Okay, some fun trivia to kick off the week. Do you know which team last year had the worst points differential in games they lost? I’ll put the answer in spoiler tags.

Where does that rank historically? I thought it would be fun to look at the teams since 1950 with the worst average margin of defeat looking exclusively at performance in losses. This was a bit of a tricky one, but Scott Kacsmar was able to guess it on twitter. The answer?



The table below shows the 100 teams with the worst average points differential in losses since 1950. As always, the tables in this post are fully sortable and searchable. For viewing purposes, I’m displaying only the top 20, but you can change that in the dropdown box on the left. [continue reading…]

Last off-season, I looked at passing performance on “third downs”, and I thought it would be fun to revisit that idea this summer. As before, I am putting that term in quotes because I’m including fourth down data in the analysis, but don’t want to write third and fourth down throughout this post.

To grade third down performance, I included sacks but discarded rushing data (again, just in the interest of time). The first step in evaluating third down performance is to calculate the league average conversion rate on third downs for each distance. Here were the conversion rates I calculated last year.

[continue reading…]

What is the value of a first down? By that I mean, how many marginal yards is a first down actually worth? Here’s another way to word the question: If 3 first downs and 80 yards are worth X, then 2 first downs and [???] many yards are equal to X?

Calculating the marginal value of a yard isn’t easy. In fact, it’s been bugging me for years, because I’ve never quite been sure how to derive them. Then, a light bulb went off in my head: I needed to reach out to Brian Burke. I had an idea, but not the data or the means to execute.

Burke, of course, runs the fantastic website Advanced Football Analytics (formerly Advanced NFL Stats). I asked him if he would run some queries, and Brian was kind enough to do so. Fortunately, Brian’s not just a guy with access to lots of data, but one of the smartest minds in the industry. I wholeheartedly endorse his methods below, and I’m very thankful for his help. On top of running the numbers, he also provided an excellent writeup on his work. What follows are Brian’s words and analysis.

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To estimate the value of achieving a 1st down without counting any of the value of the yardage gained, we can use the Expected Points model. The value of the 1st down itself minus yardage value will be the discontinuity in EPA when a play’s gain crosses the threshold for a 1st down. That discontinuity represents the value of the conversion apart from any yardage gained.

For example, on 2nd and 10, the EPA would increase smoothly for each yard gained up to 9 yards gained, then jump to a much higher EPA crossing the 10-yard mark where the conversion occurs. After that point, the EPA should increase smoothly again with each marginal yard gained above what was needed for the conversion.

Here is an illustration. The Y-axis represents Expected Points Added, the X-axis the amount of yards gained on the play.

The EPA for a 9-yd gain is 0.57, and the EPA for a 10-yd gain is 1.04. That’s a discontinuity of 0.47 EP, meaning that the 1st down itself is nearly equivalent to the 9-yards gained up to the point of conversion.

But we also need to correct for the yardage value of that 10th yard. One yard of field position is generally worth 0.064 EP. So in this case the discontinuity itself is worth 0.47 – 0.064 = 0.41 EP.

If we wanted to assign a “bonus” of yards to a player who is credited with achieving the conversion over and above the yardage itself, we could use this value’s yardage equivalent. 0.41 EP / 0.064 EP/yd = 6.4 yds. That’s the bonus for 2nd down and 10, but there are many other down and distance situations to consider.

For example, on 3rd and 10, the discontinuity is 1.57 EP, equivalent to nearly 25 yds. First and 10 is very strange because the discontinuity is negative. This makes sense, however, because an offense should prefer a 2nd & 1 to a 1st & 10 anywhere on the field. It would be silly to penalize a player for gaining the extra yard to convert, so my opinion would be to say the EP bonus for a conversion on 1st down is zero.

After examining a smattering of 2nd and 3rd down situations, the 2nd-down bonus EP is about 0.35 and 3rd-down bonus EP is roughly 1.4.

4th down conversions would obviously mean a very large bonus EP. They essentially have the value of a turnover–close to 4 EP or so. Since 4th downs are qualitatively different (and relatively rare) I’m going to set them aside.

In general, 32% of conversions come on 1st down, 38% come on 2nd down, and 30% come on 3rd down. So the weighted value of a conversion alone would roughly be:

[0.32 * 0] + [0.38 * 0.35] + [0.30 * 1.4] = 0.55 EP

The conversion bonus of 0.55 EP can be translated into yards by dividing by 0.064 EP/yd, which ultimately makes the equivalent yardage bonus for a conversion: 8.7 yards.

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Figuring out the value of a first down will have many applications for Football Perspective going forward. Please leave your thoughts in the comments, as I’d love to hear what you guys have to say. And thanks again to Brian for his great work.

Every year at Footballguys.com, I publish an article called Rearview QB, which adjusts the fantasy football statistics for quarterbacks (and defenses) for strength of schedule. I’ve also done the same thing for years (including last season) using ANY/A instead of fantasy points, which helps us fully understand the best and worst real life performances each year. Today I deliver the results from 2013.

Let’s start with the basics. Adjusted Net Yards per Attempt is defined as (Passing Yards + 20 * Passing Touchdowns – 45 * Interceptions – Sack Yards Lost) divided by (Pass Attempts plus Sacks). ANY/A is my favorite explanatory passing statistic — it is very good at telling you the amount of value provided (or not provided) by a passer in a given game, season, or career.

Let’s start with some basic information. The league average ANY/A in 2013 was 5.86, a slight downgrade from 2012 (5.93). Nick Foles led the way with a 9.18 ANY/A average last year, the highest rate in the league among the 45 passers with at least 100 dropbacks. Since the Eagles quarterback had 317 pass attempts and 28 sacks in 2013, that means he was producing 3.32 ANY/A (i.e., his Relative ANY/A) over league average on 345 dropbacks. That means Foles is credited with 1,145 Adjusted Net Yards above average, a metric labeled “VALUE” in the table below. Of course, Peyton Manning led the league in that category last year, with a whopping 2,037 Adjusted Net Yards over Average.

