one target will end up in each fifth of the field:

When it comes to pass patterns, the receivers are the players on the attack, and there’s a relatively wide variance in how effective a receiver can be (i.e., he can get open all the time, some of the, none of the time, etc.). But the players in pass coverage should be viewed in a different way: all they can do is mitigate the player in front of them. [click to continue…]

  1. While I couldn’t find the exact picture Chris used in the book, this one illustrates the same concept. []

You remember 1976, don’t you? Two teams — the Colts with Bert Jones and Roger Carr, and the Raiders with Ken Stabler and Cliff Branch — stood out from the pack when it came to pass efficiency that season. The Colts led the NFL in passing yards, ranked 2nd in passing touchdowns, and threw just 10 interceptions, tied for the fewest in the NFL. Oakland threw 33 touchdown passes — nine more than the Colts and 12 more than any other team in football — while ranking 3rd in passing yards. Both teams averaged 7.5 Net Yards per Pass Attempt, while every other team was below seven in that metric. Those two teams went a combined 24-4.

The next four best passing teams were St. Louis, Dallas, Minnesota and Los Angeles. Each of those teams went 10-4 or better. In fact, the linear relationship between pass efficiency and team record was quite strong that year. Take a look at the chart below, which plots Relative ANY/A — i.e., Adjusted Net Yards per Attempt relative to league average — on the X-Axis, and Winning Percentage on the Y-Axis: [click to continue…]


Guest Post: Questioning ANY/A

Adam Steele is back for another guest post. And, as always, we thank him for that. You can view all of Adam’s posts here.

Within the analytics community, we seem to have reached a consensus that ANY/A is the best box score metric for measuring passing efficiency. Over at the Intentional Rounding blog, Danny Tuccitto tested the validity of ANY/A using a technique called Confirmatory Factor Analysis. You can read his three part analysis here, here, and here. Essentially, he discovers that Y/A and TD % are valid statistics for measuring QB quality, while sack % and INT % are not. At first I was skeptical, but after some pondering I came up with a half-baked theory of why this might be true:

As we evaluate the potential for an athlete to succeed in professional sports, there are two kinds of statistics: Qualifying and Disqualifying. In the case of quarterbacks, I define a qualifying statistic as a minimum threshold the player must meet to even be considered NFL worthy. If we deconstruct ANY/A into its four components, Y/A and TD % emerge as qualifying statistics. In today’s NFL, I estimate that a QB must possess a true talent level of at least 6.0 Y/A and 2.5 TD % to deserve a roster spot. There are very few people in the world who can reach those thresholds against NFL caliber defenses (my best guess is around 100). With these two simple statistics, we’ve already weeded out the vast majority of quarterbacks from ever playing in the NFL.

Next, we turn to sack % and INT %, which are disqualifying statistics. By themselves, neither of these skills qualify a QB to play in the NFL. Anybody can avoid sacks or interceptions if they’re not worried about gaining yards. However, the inability to avoid sacks or interceptions will disqualify a QB from the NFL, regardless of how high his Y/A and TD % might be. I estimate these limits as roughly a true talent 12% sack rate and 4.5% INT rate. The population of quarterbacks who can stay under these limits AND perform above the minimum Y/A and TD % is very small. In most years, there aren’t enough of these QB’s to fill the 32 NFL starting spots. Among quarterbacks who receive significant NFL playing time, there is a strong survivorship bias for the disqualifying statistics of sack % and INT %, as the quarterbacks who make too many negative plays have already been weeded out of the sample. Given that Y/A and TD % are far rarer skills with no upper limits, these two statistics are the true measuring stick at the NFL level.

To test this theory, I created a very simple metric called Positive Yards Per Attempt (PY/A). It’s just passing yards plus a 20 yard bonus for touchdowns, divided by pass attempts (which does not sacks). I then converted PY/A into a value metric by measuring it relative to league average (RPY/A)1 and VALUE above average by multiplying RPY/A by attempts. We already have these variations of ANY/A (that is, RANY/A and VALUE), so comparing the two metrics is very straightforward. Since the merger, there have been 1,423 QB seasons of with least 200 dropbacks. This table lists the top 100 seasons of PY/A VALUE, as well as the ANY/A VALUE and rankings for these players. The “Diff” column signifies the gap in ranking between the the two metrics, with a positive number indicating a QB who is favored by PY/A and negative number favoring ANY/A.

