by Jim Glass

Does "the law of diminishing returns" apply to passing? If so, does it mean anything for team strategy?

Does diminishing returns apply to passing? As a QB passes more, should the effectiveness of his passing be expected to decline? Or do mismatches rule and quality win out in NFL contests, so a top-quality QB's performance should be expected to be consistent during an entire game – or even rise as he finds the weaknesses in a defense and maybe even "breaks" it?

Diminishing returns isn't really a law so much as the observation that people logically put a resource to its most productive use first, then to its second most productive, and so on, so the return from its use incrementally declines. This phenomenon is all around us in modern life.

In football the logic is that teams use the pass plays they can execute best for greatest results first. But when teams throw *a lot* they must move beyond those few plays -- so their AYA will fall to significantly below its level in few-attempt games. There's lots of anecdotal evidence supporting this idea.

## Saturday, January 29, 2011

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## Does "the law of diminishing returns" apply to passing? |

## Wednesday, January 26, 2011

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## Passing in the Post Season |

by Denis O'Regan.

Using post season data and a logistic regression approach I've taken another look at how completion rates are dependent on how far a quarterback is throwing the ball in the air.

I've made the dependent variable the outcome of the pass attempt (1= a completion and 0= an incompletion) and used the position on the field where the ball is caught or not caught by the receiver as the independent variable. Yards after the catch is discounted if the pass is caught.

I've run regressions for Rivers, Roethlisberger, Brady, Rodgers and Manning, seperately pooling all their attempts in the post season since 2006. I've also included Rex Grossman as an example of a not particularly accurate QB and Mark Sanchez, whose completion rate appears to thrive in the post season and is on an upward career curve.

## Sunday, January 23, 2011

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## Eight Football Stats I Hate and why the professional pundits put so much effort into selling them to us. |

by Jim Glass

I may be getting old and cranky, but TV analysts repeatedly, breathlessly throwing out junk stats to me during all the big games is getting to me. And I expect it will only get worse, because there is something about the culture of football that encourages them to do it, makes it profitable for them -- and football is a business.

Here are some of the stats I really dislike and why, followed by a little editorializing on why NFL game producers and their attending media put so much effort into pushing them.

## Tuesday, January 18, 2011

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## Luck point through the Divisional Playoffs |

by Bruce D

No luck, no win this past weekend for the top 2 lucky teams.

Total team luck points through the play-offs(week 19):

Luck is tracked to better analyze a team's true ability and to help predict results of upcoming games where some may not know what portion of a team's record and points performance was due to just luck.

For a more in-depth explanation of what "luck" points are, go to a previous post here.

## Monday, January 17, 2011

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## Belichick’s Overlooked Blunder |

by Bryan Davies

Amidst the expletives and tongue-in-cheek comments thrown around by Jets and Patriots this past week (ok, mostly Jets) was an actual game to be played on Sunday. And, like any football game, there are a number of decisions that coaches are given the opportunity to screw up. With the underdog Jets ahead for nearly the entire game, it seemed that a lot of the tougher decisions needed to be made by Belichick and the Patriots. A fake punt on 4th and 4 from their own 38 with time winding down in the first half, a two-point conversion in the third quarter, a 4th and 13 rather than a 52-yard field goal. Well, we know which ones turned out to be good decisions, but were they objectively good decisions without the benefit of hindsight?

Well the truth is, I’m not going to address any of those situations. I’m sure you’ll find enough analysis, both good and bad, that will address them extensively. In the spirit of being an overly pedantic statistically-minded football fan, I thought I’d address Belichick’s *incorrect* decision to go for an extra point rather than a two-point conversion following the Brady-Branch touchdown with less than 30 seconds to go in the game. In fact, when down 14 points, it’s almost always a better decision to go for two following a touchdown*late in the game*.