Manning paces in the field in Value over average, of course: that’s not surprising when the future Hall of Famer set the single-season record for passing yards and passing touchdowns. Foles, Drew Brees, and Philip Rivers formed the next tier of quarterbacks, far behind Manning but well ahead of the rest of the league.

And at the bottom of the list was the defending Super Bowl MVP, Joe Flacco. With a 4.50 ANY/A average, Flacco only edged out four other quarterbacks in that statistic, and none of the other passers came close to accumulating as many dropbacks as Flacco. After him comes the two New York quraterbacks, Geno Smith and Eli Manning.

But the point of today’s post is to adjust those numbers for strength of schedule. The solution is this post — a methodology I’ve labeled Rearview adjusted net yards per attempt, which adjusts those numbers for strength of schedule. The system is essentially the same as the one used in the Simple Rating System. Let’s look at Matt Ryan, who averaged 5.72 ANY/A last season, on 695 dropbacks. If we want to find Ryan’s SOS-adjusted rating, we need an equation that looks something like this: [continue reading…]

Yesterday, I explained the methodology behind the formula involved in ranking every quarterback season since 1960. Today, I’m going to present the career results. Converting season value to career value isn’t as simple as it might seem. Generally, we don’t want a player who was very good for 12 years to rank ahead of a quarterback who was elite for ten. Additionally, we don’t want to give significant penalties to players who struggled as rookies or hung around too long; we’re mostly concerned with the peak value of the player.

What I’ve historically done — and done here — is to give each quarterback 100% of his value or score from his best season, 95% of his score in his second best season, 90% of his score in his third best season, and so on. This rewards quarterbacks who played really well for a long time and doesn’t kill players with really poor rookie years or seasons late in their career. It also helps to prevent the quarterbacks who were compilers from dominating the top of the list. For visibility reasons, the table below displays only the top 25 quarterbacks initially, but you can change that number in the filter or click on the right arrow to see the remaining quarterbacks. ^[1]Note that while yesterday’s list was just from 1960 to 2013, the career list reflects every season in history, using the same methodology as used in GQBOAT IV.

Here’s how to read the table. Manning’s first year was in 1998, and his last in 2013. He’s had 8,740 “dropbacks” in his career, which include pass attempts, sacks, and rushing touchdowns. His career value — using the 100/95/90 formula ^[2]And including negative seasons. is 12,769, putting him at number one. His strength of schedule has been perfectly average over his career; as a reminder, the SOS column is shown just for reference, as SOS is already incorporated into these numbers (so while Tom Brady has had a schedule that’s 0.25 ANY/A tougher than average, that’s already incorporated into his 10,063 grade). Manning is not yet eligible for the Hall of Fame, of course, but I’ve listed the HOF status of each quarterback in the table. Note that I only have quarterback records going back to 1960; therefore, for quarterbacks who played before and during (or after) 1960, only their post-1960 record is displayed. In addition, SOS adjustments are only for the years beginning in 1960. [continue reading…]

Colin Kaepernick won’t be hurting for weapons this year, which may be why San Francisco decided to give him a massive contract extension prior to the season. So will this be a career year for the young quarterback? Even if he plays well, he may not throw for 4,000 yards due to game script; after all, the 49ers held an average lead 5.9 points last year, and as a result, the team ranked 31st in pass attempts. San Francisco figures to be excellent again, but Kaepernick should produce very strong efficiency numbers in 2014. Assuming they all stay healthy and make the roster, check out the quintet of weapons Kaepernick will have at his disposal:

• Anquan Boldin was dominant for San Francisco last year, and 2013 marked the sixth time in his career he’s topped the 1,000-yard mark. He maxed out with a 1,402-yard season with Arizona in 2005.
• Michael Crabtree was limited to just five games after recoving from a torn Achilles, but he recorded 1,105 yards on a run-heavy 49ers team in 2012.
• Steve Johnson had 1,000-yard seasons in 2010, 2011, and 2012 (with a high of 1,073 in ’10) with the Bills, but will be a 49er in 2014.
• Tight end Vernon Davis has actually never had a 1,000-yard year, but he did gain 965 yards and score 13 touchdowns in 2009.
• Brandon Lloyd may not even make the roster, but the man drafted by San Francisco 11 years ago has seen some success in between his stops with the 49ers.  Two years ago, he gained 911 yards for the Patriots, and in 2010, he led the league with 1,448 receiving yards while playing in Denver.

As of a year ago, only eight teams in NFL history had ever fielded a roster with five players who gained 1,000 receiving yards in a season at some point in their careers. But none of those teams entered a season with five former 1,000-yard receivers: for each of those teams, at least one of the five players had a 1,000-yard season at some point in the future.

But the 2014 49ers would only become the second team to enter a season with five players who had previously gained at least 965 receiving yards in a season. Can you guess the first? [continue reading…]

It’s no secret that Andrew Luck’s efficiency numbers aren’t quite up to par with his reputation. Over the past two seasons, Luck ranks just 18th in ANY/A, far behind some of the other young quarterbacks in the NFL. Nick Foles, Russell Wilson, and Colin Kaepernick rank in the top 6th in that metric, Robert Griffin is 11th, Cam Newton is 14th, and even Andy Dalton is 16th. Luck tends to fare much better in ESPN’s QBR than in ANY/A (and Andy Benoit wrote an interesting pro-Luck piece yesterday), but today I wanted to try to quantify another issue: quarterback help.

A quick disclaimer: there are probably a zillion different ways to quantify quarterback help. This is certainly not not not the best way, but it’s the way that was easiest and most intuitive to me. On the scale of “this feels right” to “rigorous quantitative analysis” this certainly falls closer to the former end of the scale. But it’s Friday and we’re having fun, so here’s what I did.

1) Calculate how many standard deviations from average each team was in Points Allowed (negative means fewer points allowed).

2) Calculate how many standard deviations from average each team was in Pass Ratio (negative means more run-heavy).

3) Add the two standard deviations to see how much each team relied on each quarterback’s arm.