1Peyton ManningIND20045103.2916374.27217621
2Dan MarinoMIA19845772.8315984.0923591-1
3Aaron RodgersGNB20115383.0815443.6193652
4Kurt WarnerSTL20015842.714722.2913392521
5Kurt WarnerSTL19995282.914483.22170161
6Tom BradyNWE20075992.4314023.4820834-2
7Peyton ManningDEN20136772.0513483.1121043-4
8Kurt WarnerSTL20003673.6512652.8210357668
9Lynn DickeyGNB19835242.5512321.71898112103
10Steve YoungSFO19944922.6712302.961454155
11Steve YoungSFO19934932.6412182.5212413524
12Ken StablerOAK19763103.912123.4811504533
13Daunte CulpepperMIN20045942.1611812.471468130
14Boomer EsiasonCIN19884183.0411782.8511924026
15Chris ChandlerATL19983723.5511612.35876119104
16Drew BreesNOR20116811.7511472.4216507-9
17Randall CunninghamMIN19984452.6911433.32147912-5
18Tom BradyNWE20116431.8611332.4315628-10
19Bert JonesBAL19763723.0811283.8415259-10
20Philip RiversSDG2010579210842.112173818
21Drew BreesNOR20095342.1110842.74146514-7
22Daunte CulpepperMIN20005082.2410612.1310836240
23Philip RiversSDG20095112.1510462.73139519-4
24Philip RiversSDG20085032.1510252.412093915
25Joe MontanaSFO19894192.589963.161322272
26Tony RomoDAL20075441.849551.79279973
27Aaron RodgersGNB20145481.839512.59142118-9
28Mark RypienWAS19914282.249443.25139120-8
29Steve YoungSFO19985651.829412.0511564314
30Steve YoungSFO19924312.39253.33143617-13
31Jim KellyBUF19915051.959231.8392510069
32Ben RoethlisbergerPIT20095561.829211.5284513098
33Nick FolesPHI20133452.869083.371162429
34Peyton ManningIND20054701.999042.76130029-5
35Brett FavreGNB19956031.568911.911474611
36Tony RomoDAL20144652.028781.9891910670
37Drew BreesNOR20086481.388761.92124234-3
38Steve BeuerleinCAR19996211.538741.6410197941
39Dan FoutsSDG19823422.038573.07134223-16
40Roger StaubachDAL19733292.778462.09735169129
41Aaron RodgersGNB20095911.548321.8811115918
42Ken AndersonCIN19754092.058253.04132526-16
43Matt SchaubHOU20096081.418221.861130529
44Dan FoutsSDG19854481.918192.229938440
45Ken StablerOAK19743282.458093.231128549
46Jeff GeorgeMIN19993572.458081.88672193147
47Boomer EsiasonCIN19864951.728072.1410606922
48Peyton ManningIND20005911.418052.08123236-12
49Dan MarinoMIA19866401.298022.12135522-27
50Peyton ManningDEN20126041.378012.02122237-13
51Jim EverettRAM19895471.547971.9810826312
52Eli ManningNYG20116171.357961.69868735
53Warren MoonHOU19906201.367952.08128732-21
54Donovan McNabbPHI20045011.687902.3115444-10
55Peyton ManningIND20065711.417872.63150310-45
56Philip RiversSDG20135741.447841.98113651-5
57Joe NamathNYJ19723352.237712.2179114689
58Tom BradyNWE20105171.567682.59133924-34
59Vinny TestaverdeBAL19965831.397651.27743163104
60Steve YoungSFO19973912.157642.3692210444
61Drew BreesNOR20136871.177631.7116541-20
62Aaron RodgersGNB20105061.617631.8291910745
63Joe MontanaSFO19844541.767593.02137021-42
64Brett FavreGNB19975381.477551.7292310238
65Drew BreesNOR20126961.127511.2989511449
66Steve YoungSFO19912922.677463.1692210337
67Steve McNairTEN20034191.857412.67111958-9
68Trent GreenKAN20045881.337371.4585612658
69Brett FavreMIN20095651.387352.03114447-22
70Terry BradshawPIT19783891.997322.0881114171
71Drew BreesNOR20065721.327292.28130428-43
72Tony RomoDAL20095841.327281.95114049-23
73Brett FavreGNB20015321.437281.881003818
74Neil LomaxSTL19846091.297251.76107166-8
75Tony RomoDAL20063582.147231.85662200125
76Peyton ManningIND20095811.267221.93112057-19
77Aaron RodgersGNB20126031.37191.4487112144
78Peyton ManningIND20075361.397151.839798911
79Ben RoethlisbergerPIT20052912.647082.22647208129
80Ken AndersonCIN19743642.027072.459519414
81Dan FoutsSDG19816281.157022.37148611-70
82Dan FoutsSDG19806211.197011.69104871-11
83Jeff GarciaSFO20005851.257012.21129031-52
84Ben RoethlisbergerPIT20074511.736991.06476299215
85Trent GreenKAN20024961.476931.7285412742
86Peyton ManningDEN20146141.156881.59979882
87Ben RoethlisbergerPIT20146411.126841.75112156-31
88Craig MortonDEN19814301.86751.06455318230
89Peyton ManningIND20035841.176642.22129430-59
90Trent GreenKAN20035431.256541.95105670-20
91Peyton ManningIND19995471.226511.94106267-24
92Brett FavreGNB19965831.196481.5288911624
93Dan FoutsSDG19833541.96452.3884313239
94Greg LandryDET19712902.316442.13660201107
95Carson PalmerCIN20055281.266441.97104174-21
96Roger StaubachDAL19712342.866433.9799185-11
97Carson PalmerCIN20065561.236421.4681214043
98Joe MontanaSFO19874201.41640295893-5
99Tom BradyNWE20055561.216391.5686912223
100Dan FoutsSDG19784031.676362.1285212828

This list makes a strong case for the validity of PY/A. It’s populated by the greatest QB seasons of all time at the top, and filled out by a number of other notably great and very good seasons. There are a few head scratchers (most notably Lynn Dickey at #9), but for the most part it’s a very credible list that closely mirrors the ANY/A rankings. That’s the point, really. When we remove sacks and interceptions from ANY/A, it doesn’t lose much accuracy, if any. At first glance, I was concerned that PY/A systematically overrates certain quarterbacks and underrates others. That’s probably true to a certain degree. However, I would argue that ANY/A has the same issue, except it’s a different set of quarterbacks who are over- and underrated by it. The true balance almost certainly lies somewhere in between the two metrics. FWIW, the correlation between RPY/A and RANY/A is a robust 0.877, with an r-squared of 0.769.

Now lets look at the other end of the spectrum – the 100 worst PY/A VALUE seasons since 1970.