## Thursday, January 13, 2011

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## An Example of TWP Calculation |

by Andrew Foland

I scanned in about 20 points of WP by hand from the New Orleans-Seattle game WP chart, and used the previously described method for generating the “TWP” that combines the WP model with the input MWP (which favored NO by 59%, in this case.) The plot of the TWP is shown below together with the WP chart.

As you can see, late in the game the MWP consideration doesn’t change the WP very much. This is actually as expected. The better team is expected to have already done better by late in the game. If it is not already ahead, the high randomness of the few remaining possessions overwhelm the average expected advantage of the better team. This is a restatement of the “variance is the friend of the underdog” motto.

[+/-] |
## Win Probability and Point Differential |

by Andrew Foland

This article is an exercise in extreme pedantry: I’m going to ask a question whose answer is obvious, conduct some research, and conclude that the answer is, in fact, the obvious one.

As noted in my earlier writeup, an average team with a 13 point lead after five minutes would have a win percentage of 80%. (This, of course, is nothing more than inputting some numbers into the front end of Brian’s WP calculator—all the real work is Brian’s in creating that WP and the calculator front end.) Being only 5 minutes in, one can approximately take this result as a proxy for the result of, “If an average team had started the game with a 13 point lead, it would win 80% of the time.” (We’ll do something a mite more sophisticated in a moment, but this is the basic idea.)

Of course, no team begins the game with a 13 point lead. However, some teams do have a 80% generic win percentage. Is there a useful relationship between these two points?

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## Why Does WP Start at Zero? (And what can we do about it?) |

by Andrew Foland

All of my recent articles came from looking at the WP charts and realizing, “Hey, these start at 50/50! But Brian just told me at the start of the game, my team has a 65% chance of winning! How can this be right?!”

First I should say that I think it is actually correct to write WP in terms of average teams. It’s the only way to track WPA, which in turn, is the only way to provide an accounting of how, exactly, a team came to be the winners. That a team has a 65% chance of winning is due to the fact that it has a higher-than-average likelihood to produce positive-WPA plays. But if you start it at 65%, you won’t see that effect.

Nonetheless, it seems like one ought to be able incorporate one’s previous knowledge about the team in some systematic way. The generalized MWP(t) described previously is the main tool to do so.

[+/-] |
## Generalizing Matchup Win Probability |

by Andrew Foland

GWP as Brian calculates it is the probability, before the game starts, that a team at a neutral site will win a game against an average team. Which is to say, it is the probability, based on information that existed before the game started, that the team wins a game that in all other respects would present a 50/50 chance to win.

We may find ourselves interested in a quantity that describes the time dependence of GWP as the game progresses. It is not necessarily obvious how to define such a quantity. For instance, one may believe that the GWP of a team is unchanging over the course of a game. However, it is certainly not the case that WP is unchanging over the course of a game. So it’s not obvious that GWP is unchanged. As we will see, in fact it is not.

Brian also calculates a matchup win probability based (more or less) on the GWP of the two teams, including factors such as home field advantage. Let us call this MWP.

Let us next stipulate that once a week, Brian calculates a quantity we will call MWP(0) for each game. That is, it is the win probability at time t=0 of the game. How can we consistently define an MWP at other times, and what might we mean by it?

Let us generalize the concept of MWP to MWP(t) as meaning, “the probability, based only on information prior to the start of the game, that the team will win the game, given that at time t in the game, all other generic indications are that it has a 50/50 chance of winning.” Now, how shall we estimate MWP(t), given MWP(0)?

Let us first stipulate that MWP(0), as defined by Brian, reflects an underlying unchanging quantity that does reflect team quality. (It may do so with more or less accuracy; let us just assume that it does reflect so on average.) The time-invariant quantity that best defines team quality in the advancednflstats world is EPA / play.

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## Combining Information About Winning |

by Andrew Foland

Suppose that you are in possession of a nugget of knowledge that a team will win with probability p. The question, “What do you believe the probability of winning is?” is a very easy one to answer: p!