Here were the 2013 results. According to this, no quarterback was asked to do more than Matt Ryan. Here’s how to read the table below: The Falcons allowed 443 points last year, which was 1.05 standard deviations more than the average team. Atlanta also passed on 68.7% of all plays, which was 1.99 standard deviations above average. Add those together, and the Falcons get a grade of +3.04, the most in the NFL in 2013. [continue reading…]

It’s fun to play with weighted averages to see how the NFL has (or hasn’t) evolved. For example, the Giants led the league with interceptions: as a result, 5.8% of all interceptions thrown in the NFL last year were by Eli Manning or Curtis Painter. Since the Giants went 7-9 in 2013, that means 5.8% of all interceptions were thrown by a team that had a 0.438 winning percentage. Meanwhile, Kansas City and San Francisco each threw just 8 interceptions, or 1.6% of all NFL interceptions, and the Chiefs and 49ers had an average winning percentage of 0.719.

So while the average winning percentage of all NFL teams is of course 0.500, the average weighted (by interceptions) winning percentage of all NFL teams will be below .500 because bad teams tend to throw more interceptions than good teams. Last year, the averaged weighted winning percentage was 0.464 for all NFL teams.

What’s interesting is how little variation there has been over the years in weighted winning percentage. In fact, it’s been between 45% and 50% in just about every year since 1950: [continue reading…]

Josh Gordon led the league with 1,646 receiving yards last year. That’s impressive: perhaps even more impressive is that he did it on “only” 159 targets, meaning he averaged 10.35 yards per target. ^[1]That’s the most of any receiver with over 130 targets. It’s the second most among players with 100 targets, behind DeSean Jackson‘s 10.6 average on 126 targets. It’s the … Continue reading But the most impressive part, of course, was that he did it for the Browns. You know, the Browns, quarterbacked by a three-headed monster of Jason Campbell, Brandon Weeden, and Brian Hoyer, each of whom managed to average a around the same mediocre 6.4 yards per attempt.

Here’s another way to think of it. While Jordan Cameron was somewhat efficient (7.7 yards per target), the other three Browns to finish in the top five in Cleveland targets were Greg Little (4.7 yards per target), Chris Ogbonnaya (4.6), and Davone Bess (4.2!). And here’s yet another way to think of it: the Browns threw 681 passes last year and gained 4,372 passing yards. But 1,646 of those yards came on the 159 passes intended for Gordon. Remove those plays, and Cleveland averaged just 5.22 yards per pass attempt on passes to all other Browns last year.

That means Cleveland averaged 5.13 more yards per target on passes to Gordon in 2013 than on passes to everyone else. That’s insane, particularly over 159 targets. How insane? If we multiply those two numbers, we get a “value relative to teammates” metric: Gordon gained 816 more yards on his targets than the other Browns averaged per target. Now, in the abstract, maybe 816 doesn’t mean much to you. But it’s the most of any player since at least 1999. The table below shows the top 75 wide receivers in value relative to teammates: the columns should be self-explanatory, and the “ROT Y/A” shows the yards per attempt on passes to the rest of the team. As always, it’s fully sortable and searchable; by default, it displays only the top 25 receivers, but you can switch that by clicking on the dropdown box to the left. [continue reading…]

Comparing wide receivers across teams is tricky. Pierre Garcon led the NFL in targets, ^[1]All target data comes courtesy of Footballguys.com. but that’s partially because Washington didn’t have much help at wide receiver. ^[2]And in the offseason, Washington signed DeSean Jackson and Andre Roberts Vincent Jackson was 2nd in percentage of team targets (we’ll get to who was first in a few minutes) for a similar reason: Jackson is a very good receiver, but Tampa Bay had limited weapons in 2014. ^[3]And in the 2014 NFL Draft, the Bucs added Texas A&M wide receiver Mike Evans and Washington tight end Austin Seferian-Jenkins. At least in theory, the high target numbers for Garcon and Jackson should be considered in light of the fact that both teams had below-average passing offenses.

The flip side of that coin is a player like Demaryius Thomas. In 2012, while “competing” with another very good receiver in Eric Decker, Thomas saw 24.2% of Denver targets.  Last year, with the addition of Wes Welker and a breakout season from Julius Thomas, Thomas saw just 21.2% of Broncos targets. But the team’s passing game was better, so arguably Thomas should receive a “bump” in his target percentage because he played for a great offense.

That’s just in theory. The unspoken elephant in the analysis is the quarterback. It’s not just a player’s supporting cast of weapons that determines whether his team has a good or bad passing attack: Thomas obviously benefited greatly from playing with Peyton Manning, too. Regular readers may recall that last year, for each team’s leader in targets, I compared their target percentage (defined as targets divided by all team targets) to their team’s passing efficiency (defined by Adjusted Net Yards per Attempt). I thought it would be fun to perform the analysis again, even if it may make more sense in theory than in practice. Take a look: the Y-axis shows percentage of team targets, and the X-axis respects Team ANY/A. In theory, the best WR1s should be up and to the right, with the worst WR1s (or tight ends masquerading as WR1s) in the bottom left corner of the chart.

[continue reading…]

Over the last three years, Calvin Johnson has 5,137 receiving yards in 46 games.  That’s an average of 111.7 receiving yards per game, the most by any player over a three-year stretch in NFL history.  That mark comes with a bit of an asterisk, of course, as the Lions have attempted 2,040 passes since the start of the 2011 season, also an NFL record; that’s why I like using True Receiving Yards and various other WR Ranking Systems rather than just raw receiving yards.

But hey, trivia is trivia, and Johnson is the current record holder.  But prior to 2013, do you know who held the record for receiving yards per game over a three-year stretch? The answer is not Jerry Rice, or else this would be a really lame trivia question.  Rice averaged 101.0 receiving yards per game from 1993 to 1995, and is one of just three players to average over 100 receiving yards per game for a three-year stretch.  Megatron also averaged 101.4 receiving yards per game from 2010 to 2012, but he only became the 3-year king after the conclusion of the 2013 season.