1423Derek CarrOAK2014623-2.02-1209-1.36-8481395-28
1422Drew BledsoeNWE1995659-1.71-1086-1.09-7161366-56
1421Jon KitnaCIN2001606-1.67-972-1.48-8981408-13
1420Chris WeinkeCAR2001566-1.79-964-1.5-8481396-24
1419Joey HarringtonDET2003563-1.67-928-1.38-7791380-39
1418Kyle BollerBAL2004499-1.93-894-1.51-7551374-44
1417Blaine GabbertJAX2011453-2.16-894-2.28-103214192
1416Jack TrudeauIND1986446-2.14-893-1.96-8741405-11
1415Vince EvansCHI1981459-2.02-883-1.78-8181391-24
1414Ryan FitzpatrickCIN2008410-2.23-828-2.18-8921407-7
1413Archie ManningNOR1975387-2.23-803-2.76-113914229
1412Sam BradfordSTL2010624-1.36-801-1.04-6461349-63
1411Mark RypienWAS1993335-2.47-788-2-6711354-57
1410Bobby HoyingPHI1998259-3.46-775-3.94-102014188
1409Kordell StewartPIT1998491-1.68-769-1.78-8731404-5
1408Kyle OrtonCHI2005398-2.05-753-2.19-8721403-5
1407Jimmy ClausenCAR2010332-2.51-749-2.8-93014136
1406Blake BortlesJAX2014530-1.57-745-2.39-1268142317
1405Colt McCoyCLE2011495-1.59-736-1.19-5911329-76
1404Mark MalonePIT1987354-1.91-734-2.24-90714106
1403A.J. FeeleyMIA2004379-2.06-732-2.25-8511399-4
1402Joey HarringtonDET2002437-1.66-711-1.4-6131337-65
1401Akili SmithCIN2000303-2.65-708-2.44-7381371-30
1400Bruce GradkowskiTAM2006353-2.07-679-1.76-6211342-58
1399Jake PlummerARI2002566-1.27-676-1.54-87014023
1398Rusty HilgerDET1988337-2.19-672-2.38-8021386-12
1397Gary MarangiBUF1976254-2.62-649-3.14-85214014
1396Joe FlaccoBAL2013662-1.05-648-1.42-942141620
1395Matt CasselKAN2009535-1.27-627-1.43-7631378-17
1394Dan PastoriniHOU1973320-2.02-626-2.39-8161390-4
1393Steve SpurrierTAM1976343-1.84-610-1.3-4771265-128
1392Joe FergusonBUF1983535-1.2-609-1.06-5701321-71
1391Jeff GeorgeIND1991541-1.25-608-1.37-7431372-19
1390Sam BradfordSTL2011393-1.69-604-1.44-5651318-72
1389Jake PlummerARI1999408-1.57-600-2.65-1079142031
1388Joe NamathNYJ1976246-2.44-598-2.91-7631377-11
1387John FrieszSDG1991519-1.22-596-0.89-4601254-133
1386Mark MalonePIT1986438-1.38-588-0.78-3441159-227
1385Mike PhippsCLE1975341-1.76-587-2.01-7311368-17
1384JaMarcus RussellOAK2009279-2.37-584-3.39-945141733
1383David CarrHOU2002520-1.31-583-2.17-1127142138
1382Brad JohnsonTAM2001603-1.04-580-0.4-2381041-341
1381Bernie KosarCLE1990460-1.37-580-1.27-5851327-54
1380Ryan LeafSDG1998267-2.31-566-3.44-918141131
1379Phil SimmsNYG1980438-1.41-565-1.41-6161338-41
1378Mark BrunellWAS2004252-2.35-558-1.85-4671261-117
1377Steve DeBergSFO1978319-1.84-554-2.25-7191367-10
1376Christian PonderMIN2012515-1.14-551-0.97-4991285-91
1375Browning NagleNYJ1992414-1.42-549-1.45-5981332-43
1374Rick MirerSEA1993533-1.13-547-1.27-6761356-18
1373Joe KappBOS1970246-2.34-546-3.55-933141441
1372Josh FreemanTAM2011580-0.99-543-1.18-6851359-13
1371Chad HenneJAX2013541-1.08-543-1.04-5651319-52
1370Steve DilsMIN1983481-1.22-542-0.68-3281142-228
1369Alex SmithSFO2007210-2.79-539-2.43-5111290-79
1368Chuck LongDET1987433-1.13-535-0.93-4611257-111
1367Todd BlackledgeKAN1984308-1.82-535-1.14-3521169-198
1366Joe FergusonBUF1984379-1.55-532-2.13-807138721
1365Donovan McNabbPHI1999244-2.45-530-2.8-6841358-7
1364Stan GelbaughSEA1992289-2.08-529-2.63-759137511
1363Jack ConcannonCHI1970409-1.29-528-0.68-2951104-259
1362Jim HartSTL1979403-1.4-528-1.39-5591315-47
1361Josh McCownARI2004439-1.29-525-1.06-4671260-101
1360Tommy KramerMIN1979602-0.93-524-0.43-2581062-298
1359Jim ZornSEA1976464-1.11-521-1.09-5411305-54
1358Mike LivingstonKAN1978308-1.79-520-1.08-3321144-214
1357Kerry CollinsCAR1997408-1.36-518-2.28-930141255
1356Rick MirerSEA1994408-1.35-515-0.71-2911100-256
1355Trent DilferTAM1996510-1.07-515-1.18-6011333-22
1354Donovan McNabbPHI2000614-0.9-514-0.44-2681071-283
1353Craig WhelihanSDG1998335-1.6-511-2.38-798138532
1352Brady QuinnCLE2009275-1.99-509-1.75-4811268-84
1351Boomer EsiasonCIN1992297-1.82-505-2.23-66213521
1350Dan PastoriniHOU1972336-1.57-502-1.35-4831270-80
1349Joey HarringtonMIA2006403-1.29-501-1.23-4941279-70
1348Kordell StewartPIT1999297-1.82-501-1.83-5451308-40
1347Doug PedersonCLE2000227-2.38-500-2.55-5781325-22
1346David KlinglerCIN1993383-1.45-499-1.37-5241297-49
1345Kelly StoufferSEA1992216-2.62-497-3.39-732136924
1344John HadlGNB1975388-1.32-496-1.55-64213484
1343Cleo LemonMIA2007334-1.6-496-1.17-3921212-131
1342Vince FerragamoBUF1985306-1.71-491-2.04-62313431
1341Danny KanellNYG1998321-1.63-488-1.6-5131291-50
1340Steve FullerKAN1979307-1.8-485-2.28-701136323
1339Steve DeBergSFO1979595-0.83-4800.32193537-802
1338Tony BanksSTL1998449-1.17-479-1.32-5921330-8
1337Bobby DouglassCHI1971255-1.98-474-2.6-708136427
1336Joey HarringtonDET2004525-0.97-474-0.52-2741075-261
1335Marc BulgerSTL2008478-1.07-472-1.36-652135015
1334Steve BonoKAN1996460-1.07-470-0.66-3051120-214
1333Mark SanchezNYJ2012487-1.02-462-1.61-786138350
1332David WoodleyMIA1980344-1.4-459-1.3-4461244-88
1331Matt HasselbeckSEA2009520-0.94-458-1.07-5581314-17
1330Mike PagelBAL1982237-1.62-458-0.83-2511055-275
1329Brett FavreGNB2006634-0.74-456-0.18-114901-428
1328Roman GabrielPHI1974373-1.26-456-0.59-2341036-292
1327Neil LomaxSTL1986473-1.08-454-0.92-4361241-86
1326Ken DorseySFO2004239-2-451-2.1-5011286-40
1325Brandon WeedenCLE2012545-0.87-449-0.98-5361301-24
1324Mike BorylaPHI1976275-1.71-448-2.07-608133511

I actually find the Worst list even more validating of PY/A than the Best list. When we think of bad quarterbacks, most us reflexively focus on quarterbacks who make a lot of mistakes and sink their teams in obvious and memorable ways. And this list is filled with conventionally terrible quarterbacks. But remember, nearly all of their negative plays have been removed, so it’s not their mistakes putting them on the list. It’s their impotence. These guys couldn’t make plays or move the ball down the field, killing their teams slowly and agonizingly. At the very top (err, bottom), we find Derek Carr’s rookie year. A lot of fans and pundits classify Carr as a budding franchise QB who showed “flashes of potential”. Actually no, he showed the exact opposite. While the younger Carr avoided sacks and interceptions at a reasonable rate, his Y/A was absolutely pathetic. Even accounting for his lousy supporting cast, that is a major red flag. It’s much easier for a young QB to reign in his mistakes than it is for him to suddenly learn how to make positive plays down the field. Blake Bortles fits precisely the same troubling profile, so I don’t have much hope for the class of 2014.

Does this change your feelings about ANY/A? Do you think Danny and I are wasting our time? If anyone else has created their own passing metric using basic stats, I’d love to hear about it.

  1. Note that in calculating league average, I excluded the player in question from the league average totals. So each player is compared to a slightly different definition of league average. []

In terms of NFL averages, completion percentage is way up, interception rate is way down, pass attempts are way up, and the passing game has never been more valuable. We all know that. But sometimes, when everyone is zigging, a lone team might be better off zagging.

The question here is does that theory apply to trying to build an offense that revolves around a power running game? Defenses are looking for lighter and faster defensive ends and linebackers who can excel in pass coverage; just about every defense is taking linebackers off the field for defensive backs more than they did a decade ago. And defenses spend the majority of their practice reps focusing on stopping the pass, too. As defenses try to become faster, quicker, and lighter — and better against the pass — should a team try to respond by developing a power running game?