However, suppose you are in possession of two nuggets of knowledge. One nugget indicates that the probability of the team winning is p. The other nugget indicates, wholly independently, that the probability of the team winning is q. Now, if you are asked, “What do you believe the probability of this team winning is?”, the question is not as obvious to answer.

What is the best way to combine the information from p and q? (It is not, incidentally, to average the two!) Put another way, what should the formula f(p,q) be that creates the best estimate from the two?

## Wednesday, January 12, 2011

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## Final "BigWin%" Ratings for 2010, Looking to the Playoffs |

by Jim Glass

Two earlier posts here covered the subject of how team records in one-sided games – "Big Wins" and "Big Losses" – can be a much better predictor of future performance than overall won-lost record, or even Pythagorean expectation – particularly when predicting performance in the playoffs.

Define a Big Win/Big Loss as being by 10+ points, treat all other games as ties (half a win), and compute each team's "BigWin%". The concept is that the result will be a better indicator of true team strength than regular W-L percentage. The inspiration for this idea was a post on this site showing that nearly half of all NFL game outcomes are determined by luck. It is reasonable to assume that most of those games are the closest games where a few chance events can tip the outcome – so if those close games are treated as ties (the median point differential in NFL games is about 10 points) the "noise" injected by chance into regular W-L records will be largely eliminated, giving a truer picture of team strength. The statistical record backs this up.

## Tuesday, January 11, 2011

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## YAC may be a Quarterbacking Skill |

by Denis O'Regan

The distance a completed pass travels in the air would appear to be a significant factor in how much YAC a pass is going to generate. A flat pass to a running back is likely to have more potential YAC than a longish sideline pass where the defense has more time to converge around the potential receiver. Therefore, I regressed the average length of a QB's completion (his air yards), against the amount of YAC he generated. I used all QBs from 2006-2010 who had been their teams primary starter.

Air yards were statistically significant as an indicator and the correlation was just over 0.16.

[+/-] |
## Total team luck points through the playoffs |

by Bruce D

Team luck points = (bad luck points)-(good luck points), so negative numbers are the luckiest

For a more in-depth explanation of what "luck" points are, go to a previous post here.

Luck is tracked to better analyze a team's true ability and to help predict results of upcoming games where some may not know what portion of a team's record and points performance was due to just luck.

## Monday, January 10, 2011

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## It Could've Been Worse, Saints and Giants Fans |

by James Sinclair

All the talk about the fairness, or lack thereof, of Seattle hosting a first-round game after a 7-9 season, while New York and Tampa Bay went 10-6 and missed the playoffs, made me wonder what would be the most "unfair" scenario possible, in terms of both the records of the home and away teams in a round one matchup, and the record of the best team that doesn't make the playoffs. So here goes. Obviously, highly improbable (but not impossible) assumptions abound.

First of all, it's fairly intuitive that the worst possible record for a division winner (and, by extension, any playoff team) is 3-13, which would happen if and only if all four teams go 3-3 within the division and 0-10 against everyone else. So let's say the Seahawks, Rams, Cardinals, and 49ers have four identically-awful 3-13 seasons. On the last tiebreaker, a complex series of coin tosses, Seattle wins the division.

## Sunday, January 9, 2011

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## Completion rates aren't the complete story |

by Denis O'Regan

In a follow up to my post about interception rates for quarterbacks corrected for air yards per throw, I've taken a similar look at completion rates.

A completion rate taken in isolation can be a very misleading indicator of a player's real skill level. For example Michael Vick's average completion rate for his last season in Atlanta and his first year in Philadelphia was just 58%. By contrast the 2006 version of David Carr had a success rate of over 68% and tied the record for most consecutive completions in a game. Two rates at polar extremes, but whereas Carr's passes on average only travelled just over 5 yards per attempt, Vick's went nearly twice that distance.