I suspect you’ll also be surprised to see who would is number 4 on the list of most receiving yards per game over a three-year span (counting each player only once, of course).

[continue reading…]

Last week at Five Thirty Eight, Nate Silver noted that San Antonio Spurs head coach Gregg Popovich has produced an excellent record against the spread. He also checked in football’s version of Pop, Bill Belichick, and came to the same conclusion: Belichick hasn’t just been great, but he’s been great against the spread, too.

My database on point spreads goes back to 1978, so I went ahead and calculated the Against-The-Spread record of each head coach over the last 36 seasons. According to my numbers, Belichick has “covered” or won 40 more games against the spread than he’s lost, the most over this period. ^[1]My numbers differ slightly from Silver’s, although that’s not surprising. There is always some variation in point spread data, which is, of course, not official.  The table below shows the 122 men who  have coached at least 50 games or who were active in 2013.

Here’s how to read Belichick’s line: He has been coaching since 1991 (coaches who began before 1978 are included, but only their post-1977 seasons are counted (and only if they coached 50+ games since 1978)) and was last coaching in 2013. Over that time, he has coached in 332 games, including the post-season. His record against the spread is 182-142-8, which gives him a 0.562 winning percentage (ignoring ties). ^[2]When calculating regular winning percentage, we treat ties as half-wins and half-losses.  In his article, Silver excluded ties from calculating ATS winning percentages. I don’t know … Continue reading His real record is 218-114-0, which gives him a 0.657 winning percentage (again, including the playoffs). The table is sorted by the last category, which represents the difference beteween his number of wins against the spread and his number of losses against the spread. [continue reading…]

Peyton Manning’s time in Indianapolis was peppered with record-breaking moments that have been very well-publicized. But a relatively unknown record occurred during the nascent days of the Manning Era. In 1999, Edgerrin James rushed for 1,553 yards, an impressive accomplishment in any era. But here’s what’s really crazy: Manning was second in the team in rushing yards with 73! Keith Elias was the only other running back to record a carry, and he finished with 28 yards (Marvin Harrison and Terrence Wilkins added six total rushing yards). This means James recorded 93.6% of all Indianapolis rushing yards that season, still an NFL record, and one that is in no danger of being broken in the near future.

Second on the list of “largest percentage of the rushing pie” is … Edgerrin James for the Colts the following season. In 2000, he was responsible for 91.9% of all Indianpolis rushing yards. Only three other players have ever gained 90% of all team rushing yards: Emmitt Smith, Barry Sanders, and … Travis Henry. The table below shows the top 100 seasons as far as percentage of team rushing yards: [continue reading…]

In case you haven’t heard, the St. Louis Rams are running a contest to predict the team’s 2014 schedule. lThe prize is $100,000, which sounds nice until you realize that to win, you must accurately predict not only the opponent each week, but the location and the exact day of the game. Nobody is going to win this contest. Nobody is going to come close to winning the contest. It’s a personal information/PR grab and nothing more.  Normally, this wouldn’t bother me, but it’s not like the Rams are giving away a billion dollars.  For a hundred grand — which is less than two percent of the amount of dead cap space being allocated to Cortland Finnegan this season — the team shouldn’t have needed to make it impossible for anybody to win. Considering the rules, St. Louis might as well have announced that the grand prize is eleventy billion dollars.

So what are the odds of winning this contest? Let’s start with an easier problem than the one at hand: predicting the Rams opponent in each week of the season.

With 17 weeks, there are 17 possible opponents once you include home/road designations and the bye week. Therefore, you have a 1-in-17 chance of correctly guessing the Rams opponent in week one. By extension, you have a 1-in-16 chance of correctly guessing who St. Louis plays in week two, assuming you were correct with your guess in week one (this is what we mean by conditional probabilities). Do this for every week of the season, and by week 17, you have a 100% chance of correctly guessing who is on the team’s schedule.

It may not be intuitive exactly how daunting a task this is. But this is much, much harder than Warren Buffet’s bracket contest.  For example, you only have a a 1-in-272 chance of correctly guessing who the Rams opponents will be in the first two weeks of the season. That drops to 1-in-4,080 through three weeks, 1-in-8.9 million through six weeks, and 1-in-8.8 billion through nine weeks. That already makes it harder than the bracket contest, and you still have the back eight to play. The odds of correctly guessing the opponent each week is 1-in-356 trillion. And remember, this is quite a bit easier than the actual contest!

But let’s make some adjustments based on the information we know (which will lower the odds) and the added conditions one must satisfy (which will drastically increase the odds).

Adjustment #1

The first adjustment to our 1-in-356 trillion likelihood lowers the odds. If we assume that each team plays a division opponent in week 17, that makes the contest ever so slightly easier. If we work in reverse order, you now have a 1-in-6 chance of guessing the week 17 opponent (remember, you need to specify game location), a 1-in-16 chance of guessing the week 16 opponent assuming your week 17 selection was correct, and so on. This improves your odds all the way to 1-in-126 trillion. Hooray? [continue reading…]

Is Matt Schaub washed up? Is he the next Jake Delhomme? For the first six seasons of his Texans career, Schaub was an above-average quarterback in both Net Yards per Attempt and Adjusted Net Yards per Attempt. But last year was disastrous in a way that his poor conventional stats fail to completely capture (for example, Schaub threws picks six in four straight games).