On one hand, it’s tempting to say of course that model could work: just look at the Seahawks and Cowboys. Seattle does have a dominant running game, of course; what the Seahawks did to the Giants last year is not safe for work. But Seattle also has Russell Wilson, perhaps the most valuable player in the league when you combine production, position, and salary. And the best defense in the NFL. So yes, the Seahawks are successful with a power running game, but that’s not really a model other teams can follow. And for all the team’s success, Seattle doesn’t even have a very good offensive line, which would seem to be the number one focus for a team that is trying to build a power running attack.

The team with the best offensive line in the NFL is probably in Dallas. But the Cowboys also have Tony Romo and Dez Bryant, so again, that’s not really a model capable of imitation.

I’m thinking about some of the teams in the middle class of the AFC — the Bills, the Jets, the Browns, the Texans — teams that are currently trying the all defense, no quarterback approach. Finding a quarterback is the most difficult thing there is to do in the NFL, and these four teams can attest to that. By trading for LeSean McCoy, it appears as though Buffalo is trying to do what this article implies, but there are two problems with that plan. One, the Bills have one of the worst offensive lines in the NFL, and two, McCoy is not necessarily the right guy to build a move-the-chains style of offense.

The Jets have invested a ton of money in their offensive line, courtesy of hitting on first round draft picks in 2006 with Nick Mangold and D’Brickashaw Ferguson, and spending to acquire mid-level free agents from Seattle (James Carpenter this year after Breno Giacomini last offseason). But the Jets offensive line is far from dominant, and the team isn’t really building around a power running game (the team’s top two tight ends are below-average blockers, and the Jets are investing more in wide receivers than running backs).

Houston is an interesting case, because the Texans led the NFL in rushing attempts last year. The Texans do have a very good run-blocking offensive line and Arian Foster, but it still feels like that’s just not enough. Houston’s efficiency numbers were harmed by giving carries to Alfred Blue — the Texans were 8-5 when Foster was active — but the team also doesn’t have much in the way of run blockers at tight end or fullback. [click to continue…]


Re-Post: Data Snooping

In lieu of weekend trivia, I am going to begin reposting old articles that I think people would still find relevant. If you’re a new reader, I hope you enjoy; if you’re an old-timer, my hunch is you still will get something new out of reading these again, just like I did. Today’s post is on Data Snooping, originally posted by me in June 2013.

Reggie Wayne dominates when seeing blue

Reggie Wayne dominates when seeing blue.

Over the last few years, the football analytics movement has made tremendous progress. There are many really smart people with access to a large amount of useful information who have helped pioneer the use of statistics and analytics in football. Major news organizations and NFL teams seem to be embracing this movement, too. Unfortunately, there are some less-than-desirable side effects as the reward for presenting “statistical information” seems larger than ever.

Data snooping is the catch-all term used to describe a misuse of data mining techniques. There are perfectly legitimate uses to data-mining, but data snooping is a big ‘no-no’ for the legitimate statistician. If the researcher does not formulate a hypothesis before looking at the data, but instead uses the data to suggest what the hypothesis should be, then he or she is data snooping. [click to continue…]


In 2013, eight teams hired new head coaches.  Three teams tapped rising offensive coordinators – Mike McCoy, Bruce Arians,1 Rob Chudzinski – while four other hires were head coaches with offensive backgrounds (Andy Reid, Doug Marrone, Chip Kelly, and Marc Trestman).  That means just one head coaching hire came from a defensive background: Gus Bradley in Jacksonville.

Given the current era where the rules are slanted towards the offense, one can understand how teams might be inclined to look towards offensive coaches when selecting a head coach. Consider that scoring is about 60% of the game, which could make owners and general managers break ties in favor of offensive candidates. Then, remember that the pool of teams looking for a new head coach: teams that struggled the prior year. And since offense is so important, that usually means a team that had a bad offense. It’s a bit of an oversimplification, but it’s easy to imagine the average team looking for a head coach as one that just went 5-11 with a bad offense and is looking to turn things around with a new, sexy offensive hire.

There was something else you may recall from 2013: the lack of minority hires. At the end of the 2012 season, there were 15 job openings for general managers and head coaches; none went to a minority candidate. The hiring process for GMs is much more opaque than it is for head coaches, but there was one main explanation given for the fact that all 8 head coaching hires were white: black coaches are disproportionately defensive coaches, and the league was shifting towards offense when it came to coaching hires because of the reasons stated above. [click to continue…]

  1. Who, of course, was also coming off an award-winning season as interim head coach of the Colts. []

Are NFL Playoff Outcomes Getting Less Random?

In September 2012, Neil Paine wrote a great article at this website titled: Are NFL Playoff Outcomes Getting More Random? In it, Neil found that randomness had increased significantly in the NFL playoffs, with “recently” defined as the period from 2005 to 2011.

In fact, while 2005 was a pretty random postseason, 2006 was one of the more predictable playoff years.  But the five-year period from 2007 to 2011 was a really random set of years. Consider that:

  • In 2007, the Giants won three games as touchdown underdogs, including the Super Bowl as a 12.5-point underdog.  The Chargers also won a playoff game against the Colts as an 11-point dog.
  • In 2008, five of the eleven playoff games were won by underdogs! That list was highlighted by the Cardinals winning in Carolina as a 10-point underdog in the divisional round.
  • The following year, five of the eleven playoff games were upsets, including the Jets winning as 9-point underdogs in San Diego.
  • In 2010, for the third straight year, there were five playoff upsets, including two huge ones: the Jets as 9.5 point dogs in Foxboro, and the Seahawks as 10-point home dogs against the Saints.
  • Noticing a trend? Well, in 2011, five of the playoff games were again won by the underdog. The two big upsets here were the Tim Tebow-led Broncos against the Steelers, and the Giants winning in Lambeau Field against the 15-1 Packers.

[click to continue…]


Guest Post: Are Interceptions Overrated?

Guest contributor Adam Steele is back again. You can read all of Adam’s articles here.

Are Interceptions Overrated?

There’s nothing worse than throwing an interception. Everyone seems to agree on this, from fans to media to advanced stats guys. But is it really true? In this quick study, I looked at the tradeoff between interception avoidance and aggressive downfield passing to see which strategy has a larger impact on winning. To measure this, I created two categories of quarterbacks: Game Managers and Gunslingers.

First, the Game Managers, which includes all post-merger quarterback seasons with an INT%+ of at least 1101 and a NY/A+ of 90 or below (min 224 attempts).2 These guys avoided picks but failed to move the ball efficiently, the hallmark of a conservative playing style.

[click to continue…]

  1. Which means the player was at least 0.67 standard deviations better than league average at avoiding interceptions. []
  2. Which means the player was at least 0.67 standard deviations worse than league average in net yards per attempt. []

Betting Bad: Thinking About Uncertainty in Prediction

Barack Obama was not the only winner in the 2012 presidential election. Nate Silver, now founder and editor in chief of Five Thirty Eight, and other stats-y election forecasters basked in the praise that came when the returns matched their predictions.