To try to introduce air yards per attempt into the equation I firstly regressed air yards against completion rates for ever primary starting QB since 2006. This produced a fairly smeared out scatterplot and although increased pass length per attempt reduced the completion rate, correlation was very low at 0.09.

[+/-] |
## Probability Isoclines in the WP Model |

by Andrew Foland

I have been asking myself an amusing question about the WP graphs the last few weeks, and it will take a couple of little pieces of work to set up to answer it. This writeup is one of these pieces.

Given a probability to win at time T0, how must the score differential change as time passes to a later time T to maintain the same probability of winning? Note that the score differential to maintain a constant winning percentage goes down as the game progresses—a ten point lead early in the game is often less likely to win than a one point lead late in the game.

I decided to set a fixed situation, namely 1st and 10 from own 20—and see how the score differential evolved at constant win probability. I did this using the win probability calculator and lots of trial and error. I evaluated this at 6 difference values of WP: 55, 60, 65, 70, 75, and 80. I evaluated the WP at 6 different time points: five minutes into the game, at the end of the first quarter, at half, at the end of the third quarter, with 7 minutes in the 4th, and with 3:30 in the 4th. At around 3:30, point differential starts behaving very idiosyncratically. It’s also worth noting that Brian probably has little data for some point differentials early in the game, so there will be some systematic dependence on the form of his functional extrapolations into that region.

## Wednesday, January 5, 2011

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## "Clutch” playoff teams |

by Steven Buzzard

It seems the same questions get brought up every year during the playoffs. Which quarterback do you trust with your playoff lives on the line? What team is full of the most clutch players? Coach “X” just can’t win in the playoffs, normally Norv Turner but not this year. I don’t know of any study that has been able to prove such an existence of a clutch player or team and I am not going to try to do so here. What I wanted to do was to simply give a quantitative value to how much each team has actually over/under performed in the last decade.

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## Total team luck points and no luck power through week 17 |

by Bruce D

Team luck points = (bad luck points)-(good luck points), so negative numbers are the luckiest

For a more in-depth explanation of what "luck" points are, go to a previous post here.

Luck is tracked to better analyze a team's true ability and to help predict results of upcoming games where some may not know what portion of a team's record and points performance was due to just luck.

Luck points are valued as follows:

Points for(+) the unlucky team, are the same amount of points against(-) the lucky team.

punts blocked=3

interceptions=2.5

fumbles lost=2.5

field goal miss/block=2.5

punt returns for a TD=4.5

ko returns for a TD=4.5

## Monday, January 3, 2011

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## Quarterback Interceptions |

by Denis O'Regan

This is an attempt to attach a fairer number to a quarterback's interception rate. Raw interception numbers are naturally improved by taking into account the number of passing attempts a player makes in throwing those picks. However, this still does not differentiate between players who are being asked to throw deeper more often,thus increasing the risk of being picked off. I therefore decided to use play by play data to measure the distance each quarterback's throws travel in the air and divided this by his number of interceptions thrown.I'll call the resulting number airyards per pick. I did this no only for completions, but also for non completed passes.

I've initially just looked at the previous five seasons and I've analysed the quarteback who threw the most passes for each team during each season.As a comparison I've ranked each player for airyards per pick and also for the conventional interception per pass attempt percentage.

## Saturday, January 1, 2011

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## Kickoff or Receive? |

by Ed Anthony

A little known fact is that the team losing the initial cointoss has the option of electing to receive the ball at the beginning of the second half to electing which side to defend. THis means that if the home team loses the cointoss and begin the game with a kickoff they can then elect to kickoff at the start of the second half.

Conventional wisdom is that there is an advantage to have first possession in a half. For this reason teams always elect to receive the ball at least once during the game. But the rules are clear that the game need not develop this way.

Over the years there has been much discussion whether a team should has an advantage receiving in the first half. An argument can be made that receiving to open the second half gives a team the advantage of knowing whether they are in the lead and can play accordingly. arguments have also been made that first possession puts pressure on the kicking team to "catch up."