But does that mean hope is lost? Schaub turns 33 in June, which means more than you might think. Sure, Peyton Manning and Tom Brady can defy the odds, but 33 is still six years to the right side of the peak age for passers. Perhaps even more damning, Schaub’s steep decline in 2013 was his second in two years; he averaged 7.8 ANY/A in 2011, 6.5 in 2012, and then 4.5 last year; his NY/A averages (7.7, 6.6, 5.7) have followed a similar pattern. The graph below shows Schaub’s Relative NY/A and Relative ANY/A — i.e., his averages compared to league average — for each year of his Texans career:

[continue reading…]

We all know that scoring is on the rise. The 2013 season was the highest scoring season in NFL history, just narrowly edging out the … 1948, 1950, and 2012 seasons. Scoring soared in the aftermath of World War II, but quickly dropped off in the middle of the 1950s. Scoring fell to its nadir in 1977, prompting the 1978 rules changes regarding pass blocking and pass coverage. After another lull in the early nineties, scoring has steadily increased over the last twenty years. Take a look at the average points per game for professional teams (including the AAFC and AFL) since 1940:

[continue reading…]

One of the very first posts at Football Perspective measured how various passing stats were correlated with wins.  One of the main conclusions from that post was that passer rating, because of its heavy emphasis on completion percentage and interception rate, was not the ideal way to measure quarterback play. But what about ESPN’s Total QBR, a statistic invented specifically to improve on — and supersede — traditional passer rating?

As a reminder, we can’t simply correlate a statistic with wins to determine the utility of that metric. The simplest way to remember this is that 4th quarter kneeldowns are highly correlated with wins. Just because you notice it’s raining when the ground is wet doesn’t mean a wet ground causes rain; i.e., just because two variables are correlated doesn’t mean variable A leads to variable B (alternatively, variable B could lead to variable A, variable C could lead to both variable A and B, or the sample size could be too small to determine any legitimate causal relationship). That said, it at least makes sense to begin with a look at how various statistics have correlate with wins.

The Sample Set

Throughout this post, I will be looking at a set of quarterback data consisting of the 152 quarterback seasons from 2006 to 2013 where the player had at least 14 games with 20+ action plays. Games where the quarterback had fewer than 20 plays were excluded, but the quarterback was still included if he otherwise had 14 such games.

The next step was to sum the weekly quarterback data on various metrics, including wins, and create season data. ^[1]For ESPN’s QBR, I took a weighted average of the weekly QBR data. I should note that this is not the way ESPN calculates QBR. As explained to me via email, the scaling function that gives the … Continue reading This allowed me to measure the correlation between a quarterback’s statistics over those 14+ games with that player’s winning percentage in those games.

As it turns out, ESPN’s Total QBR is very highly correlated with wins, with a 0.68 correlation coefficient. ^[2]As a reminder, the correlation coefficient is a measure of the linear relationship between two variables on a scale from -1 to 1. If two variables move in the same direction, their correlation … Continue reading This is to be expected; after all, Total QBR is based off Expected Points Added on the team level, which generally tracks wins and losses. The second most correlated statistic with wins was Adjusted Net Yards per Attempt, my favorite non-proprietary quarterback metric. After ANY/A, both traditional passer rating and touchdowns per attempt were the next most correlated statistics with wins (after all, this is only a step or two away from saying scoring points is correlated with wins). In another unsurprising result, passing yards had almost no correlation with wins, while pass attempts had a slight negative correlation (as any Game Scripts observer would know).  Take a look:

When ESPN first introduced QBR, I wrote that I was intrigued by the possibility of this metric, but frustrated that the specific details of the formula remained confidential. At the time, a clutch weight feature was included in the calculations, which made the metric more of a retrodictive statistic than a predictive one. Since then, ESPN has tweaked the formula several times, and the clutch weight has been capped. ^[3]When Dean Oliver was on the Advanced NFL Stats podcast, he noted that the formula was tweaked in 2013 so that the “clutch index” part of the formula was essentially capped. He added … Continue reading ESPN is not engaged in academia, so I understand why they have not published all the fine print; as a researcher, I’m still frustrated by that decision. Still, with 8 years of QBR data now publicly available, we can answer two questions: does Total QBR predict wins and how sticky is Total QBR?

We know that a high Total QBR is correlated with winning games, but we also know that there’s limited value to such a statement. If having a high Total QBR was one of the driving factor behind winning games, than such a variable would manifest itself in all games, not just the current one. So with my sample of 152 quarterbacks, I used a random number generator to divide each quarterback season into two half-seasons. Then I calculated each quarterback’s average in several different categories and measured the correlation between a quarterback’s average in such category in each half-season with his winning percentage in the other half-season. ^[4]Then I did the entire process again, using a new set of random numbers, and averaged the results. The results:

As you would expect, all of our correlations are now smaller. But ESPN’s quarterback rating metric remains the best measure to predict wins. Perhaps even more impressively, Total QBR is more correlated with future wins than past wins. That’s pretty interesting. Another interesting result is that passer rating fares pretty well here, although much of the same issues as before remain with using correlation to derive causal direction. ^[5]For example, because passer rating is biased towards high completion percentage and low interception rates, quarterbacks who play with the lead tend to produce strong passer ratings; well, playing … Continue reading

One other concept to remember is that our sample of quarterbacks consists of players who were heavily involved in at least 14 games. That makes sure Peyton Manning, Tom Brady, and Drew Brees are involved, while filtering out some Christian Ponder, Blaine Gabbert, and Brandon Weeden seasons. In other words, the data set contains more above-average quarterbacks than a random sample would, so we may not be able to justify certain conclusions from this study.

The other important question is whether Total QBR is predictive of itself; i.e., how “sticky” is this metric over different time periods. We know that interceptions are very random, and knowing a quarterback’s prior interception rate is not all that helpful in predicting his future interception rate. Where does Total QBR fall along those lines?

The most “sticky” stats were passing yards and pass attempts, which in retrospect isn’t too surprising. These reflect the style of the offense, the talent of the quarterback, and the quality of the defense, so they should be easier to predict. The second-least sticky metric was wins, which also makes sense. After that, ESPN’s Total QBR fits in a narrow tier with most of our other metrics as being somewhat predictable.

Conclusion

The numbers here indicate that Total QBR is worth examining.  It may be a proprietary measure of quarterback play, but it’s not a subjective one with no basis in reality.  It does seem to be the “best” measure of quarterback play, although whether the tradeoff in accuracy for transparency is worth it remains up to each individual reader. One of the drawbacks I see in Total QBR is the failure to incorporate strength of schedule. And while no other traditional passer metric does, either, it’s also easy enough to make those adjustments. Hopefully, an SOS-adjusted Total QBR measure will be released soon (I’ll note that the college football version does include a strength-of-schedule adjustment).  My sense is that Total QBR is underutilized because (1) ESPN haters hate it because it’s an ESPN statistic, (2) it’s proprietary, and (3) analytics types disliked it because of the (now-eliminated) clutch rating.  While I would not suggest making it the only tool at your disposal, it does appear to deserve a prominent place in your toolbox.