But part of the praise was overstated. At the very end, Silver’s models essentially called Florida a toss-up, with the probability of an Obama win going just a few tenths of a percentage point above 50%. But because his model gave Obama the slightest of edges in Florida, his forecast in most of the media essentially became a predicted Obama win there. In addition to accurately forecasting the national popular vote, Silver then received credit for predicting all fifty states correctly.

I am all in favor of stats winning, but the flip side of this is the problem. If Obama had not won Florida, Silver’s prediction―which, like that of other forecasters such as Sam Wang of the Princeton Election Consortium, was excellent―would have been no less good.1 And if stats folks bask too much in the glow when everything comes up on the side where the probabilities leaned, what happens the next time when people see a 25% event happening and say that it invalidates the model?2

Lots of people have made this point before — heck, Silver wrote about this in his launch post at the new 538 — but it is really useful to think carefully about the uncertainty in our predictions. Neil has done that with his graphs depicting the distribution of team win totals at 538, and Chase did so in this post last Saturday. Football Outsiders does this in its Almanac every year, with probabilities on different ranges of win totals. [click to continue…]

  1. This is a column about football, but you might want to check out some of the stuff through that link on the differences between Silver and Wang on the upcoming midterm elections. They both know way more than I do, but for the small amount that it is worth, I lean more towards Wang on this one. []
  2. Of course, maybe Football Outsiders has already run into that with the 2007 Super Bowl prediction. Perhaps sports people are ahead of politics on this stuff. []

Super Bowl Champions and Top-Heavy Divisions

The NFL realigned its divisions in 2002, placing four divisions of four teams each in each conference. Some divisions have been top-heavy, with the most obvious example being the 2007 AFC East. The Patriots won 16 games, while the Jets, Dolphins, and Bills combined to win just twelve games (with six of those twelve wins by the Bills or Jets against the Dolphins or Jets). That means New England was responsible for 57% of all wins by AFC East teams in 2007, easily the highest percentage of any team in a division since realignment.

Having an easy division brings some advantages: being the best team in a bad division makes it easier to get the best record in the conference, which leads to a bye week and home field advantage.  It also could allow a team to rest its starters at the end of the year.  Conversely, there’s the notion that teams in tough divisions “beat up on each other,” so presumably that’s another benefit to being the best team in a bad division.

But New England, of course, didn’t win the Super Bowl in ’07.  That year, the title went to the NFC East, which was not a top-heavy division; the Cowboys had just 33% of NFC East wins that year, placing it as the 3rd least top-heavy division in the NFL.  The last three years, things have been even more stark:

  • The NFC West was one of the strongest divisions in NFL history last year; but while the Seahawks may have been beaten up by the 49ers, Cardinals, and Rams, that didn’t stop Seattle from winning the Super Bowl.  Seattle won “just” 31% of the games won by the NFC West last year — only the NFC North (Green Bay, 29%) was less top-heavy.
  • The least top-heavy division in football in 2012 was the AFC North. Baltimore won 10 games, but so did Cincinnati, and the Steelers (8) and Browns (5) were not pushovers, either. The Ravens won just 30% of all games won by AFC North teams in 2012, but finished the year by hoisting the Lombardi Trophy.
  • In 2011, the Giants won a competitive NFC East with a 9-7 record; Philadelphia and Dallas were just one game behind, and New York won only 30% of all games won by NFC East teams that year. Only the Tim Tebow-infected AFC West was less top-heavy (Denver won 26% of all AFC West games, just barely above the minimum threshold for a division champ) that year.

The graph below displays all eight divisions for each year since 2002.  The Y-axis shows the percentage of games won by the top team in the division as a percentage of the total wins by that division.  The X-axis represents the year; the red dot represents the division with the eventual Super Bowl champ, with the blue dot for all other divisions. [click to continue…]


Let’s get the disclaimer out of the way: the traditional draft value chart is outdated, and it never made much sense in the first place. Trying to use logic to explain why teams operate in an illogical manner is a tall task, and probably a waste of time. So, let’s try anyway.

First, I recreated my draft value chart. To do that, I looked at the first 224 players selected in each draft from 1970 to 2009. PFR assigns Approximate Value grades to each player in each season, but since AV grades are gross units, we need to tweak those numbers to measure marginal value. As a result, I only gave players credit for their AV above two points in each season; that difference is a metric I’m defining as a player’s Marginal AV. For example, if a player has AV scores of 8, 1, and 3 in three straight years, those scores are translated into Marginal AV scores of 6, 0 and 1.

The graph below shows the average Marginal AV produced by each draft pick in each season from ’70 to ’09. The blue line shows the average Marginal AV produced by draft picks as rookies, the red line represents second-year players, green is for year three, purple for the fourth season, and orange for average Marginal AV in year five. [click to continue…]


xp avgThe NFL’s Competition Committee is currently considering rules changes to eliminate the boredom associated with the extra point. As you can see from the graph above, extra points are practically automatic now, to the tune of a 99.6% conversion rate in 2013. In fact, extra points have been close to automatic for awhile; the success rate was even as high as 96.8% in 1973, the last year the goal posts were still right on the goal line. The conversion rate was depressed for about 15 years before bouncing back to 97% in 1989, and there have been just 18 missed extra points total in the last three years. I don’t disagree that something could be done to improve the quality of the game.

The simplest alternative is to make touchdowns worth seven points instead of six, and to allow a team to gamble one of those points in the hopes of getting two points by “going for two.” In other words, we would have the system we have now, except that the song and dance of actually kicking the extra point is replaced with an automatic point.

Another solution is to eliminate the extra point entirely, requiring that teams go for two after every touchdown. I won’t try to answer the subjective question of whether or not this would make for a more enjoyable fan experience; the more interesting question to me is whether or not this would lead to more upsets. In other words, if teams had to go for two after every touchdown, would this lead to the better team winning more or less often? I posed this question on the Footballguys.com message boards and got into a good discussion there, much of which I’ll summarize here.

Before analyzing, we must recognize that the two-point play is not like a typical NFL play. A team that’s great in short yardage (say, Carolina) would probably be better off than most teams at converting on these attempts. Likewise, teams that excel in goal-line defense but maybe don’t have great corners (like say, Carolina) would probably be better off, too. But I think, on average, good teams are better at converting two point plays than bad teams, and, on average, good teams are better at preventing two point conversions than bad teams.

So how would such a rule change impact NFL games? One argument that this rule change would make the better team more likely to win is that this would present an additional hurdle for the weaker team. By replacing a play where everyone is successful with a competitive play, this increases the sample size, generally a bad thing for underdogs. Right now, a weaker team only needs to match the stronger team touchdown for touchdown (and field goal for field goal and safety for safety). But if the weaker team matches the better team under this new regime, the weaker team, on average, will still be trailing. By increasing the sample size of relevant plays, the weaker team needs to outplay the better team for longer, making it harder to pull the upset.

On the other hand, the argument is probably more convincing the other way that a mandatory “go for two” rule would lead to more upsets. That’s because the 2-point conversion play is a high-leverage play, and the inclusion of more high-leverage plays is generally a positive circumstance for the underdog. Imagine a rule change where the NFL made going for 2 mandatory, but made the successful outcome worth 20 points. That environment would almost certainly make things better for weaker teams: instead of having to outplay the better team for 60 minutes, the weaker team could be outplayed and win as long as they won on two or three key plays. That’s taking the example to its extreme, but one could argue that the same idea holds with the conversion worth two points, even if the effect would obviously be muted.

Here’s another way to think about it.  Let’s ignore games that aren’t very competitive, because the outcomes of those games won’t change under the current format or the “mandatory go for two” environment.  But there are three other types of games: [click to continue…]


When will a team go an entire game without running?

Belichick checks to see if anyone has gone a whole game without calling a run yet

Belichick checks to see if anyone has gone a whole game without calling a run yet.

The record for fewest rush attempts in a game is 6, set by the 2004 Patriots and tied by the ’06 Cardinals. The circumstances there are as you would expect. The Patriots fell behind 21-3 in the first quarter to the Steelers in 2004, and Pittsburgh owned the league’s top rush defense. In 2006, the Cardinals faced the Minnesota Vikings, owners of one of the greatest rush defenses in history. Minnesota allowed just 985 yards (the second lowest in modern history) on 2.8 yards per carry (the third lowest mark of the modern era) in 2006. That day, the Cardinals didn’t fall behind early, but called on Matt Leinart to throw 51 passes compared to just four Edgerrin James runs. It was not a winning formula, but I’m not sure Denny Green had the wrong strategy.

But will a team ever go a full game without attempting a run? In college, the floor has also been six runs, at least in recent memory. Baylor — with coach Guy Morris, who coached under Hal Mumme and next to Mike Leach at both Valdosta State and Kentucky — was the first, calling just six runs on the road against the 2006 Texas Longhorns. A year later in Austin, it was Leach who orchestrated the only other six-carry game since 2005. That day, he put the game in the hands of Graham Harrell (36/48, 466 yards, 5 TDs, 1 INT), Michael Crabtree (9/195/2), Danny Amendola (8/82) and Edward Britton (8/125/1), but alas, the Red Raiders defense couldn’t stop Jamaal Charles.

I suppose we should wonder when the first 5-carry game will occur before asking about the first 0-carry game. But it’s a Sunday in the offseason, so I’ll throw this one out to the crowd. Will we ever see a 0-carry game? If so, how many years from now until it occurs? Against the Bills this year, the Ravens called 31 straight passing plays but still passed on “only” 86% of all plays from scrimmage. What will it take to get that percentage to 100?


Insane Ideas: Rules Changes

Should the depth of the NFL end zone be extended from 10 to 20 yards? Practically, this is probably impossible, as adding 20 yards to certain fields would be an issue in many NFL stadiums. But let’s ignore that issue for today. I recently had lunch with a baseball friend of mine who suggested this change. My initial reaction was that this would be a bit odd, but there are several reasons to like his idea:

1) My baseball friend — let’s just call him Sean — doesn’t like how compressed things are at the goal line. Why are teams in effect penalized for getting down to the 1 yard line? Why make things easier on the defense?

If you think about it, there’s no reason for the end zone to be ten yards deep. If you are someone who believes we need more rules to promote defense, would you be in favor of making the end zone five yards deep? If not, why not? What makes ten the right number?

We have been conditioned by announcers to believe that life is tougher near the goal line for NFL offenses, and that this is a good thing. Does that make sense?

2) The goal posts would remain at the back of the end zone, which has three benefits. One, the extra point would now be slightly more difficult, which would quiet that controversy. Two, teams might be a little more likely to go for it on 4th and goal, as a 30-yard field goal isn’t as much of a gimme as a 20-yarder. But most importantly, when it’s fourth-and-three from the 30 yard line, teams would now go for it. Perhaps idiot-proofing coaching isn’t a desirable reason for change, but I am in favor of most rules that result in less kicking.

3) This would allow for 119-yard returns, a trade-off that I’m willing to make even if it lowers the possibility of an Orlovsky happening.

So what do you guys think? Feel free to leave your thoughts in the comments, or go in a different direction and post your own insane idea rules change. Here’s one of mine: in the final two minutes of the fourth quarter, the clock stops on a play that does not gain yards.

The purpose of this hypothetical rule change would be to stop teams from taking a knee to end the game. I don’t expect this to be a very popular idea, although the Pro Bowl actually implemented this rule this year. But watching teams battle for 58 minutes and then have the game essentially end with 2 minutes left always rubbed me the wrong way. I know, I know, the winning team earned the right to do it. That doesn’t mean I have to like it. I’d rather see a team have to at least gain a yard to end the game. I’m pretty sure all 32 coaches would hate this rule, but it would certainly make the end of certain games more exciting. That’s a pretty risky statement, I know, because it’s hard to top the victory formation for excitement.


One of my favorite sabermetric baseball articles of all time was written by Sky Andrecheck in 2010 — part as a meditation on the purpose/meaning of playoffs, and part as a solution for some of the thorny logical concerns that arise from said mediation.

The basic conundrum for Andrecheck revolved around the very existence of a postseason tournament, since — logically speaking — such a thing should really only be invoked to resolve confusion over who the best team was during the regular season. To use a baseball example, if the Yankees win 114 games and no other AL team wins more than 92, we can say with near 100% certainty that the Yankees were the AL’s best team. There were 162 games’ worth of evidence; why make them then play the Rangers and Indians on top of that in order to confirm them as the AL’s representative in the World Series?

Andrecheck’s solution to this issue was to set each team’s pre-series odds equal to the difference in implied true talent between the teams from their regular-season records. If the Yankees have, say, a 98.6% probability of being better than the Indians from their respective regular-season records, then the ALCS should be structured such that New York has a 98.6% probability of winning the series — or at least close to it (spot the Yankees a 3-0 series lead and every home game from that point onward, and they have a 98.2% probability of winning, which is close enough). [click to continue…]


Is that Bayes?

Is that Bayes?

Peyton Manning is not a 51 touchdown per-season quarterback, but that doesn’t mean he won’t average the necessary 2.9 touchdowns per game over his final ten games this season to break Tom Brady’s touchdown record. Before the season, Footballguys.com projected Manning as a 2.38 passing touchdown per game player.  And while he has looked unstoppable thus far, with 22 touchdown throws in six games, Manning has been known to have great spurts before, too.  All quarterbacks have hot and cold streaks, Manning included.  From 2003 to 2012, after removing games where he sat late in the season, Manning averaged 2.17 passing touchdowns per game with a standard deviation of 1.31 touchdowns.1  In the ’04 season, Manning threw at least 20 touchdowns in each of his trailing six game stretches from week 7 all the way through week 15, with a peak of 27 touchdowns in his prior six games in weeks 11 and 12.  Manning also threw 19 touchdowns in his last two full regular season games of 2010 and his first four games of 2011.  White-hot streaks happen, even to the best players, so we shouldn’t just assume that he’s now a 3.67 touchdown per game player.