There are few statistics more random in all of sports than fumble recoveries. When a football is on the ground, it’s not the case that better teams are more likely to fall on the ball than bad teams: in the NFL, recovering fumbles is nearly all luck and little skill. This is a fact widely accepted by all statisticians, but I figured I would still crunch the numbers just to confirm.

I looked at all teams from 1990 to 2012. First, I looked at fumble recovery rates for teams on their own fumbles. The correlation coefficient between fumble recovery rate in Year N and fumble recovery rate in Year N+1 was 0.00. In other words, there is simply no correlation between fumble recovery rates from year to year. Nada. Zilch. (Of course, fumble recovery rates do vary by type, but that appears to be muted when analyzing fumbles in the aggregate.)

I then looked at fumble recovery rates for teams on their opponent’s fumbles. The correlation coefficient there from year-to-year was -0.02. In other words, there is simply no correlation between recovering your opponent’s fumbles in one year and the next. The best way to predict each team’s fumble recovery rate is to simply project teams to recover about half of all their fumbles. ^[1]Actually, the best number is usually just shy of fifty percent. If words like regression cause your eyes to roll over, consider this: from 1990 to 2012, the top 20 teams in fumble recovery rate recovered 75.4% of their own fumbles; the following year, they recovered 50.4% of their own fumbles.

With that disclaimer out of the way, who were the best and worst teams at recovering fumbles in 2013? Let me walk through the Cowboys as an example. Last year, Dallas fumbled on offense 18 times, and lost 8 of them. Based on the league-wide average 47.6% recovery rate last year, the Cowboys lost 0.6 fewer fumbles than expected (a negative number here means the team did not lose as many fumbles as they “should” have). Cowboys opponents fumbled 16 times and lost 13 of them; as a result, Dallas recovered 5.4 more fumbles than we would have expected. Overall, this means the Cowboys recovered 6.0 more fumbles than expected, the highest number from last season; overall, on the 31 fumbles in Cowboys games, Dallas recovered 67.6% of them. [continue reading…]

Some quarterbacks and wide receivers just go together. Peyton Manning and Marvin Harrison. Dan Marino and Mark Clayton and Mark Duper. Joe Namath and Don Maynard. John Hadl and Lance Alworth. But quarterbacks play with lots of receivers, and receivers generally play with several quarterbacks. We don’t remember most combinations, but that doesn’t mean they were all unproductive. So I thought it might be interesting to look at every wide receiver since 1950, find his best single season in receiving yards, and record who was his team’s primary quarterback that season.

Jerry Rice’s best year came with Steve Young, not Joe Montana. Randy Moss set the touchdown record with Tom Brady, but his best year in receiving yards was with Daunte Culpepper. Lynn Swann’s best year was with Terry Bradshaw, but John Stallworth’s top season in receiving yards came with Mark Malone. James Lofton’s best season was with Lynn Dickey, Isaac Bruce’s best year was with Chris Miller, Torry Holt’s top season came with Marc Bulger, and Tim Brown’s top year was with Jeff George.

This is little more than random trivia, but this site does not have aspirations for March content higher than random trivia. In unsurprising news, 25 different players had their best season in receiving yards (minimum 300 receiving yards) while playing with Brett Favre. That includes a host of Packers, but also a couple of Jets and Vikings, too (including one future Hall of Famer).

After Favre, Marino is next with 22 players, and he’s followed by Manning and Fran Tarkenton (20). From that group, I suspect that Tarkenton might surprise some folks. That is, unless they realized that he was the career leader in passing yards when he retired and played for five years with the Giants and thirteen with Minnesota.

The table below shows every quarterback who was responsible for the peak receiving yards season of at least five different receivers (subject to the 300 yard minimum threshold). For each quarterback, I’ve also listed all of his receivers. [continue reading…]

The 2013 season was a disaster for Ray Rice, and 2014 isn’t off to a very good start, either. Last season, Rice carried 214 times for just 660 yards and four touchdowns, producing an anemic 3.1 yards per carry average. On November 9th, I asked whether Rice was already washed up; at the time it felt a bit premature, but in retrospect, such a view seems much more reasonable. Averaging so few yards per carry over such a large number of carries is pretty rare. How rare?

As a disclaimer, I’m in the camp that thinks YPC is an overrated statistic. In 2013, Marshawn Lynch, Eddie Lacy, and Frank Gore all averaged around the league average of 4.17 yards per carry, but that doesn’t make them average backs. So consider much of this post to be a bit of trivia and fun with stats, rather than the best way to identify running back productivity. With that disclaimer out of the way, I calculated each player’s “yards above league average” for each season since 1950, which is the product of a player’s number of carries and the difference between his YPC average and the league average YPC rate.

For example, since Rice averaged 3.08 YPC on 214 carries, he gets credited for being 231 yards below average in 2013. By this measure, Rice was the worst running back in the league. He was worse than his teammate Bernard Pierce (who actually had a lower YPC average but on fewer carries, so he finished 197 yards below average), worse than Willis McGahee (-198) or Rashard Mendenhall (-217), and even worse than Trent Richardson (-220). And this wasn’t your typical worst season in the league, either: his 2013 performance ranks as the 15th worst in this metric since 1950: [continue reading…]

In Geno Smith’s first 12 NFL starts, he completed 179 of 327 passes (54.7%) for 2,256 yards, with 8 touchdowns and 19 interceptions. Those numbers translate to a 6.9 yards per attempt average, quite respectable for a rookie, and a 4.8 Adjusted Yards per Attempt average, abysmal for anybody. But over the last four weeks of the year, Smith went 68/116 (58.6%) for 790 yards with 4 touchdowns and 2 interceptions. His yards per attempt actually went down slightly to 6.8, but he averaged 6.7 AY/A, much closer to league average. Touchdowns and interceptions are less sticky statistics than yards per attempt, but Jets fans looking for reasons for optimism would cling to the massive flip in touchdown-to-interception ratio over the final quarter of the season.