On the other hand, it would be naive to assume that we should ignore the first six weeks of the season and continue to project Manning as a 2.38 touchdown per game player for the rest of the year.  The question becomes, how much do we base projection over the final 10 games on his preseason projection and how much do we base it on his 2013 results? In Part I, after four games, a regression model produced a projection of 2.56 touchdowns per game the rest of the year. But the problem with a regression analysis is that Manning is an extreme outlier among NFL quarterbacks; to project Manning, it would be best if we could limit ourselves to just quarterbacks named Manning Peyton Manning.

Before continuing, I want to give a special thanks to Danny Tuccitto, without whom this article wouldn’t be possible. Danny provided this great link and also spent a lot of time walking me through the process. To the extent I’ve mucked it up here, you should blame the student, not the teacher. But after walking through some models online, I realized that the best explanation about how to use Bayes Theorem for these purposes was on a sweet site called FootballPerspective.com. And the smartest person on that website had already laid out the blueprint.

In the comments to one of his great posts, Neil explained that we can calculate Manning’s odds using Bayes Theorem if we know four things:

His Bayesian prior mean (i.e., his historical average):

His Bayesian prior variance (the variance surrounding his historical average):

His observed mean:

His observed variance:

Let’s go through each of these:

1) Manning’s Bayesian prior mean: this is simply what we expected out of Manning before the season. I will use 2.38, since Footballguys is the gold standard of football projections in my admittedly biased opinion. But you can use any number you like, as I’ll provide the full formula at the end.
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  1. That was after removing week 17 of the ’04, ’05, ’07, ’08, and ’09 seasons, and week 16 of the ’05 and ’09 seasons, when Manning left early. Why did I pick the last ten years? I don’t know, but he won his first MVP in ’03, so that seemed like a useful starting point. []

“Worldly wisdom teaches that it is better for the reputation to fail conventionally than to succeed unconventionally.” – John M. Keynes.

Photo via phillymag.com.

Last Thursday night, Chip Kelly was widely criticized for an unconventional decision that turned out to be unsuccessful. Trailing 10-0 in the first quarter against the Chiefs, Michael Vick threw a 22-yard touchdown pass to Jason Avant. The photo above shows how the Eagles lined up for the point after. Philadelphia’s two-point conversion attempt — a play known as the the Swinging Gate — was stopped, and it was stopped in particularly ugly fashion. That made it easy to point a finger and laugh at the college coach doing something silly.

But without the benefit of hindsight, there was nothing silly or even suboptimal about the decision. Putting aside the specifics of the play — we’ll get to that at the end — the main criticism seems to be that it was “too early” to go for two, or that the Eagles were “chasing points”, or that it was simply “unnecessary.” All of those are buzz words for saying that the Eagles should have behaved conventionally.

At a baseline level, let’s recognize that a team has a roughly 50/50 chance of converting on a two-point conversion. For a good offense with a mobile quarterback, that number may be even higher, but let’s just use the 50/50 number now. If that’s the case, then teams early in the game should be indifferent between kicking the extra point and going for two. Consider this hypothetical example: if a team had the option of kicking the extra point or flipping a coin — and heads gave them two points, tail giving them zero — would choosing to flip the coin be a poor decision?

Late in games, perhaps. But early in the game? I don’t see any reason to think that the difference between having six versus seven points on the board in the first quarter is more significant than the difference between having seven or eight points. Suppose you were told that your favorite team would score first quarter touchdowns in back-to-back games. Option 1 provides that your team would the extra point both times, while Option 2 is that your team would make the two point conversion once and fail on the attempt once. So you get eight points in one game and six points in the other.

Which would you prefer, Option 1 or Option 2? And why? And, if you prefer Option 1 to Option 2, how much more preferable is it? What would you be willing to trade to land in Option 1 — how many yards on the ensuring kickoff?

I would be indifferent between Options 1 and 2, but even if you preferred one, I don’t see how anyone could strongly prefer Option 1 to Option 2. The value to having 8 points is real, which is why it is never “too early” or “unnecessary” to go for two in a world where teams convert on two-point attempts half the time. Those are red herrings, because going for two is only a high-variance strategy; is it not a high-variance, lower-expected value option. Once you understand that, then nearly all the criticism about Kelly’s decision disappears.

As for the actual play call? I think it was a good one. Keep in mind that the Eagles did not pigeon hole themselves into going for two — based on how the Chiefs reacted to that formation prior to the snap, Philadelphia could have switched back to a normal extra point formation or simply taken a delay of game penalty with minimal harm. But Kansas City did not react well to the play pre-snap: The Eagles split two players out wide to the right, and Kansas City countered with two defenders to that side. But in the middle of the field, Philadelphia had the snapper, holder, and kicker, while the Chiefs kept four players in the middle of the field. I’m quite certain the special teams coach was not pleased with how the Chiefs responded to the situation, because that left K.C. with only five defenders to the defense’s right, while the Eagles were able to match up five blockers to that side and Zach Ertz, the eventual ballcarrier.

That’s a matchup Philadelphia should win more often than fifty percent of the time, and perhaps significantly more often than that. As it turns out, Lane Johnson blew the block, Tamba Hali made a nice play, and Kelly and the Eagles had egg on their face. Failing unconventionally has its drawbacks.

Spoiler: the quarterback plays a big role in passing yards.

Spoiler: the quarterback plays a big role in passing yards.

In May, I wrote that the scoring team is responsible for roughly 60% of the points it scores, while the opponent is responsible for 40% of those points. In other words, offense and defense both matter, but offense tends to matter more.

I was wondering the same thing about passing yards. When Team A plays Team B, how many passing yards should we expect? As we all know, Team A can look very different when it has Dan Orlovsky instead of Peyton Manning, so I instead chose to look at Quarterback A against Team B. Here’s the fine print:

1) I limited my study to all quarterbacks since 1978 who started at least 14 games for one team. Then, I looked at the number of passing yards averaged by each quarterback during that season, excluding the final game of every year. I also calculated, for his opponent, that team’s average passing yards allowed per game in their first 15 games of the season.

2) I then calculated the number of passing yards averaged by each quarterback in his games that season excluding the game in question. This number, which is different for each quarterback in each game, is the “Expected Passing Yards” for each quarterback in each game. I also calculated the “Expected Passing Yards Allowed” by his opponent in each game, based upon the opponent’s average yards allowed total in their other 14 games.

3) I then subtracted the league average from the Expected Passing Yards and Expected Passing Yards Allowed, to come up with era-adjusted numbers.

4) I performed a regression analysis using Era-Adjusted Expected Passing Yards and Era-Adjusted Expected Passing Yards Allowed as my inputs. My output was the actual number of passing yards produced in that game.
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Fast and Faster

Fast and Faster.

The number one storyline in the NFL in week one isn’t the health of Robert Griffin III, but the presence of two other men occupying FedEx Field that night. The football world is anxiously awaiting to see how Chip Kelly’s offense, piloted by Michael Vick, will work in the NFL. We don’t know much, but we do know that the coach plans to incorporate the fast-paced, up-tempo style that his teams used at Oregon to obliterate opponents.

In May, I took a stab at discussing tempo in the NFL, and I presented a couple of lists that measured the number of plays run per second of possession in the NFL. Today, I want to revisit the questions of tempo and pace using more precise measurements.  Let’s start with some league-wide data. The table below shows the average number of seconds between snaps for NFL teams last season. I’ve excluded a number of plays from this sample, including all plays at the start of a quarter, all overtime plays, plays after a changes of possession, and plays in the final three minutes of the first half or five minutes of the second half (where teams are less likely to operate at their normal pace).

secs btw plays
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Last night, David Wilson ran 84 yards for a touchdown on the Giants first play from scrimmage. Without being touched. How does that happen? Let’s start with a look from the end zone right at the snap:

Giants Jets Wilson Snap

The Jets are lined up with four down linemen: from left to right, you can see DE Muhammad Wilkerson, first-round tackle Sheldon Richardson, backup NT Damon Harrison, and outside linebacker/edge rusher Garrett McIntyre. At linebacker, we see Calvin Pace, David Harris, and Demario Davis — the new starter whom Rex Ryan has compared to Ray Lewis — tight inside the tackles. Left cornerback Kyle Wilson is off screen, covering Rueben Randle on the Giants right, while the Jets show a single-high safety look: Dawan Landry, the free agent addition from Jacksonville, is 13 yards off the line of scrimmage, while safety Antonio Allen (the Jets 7th round pick a year ago and expected starter in 2013) has creeped towards the line. What’s not shown: a few seconds earlier, the Giants motioned TE Brandon Myers to the offense’s left before the snap, causing Antonio Cromartie to line up right in the face of Hakeem Nicks and Allen (39) to drop down closer to the line of scrimmage (he was ten yards off the line before Myers moved).

The Giants know what is coming: a handoff to David Wilson, who will read the Jets defense to determine whether he bursts up the gut or bounces outside. From a numbers game, the Giants like what they see: even after Allen comes down, the math looks even. Assuming Nicks can handle Cromartie (he will), the Giants have the center, left guard, left tackle, Myers (a yard off the line) and TE Bear Pascoe (playing the traditional fullback slot) to block five Jets – Harrison and McIntyre on the line, Harris and Davis in the second level, and Allen.

In theory, you would think the Giants would have the C block the NT, the uncovered LG would make a beeline towards Harris (52), the LT would take care of McIntyre, and Pascoe and Myers would be assigned to Davis (56) and Allen (39). Some of that happens — the center (backup Jim Cordle) handles the nose; he also gets an assist from LG Kevin Boothe, who nudges Harrison away from the play a second before he manhandles Harris (a mismatch for most linebackers, so we can’t be too harsh on Harris). LT Will Beatty also overpowers the RDE, McIntyre, unsurprising considering (1) Beatty is a pretty good player and McIntyre is a backup 3-4 OLB, and (2) Beatty outweighs him by 64 pounds. Credit the Giants for good blocking, but blocking your assigned man doesn’t turn into 84-yard runs very often. The real cuprit on the play is Allen, but he was only the last domino to fall.
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Last week, I wrote about why I was not concerned with Trent Richardson’s yards per carry average last season. I like using rushing yards because rush attempts themselves are indicators of quality, although it’s not like I think yards per carry is useless — just overrated. One problem with YPC is that it’s not very stable from year to year. In an article on regression to the mean, I highlighted how yards per carry was particularly vulnerable to this concept. Here’s that chart again — the blue line represents yards per carry in Year N, and the red line shows YPC in Year N+1. As you can see, there’s a significant pull towards the mean for all YPC averages.

regression ypc

I decided to take another stab at examining YPC averages today.  I looked at all running backs since 1970 who recorded at least 50 carries for the same team in consecutive years. Using yards per carry in Year N as my input, I ran a regression to determine the best-fit estimate of yards per carry in Year N+1. The R^2 was just 0.11, and the best fit equation was:

2.61 + 0.34 * Year_N_YPC

So a player who averages 4.00 yards per carry in Year N should be expected to average 3.96 YPC in Year N+1, while a 5.00 YPC runner is only projected at 4.30 the following year.

What if we increase the minimums to 100 carries in both years? Nothing really changes: the R^2 remains at 0.11, and the best-fit formula becomes:

2.63 + 0.34 * Year_N_YPC

150 carries? The R^2 is 0.13, and the best-fit formula becomes:

2.54 + 0.37 * Year_N_YPC

200 carries? The R^2 stays at 0.13, and the best-fit formula becomes:

2.61 + 0.36 * Year_N_YPC

Even at a minimum of 250 carries in both years, little changes. The R^2 is still stuck on 0.13, and the best-fit formula is:

2.68 + 0.37 * Year_N_YPC

O.J. Simpson typifies some of the issues. It’s easy to think of him as a great running back, but starting in 1972, his YPC went from 4.3 to 6.0 to 4.2 to 5.5 to 5.2 to 4.4. Barry Sanders had a similar stretch from ’93 to ’98, bouncing around from 4.6 to 5.7 to 4.8 to 5.1 to 6.1 and then finally 4.3. Kevan Barlow averaged 5.1 YPC in 2003 and then 3.4 YPC in 2004, while Christian Okoye jumped from 3.3 to 4.6 from 1990 to 1991.

This guy knows about leading the league

This guy knows about leading the league.

Those are isolated examples, but that’s the point of running the regression. In general, yards per carry is not a very sticky metric. At least, it’s not nearly as sticky as you might think.

That was going to be the full post, but then I wondered how sticky other metrics are.  What about our favorite basic measure of passing efficiency, Net Yards per Attempt? For purposes of this post, an Attempt is defined as either a pass attempt or a sack.

I looked at all quarterbacks since 1970 who recorded at least 100 Attempts for the same team in consecutive years. Using NY/A in Year N as my input, I ran a regression to determine the best-fit estimate of NY/A in Year N+1. The R^2 was 0.24, and the best fit equation was:

3.03 + 0.49 * Year_N_NY/A

This means that a quarterback who averages 6.00 Net Yards per Attempt in Year N should be expected to average 5.97 YPC in Year N+1, while a 7.00 NY/A QB is projected at 6.45 in Year N+1.

What if we increase the minimums to 200 attempts in both years? It has a minor effect, bringing the R^2 up to 0.27, and producing the following equation:

2.94 + 0.51 * Year_N_NY/A

300 Attempts? The R^2 becomes 0.28, and the best-fit formula is now:

2.94 + 0.53 * Year_N_NY/A

400 Attempts? An R^2 of 0.26 and a best-fit formula of:

3.18 + 0.50 * Year_N_NY/A

After that, the sample size becomes too small, but the takeaway is pretty clear: for every additional yard a quarterback produces in Year N, he should be expected to produce another half-yard in NY/A the following year.

So does this mean NY/A is sticky and YPC is not? I’m not so sure what to make of the results here. I have some more thoughts, but first, please leave your ideas and takeaways in the comments.

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