The real question is whether any of that matters. In general, I’m a Splits Happen type of analyst, but I thought I would run some numbers. As it turns out, perhaps there is some reason to think Smith’s strong December (subject to the caveats below) is a sign of good things to come.  Here’s what I did:

From 1990 to 2013, there were 51 quarterbacks who threw at least 224 passes during their rookie season. Toss out the 2013 rookies (EJ Manuel, Smith, and Mike Glennon), along with the nine quarterbacks who threw fewer than 100 passes in year two (Jimmy Clausen, Ryan Leaf, Kyle Orton, Chad Hutchinson, Andrew Walter, Bruce Gradkowski, Chris Weinke, Ken Dorsey, and Matt Stafford), and that leaves us with 39 quarterbacks who threw at least 224 passes as a rookie since 1990 and then at least 100 passes in their second season. For those quarterbacks, I calculated their Y/A and AY/A averages over their final 4 games of the season, and their Y/A and AY/A averages over the first 1-12 games of the season (with the 224 pass attempts minimum, I felt pretty confident that we would have a large enough sample on the “early” portion of the season).  Then I looked at how those 39 quarterbacks fared in their second years.

The table below shows all 39 quarterbacks, plus the 2013 rookies.  Here’s how to read the table below.  Heath Shuler, a rookie for Washington in 1994, had 150 “early” season attempts, defined as all pass attempts before the final 4 games of the season.  His early year Y/A average was 5.0 and his AY/A average was 2.8.  Shuler had 115 “late” season attempts, defined as pass attempts in the final four games.  His Y/A in the late part of the season was 7.9, and his AY/A was 7.8.  As a result, Shuler improved his Y/A by 3.0 and his AY/A by 5.0 over the final four games of the season.  In Year N+1 — i.e., 1995 for Shuler — he had 125 pass attempts, and averaged 6.0 Y/A and 3.9 AY/A. [continue reading…]

For a decade, Football Outsiders has been using advanced analytics to measure and predict team performance. And since the Football Outsiders database now goes back to 1989, I thought it would be worthwhile to test the predictive power of Football Outsiders’ ratings.

If you’re not familiar, FO uses DVOA as its base measure of team strength. The goal here is to use DVOA ratings in Year N to predict win totals in Year N+1. Now, what expectations should we have for DVOA? The fact that the team with the best DVOA in history — Washington in 1991 — won only 9 games the following season is not a knock on DVOA. That was an outstanding Super Bowl team that declined significantly the following year. Ditto the 16-0 Patriots looking less impressive without Tom Brady in 2008. But at a minimum, DVOA must do better at predicting future wins than say, just wins. And it should also do better than Pythagenpat ratings, which only incorporate points scored and points allowed. So does it?

Let’s start with the basics. The best-fit formula ^[1]Over the period 1989 to 2012, excluding the 1994, 1998, and 2001 seasons. to project wins in Year N+1 using *only* wins in Year N is:

5.343 + 0.332 * Year N Wins (Correlation Coefficient: 0.32)

And, as shown last week, by using Pythagenpat wins, we get a correlation coefficient of 0.36. So what happens if we instead use Year N DVOA as our input? We get the following best-fit formula:

8.01 + 6.378 * DVOA (Correlation Coefficient: 0.39)

As a result, DVOA does beat both regular wins and the Pythagenpat ratings. Now, what if we use both DVOA ratings and number of wins to predict future wins? As it turns out, the wins variable was nowhere near significant (p = 0.61), which means once we know the DVOA ratings, knowing the number of wins adds no predictive power. In other words, the evidence doesn’t prove that a team with a lot of wins but an average DVOA rating is better than a team with an average number of wins and an average DVOA rating.

But can we improve on DVOA? What if instead of using Team DVOA as our input, we use Offensive DVOA, Defensive DVOA, and Special Teams DVOA? Team DVOA obviously incorporates all three of these elements, but perhaps analyzing team strength on a more granular level will tell us more about the appropriate weights. Keeping in mind that for defenses, a negative DVOA grade means an above-average defense, here is the best-fit formula to predict future wins with those three inputs:

8.01 + 6.779 * OFFDVOA – 5.642 * DEFDVOA + 6.518 * STDVOA

[continue reading…]

We were very spoiled last year. Andrew Luck, Robert Griffin III, and Russell Wilson had outstanding rookie seasons in 2012, and perhaps that set expectations a bit high for the 2013 class. No one will confuse those three with EJ Manuel, Geno Smith, and Mike Glennon, all of whom struggled for most of their rookie seasons. But while Smith and Glennon didn’t produce excellent numbers, they produced very interesting ones.

Among the 35 quarterbacks with the most pass attempts, Glennon finished a very pedestrian 27th in Adjusted Net Yards per Attempt. But he did it in a very unique way: Glennon had an outstanding 19/9 touchdown-to-interception ratio, but he ranked dead last in Net Yards per Attempt. One reason for that is Glennon averaged only 10.6 yards per completion, the 3rd worst average among the 35 passers.

Smith finished 34th in ANY/A, largely due to his horrific 12/21 TD/INT ratio. He was a bit better in NY/A, ranking 28th, but what’s interesting about the Jets quarterback is that he ranked 7th in yards per completion. That metric is not a particularly effective measure of passer quality — after all, Matt Ryan ranked 35th — but it is a pretty good way to describe a quarterback’s style. While both Glennon and Smith were below average, they were below average in very different ways. [continue reading…]

When I went on the Advanced NFL Stats Podcast in late December, I discussed my use of Z-scores to measure the Seattle pass defense. Host Dave Collins asked me if I was planning on using Z-scores to measure other things, like say, Adrian Peterson’s 2012 season. I told him that would be an interesting idea to look at in the off-season.

Well, it’s the off-season. So here’s what I did.

1) For every season since 1932, I recorded the number of rushing yards for the leading rusher for each team in each league. So for the Minnesota Vikings in 2012, this was 2,097.

2) Next, I calculated the average number of rushing yards of the top rusher of each other team in the NFL. In 2012, the leading rusher on the other 31 teams averaged 974 yards.

3) Then, I calculated the standard deviation of the leading rushers for all teams in the NFL. In 2012, that was 386 yards.

4) Finally, I calculated the Z-score. This is simply the difference between the player’s average and the league average (for Peterson, that’s 1,123), divided by the standard deviation. Peterson’s Z-score was 2.91, good enough for 15th best since 1932. The table below shows the top 250 seasons using this method from 1932 to 2013; it’s fully searchable and sortable, and you can change the number of entries shown by using the dropdown box on the left. [continue reading…]

For years, sports analysts have used Pythagorean records as more granular measure of team strength than pure record. We’re not exactly at the point where Pythagorean records are mainstream, but I think, at least with respect to readers of this blog, people are pretty comfortable using Pythagorean records.

For the uninitiated, the use of Pythagorean records in sports dates back at least 30 years, and probably longer. Bill James is generally credited with popularizing this approach in baseball, and the same analysis has since been applied to just about every other spot. The formula to calculate a team’s Pythagorean winning percentage is always some variation of:

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

My research has discovered that for football, the best-fit exponent is 2.57. However, football is subject to points inflation.  The best-fit exponent for the NFL in 1972 is not necessarily the best one for 2002 or 2013. This is particularly relevant now, as the 2013 season was the second highest scoring in history. ^[1]In fact, it came in just four hundredths of a point behind the 10-team, 12-game 1948 schedule Moreover, the same exponent that works for a Broncos game does not necessarily work for a Panthers game. [continue reading…]

The NFL playoffs began in very entertaining fashion in Indianapolis. The Chiefs lost Jamaal Charles on the first drive of the game to a concussion, but stormed out to a 38-10 lead. Then the Colts pulled off the second greatest comeback in NFL history, eventually winning 45-44. The much-maligned Alex Smith had the game of his life, finishing 30 of 46 for 378 yards, with 4 touchdowns and no interceptions while also rushing for 57 yards.

Of course, Andrew Luck had an incredible game, too, even if it wasn’t necessarily as efficient. Luck went 29/45 for 443 yards and 4 touchdowns to counter his 3 interceptions, rushed for 45 yards, and recovered a Donald Brown fumble and ran it in for the touchdown.

Which made me wonder: where does this game rank among the greatest quarterback battles? To make life simpler, I’m only going to look at passing statistics, although obviously both players added some value on the ground. Smith averaged 9.23 Adjusted Net Yards per Attempt, defined as (Passing Yards + 20*TD – 45*INT – Sack Yards) divided by (Pass Attempts + Sacks). The NFL average in 2013 was 5.87 ANY/A, which means Smith produced 3.36 ANY/A over average. And, since he had 48 pass attempts (including sacks), that means Smith provided 161 yards over average.

Luck’s averages were hurt by the three interceptions, but he still produced 8.23 ANY/A and therefore 2.41 ANY/A over average. That means, over his 46 dropbacks, he produced 111 yards of value over average. So where does that mean this game ranks among all playoff games since 1970? My initial thought was to simply add the two value over average numbers, but that ended up producing a list dominated by great games by one quarterback. To counter this, I decided to only look at games where both quarterbacks were above average and to instead take the Harmonic Mean of their values. This wound up producing a pretty good list, and it places Luck/Smith at #9. [continue reading…]

Yesterday, I looked at the average height of the receivers of each team in the NFL in 2013. Today, we’ll use the same method but look at every NFL team since 1950. As it turns out, the 2013 Bears rank as one of the third tallest group of receivers in history. The only thing Chicago didn’t have was a 6’8 Harold Carmichael.

The table below shows the 200 teams with the tallest average receivers since 1950. A couple of famous teams are at the top of the list, including the 2007 Super Bowl champion Giants. Eli Manning will never be confused with a hyper-accurate quarterback, so it was smart of the Giants to surround him with tall targets like Plaxico Burress, Amani Toomer, and Jeremy Shockey. The 1998-2000 Minnesota Vikings with Randy Moss, Cris Carter, Jake Reed, and Andrew Glover, all made the top 25. And before Chicago had Brandon Marshall, Alshon Jeffery and Martellus Bennett, the Bears had another trio of monster wide receivers: Harlon Hill, Bill McColl, and Jim Dooley. [continue reading…]

In Marc Trestman’s first year as head coach, the Chicago Bears quickly turned into one of the most explosive offenses in football. Even after losing Jay Cutler, backup quarterback Josh McCown came in and seamlessly executed Trestman’s offense.

Chicago ranked in the top 5 in passing yards, passing touchdowns, net yards per pass attempt and points, an impressive accomplishment for a franchise that seemed permanently stuck in 1958. And while the Bears have a lot of talented offensive players, the first thing that stands out to you when watching Chicago is that they look like a basketball team. I don’t write that because of the way the team throws the ball, but because the receivers actually look like basketball players. Chicago’s top three receivers are Brandon Marshall and Alshon Jeffery (each 6’4) and tight end Martellus Bennett (6’7): those are easy targets to spot for whomever is at quarterback for the Bears.

I calculated the average receiving height of each team during the 2013 NFL season by taking a weighted average of the height of each player on each team, weighted by their percentage of team receiving yards. For example, Jeffery caught 31.9% of all Chicago receiving yards, so his 76 inches counts for 31.9% of Chicago’s average height.  Bennett gained 17.1% of the team’s receiving yards, so his 79 inches counts for 17.1% of Chicago’s average height, and so on. The table below shows the average height for each team in 2013, along with the percentage of team receiving yards and height for each team’s top four receiving leaders: [continue reading…]

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%. [continue reading…]