Towards a Better Pythagorean: Should Football Outsiders "hold the update"?

by Jim Glass

The good people at Football Outsiders say they are changing the formula for Pythagorean Expectation that they use to gauge team strength, and intend to update all the Pythagorean data on their website via their new formula during the offseason.

The "traditional" Pythagorean formula they've used until now produces a win expectation with about a 91% correlation to actual team wins. They say the new, improved formula increases the correlation to .9134 from .9120.

That's something - but a much simpler adjustment to applying the standard Pythagorean formula that I've been using increases the correlation to 95%. Also, while FO's new methodology uses a log function applied to year-to-date data that will be opaque to the average fan, the method I've been using gives a clear game-by-game result that anybody can easily grasp.

So I submit, for their consideration and yours, the formula adjustment below as being more accurate, simpler to apply, and easier for fans to refer to, understand, and play with.

Betting Market Power Rankings – Week 16

by Michael Beuoy

Here are the week 16 betting market power rankings. I have provided two versions this time because I think the default methodology is breaking down this late in the season. The default methodology incorporates the following week’s spreads into the rankings, if they’re available. Because week 17 often includes meaningless games for teams trying to stay healthy for the playoffs, the spreads don’t necessarily reflect the true strength differential.

For example, the week 17 line for the Green Bay- Detroit game has Green Bay as a 3 point underdog. At home. It’s not very likely that the market thinks that Detroit is truly 5.5 points better than Green Bay, but it does appear to expect Green Bay to have things wrapped up by week 17 and not be playing at full strength.

So, I have provided two versions of the rankings. The first is the standard approach, which includes week 17 lines (probably not reliable). The second excludes week 17 from the rankings, and appears to make more sense.

Dispatches From the Anti-League: #2

by James Sinclair

In September I wrote an overview of a fantasy football league some friends and I started this year where the goal is to compile the worst team possible. Here's the long-awaited follow-up—a bit later than intended, but at least I got it in before the end of the season. Barely.

First, a few observations:

1. The draft was considerably less important than in conventional fantasy football, because in the Anti-League it's actually possible for a player to be too "good" (and with that, I'll stop using quotation marks to indicate ironic reversals of good and bad, because it would definitely get out of hand). Case in point: my first round pick, Jacksonville's Luke McCown. He put up a decent score in week 1, and then an outstanding score against the Jets in week two (the fifth-highest single-game point total of the year, as you'll see below). And even as I was watching that game I was thinking "oh crap, he's going to be benched", which is exactly what happened. Fortunately I was able to pick up Blaine Gabbert off waivers, and even more fortunately the Jaguars have stuck with Gabbert all season (presumably because their backup is Luke McCown).

The Favorite/Long Shot Bias – Analysis of Superbowl Futures

by Michael Beuoy

In the week14 post, I outlined an approach to test the validity of the rankings by looking at Superbowl futures. At the time, I thought that Chris Cox’s NFL Forecast tool allowed for customization at the team strength level. Unfortunately, it doesn’t, but Chris was nice enough to run a one-off of his model, using the GWP’s from the Week 15 Betting Market Rankings.

Here are the results of the analysis. I took Superbowl futures from footballocks.com (thanks Ed) as of December 14. I then removed the “vig” from the odds under the assumption that each bet had the same (negative) expected value. In this case, the vig turned out to be a whopping 28%.

Revisiting the Big Wins Index: the kind of wins today that do predict wins tomorrow

by Jim Glass

All wins count equally in the standings ñ but they don't count equally as a measure of team strength or indicator of probable future won-loss record.

Brian Burke has written that random chance determines more than 40% of NFL game outcomes. Thirty years ago Bill James showed that baseball teams that win many (or few) close game later consistently see their W-L record regress to their record in decisive games - indicating that close game outcomes are heavily luck, and teams with good W-L records based on luck see their luck run out. At the same time, teams with disappointing W-L records due to having a lot of close losses offsetting decisive wins are primed for a turn to the better. This has since also been well documented for football and across other sports.

Of course, all this goes 100% *against* the great popular belief in the importance of "clutch play" - but that's reality. Last year, I looked at the results of 15 years of NFL playoff games for all teams that had won 11 or more games during the regular season. Sorting them by record in terms of "big wins", by 10 points or more, and "clutch, close wins", by less, produced these numbers...

Betting Market Power Rankings – Week 15

by Michael Beuoy

Here are the week 15 betting market power rankings. As noted last week (link), I have modified the methodology to now incorporate the point spreads for the upcoming week, if they’re available (week 16, in this case).

Methodology
The goal I had was to generate a set of point-based rankings that would best predict how the betting market would set the point spread for the coming week’s matchups. The better I was able to match the point spread, the better the rankings were a reflection of the market’s estimate of team by team strength. Through trial and error experimentation, I found that using point spreads for the most recent five weeks (with higher weighting given to more recent weeks), combined with an adjustment that accounted for actual game outcomes, generated the best predictive accuracy. More detail here

Will Tim Tebow be Denver's Dick Jauron? Or: The Meaning of Clutch Victories

by Jim Glass

Is the Tim Tebow story real? I enjoy Tebow, for years have wanted to see somebody try the option in the NFL, am entertained by watching the challenges it throws up for opposing teams, and am rooting for Tebow football to work. But is the Tim Tebow story as heard everywhere from his fans and admirers (and worshipers) real?

Tebow is a type of QB unique in the modern game. But the Tebow story is very old and familiar: the tale of "clutch winning". It's the story of *not* having the stats that go with winning, but winning anyhow. Thus, credit for winning goes to character, leadership, inspiring teammates, making others better, and - most of all - coming through with big plays in the last minutes to win close games in the clutch.

Betting Market Power Rankings – Week 14

by Michael Beuoy

Here are the week 14 betting market power rankings. Here is a link to the first set of rankings I generated last week.

First off, thanks to Brian for making the Community site available as well as calling out last week’s post on the main blog. There was a lot of good feedback in the comments section. Most of it I’m still chewing over, but I have decided to incorporate a suggestion from Jim A, who has been creating a very similar set of rankings over at Nutshellsports.com. More on that later.

Methodology

The original post has more detail, but here’s an overview:

The goal I had was to generate a set of point-based rankings that would best predict how the betting market would set the point spread for the coming week’s matchups. The better I was able to match the point spread, the better the rankings were a reflection of the market’s estimate of team by team strength. Through trial and error experimentation, I found that using point spreads for the most recent five weeks (with higher weighting given to more recent weeks), combined with an adjustment that accounted for actual game outcomes, generated the best predictive accuracy. More detail here.

Betting Market Power Rankings

by Michael Beuoy

The purpose of this post is to use the point spreads from recent weeks of the season to derive an implied power ranking. Basically, the point is to try to figure out what the betting market thinks are the best and worst teams in the NFL. From a broader perspective, I hope to provide insight into how the betting market “thinks” in general. One result that emerged from this analysis was a measure of how much the betting market reacts to the result of a particular game.

The challenge in deriving a power ranking from the point spreads is that the point spread only tells you the relative strength of the two teams. For example, Green Bay is favored by 7.0 points on the road against the NY Giants this week. We know that home teams are favored on average by 2.5 points, so after removing the home team bias, the betting market appears to think that Green Bay is 9.5 points better than the Giants. New England is favored by 21(!) points at home against Indianapolis So the betting market thinks that New England is 18.5 points better than Indianapolis.

Adjusting Strength of Schedule

by Michael Beuoy

One of the more interesting components (to me) of Brian Burke's efficiency model is the strength of schedule adjustment. I found it interesting the way you could bootstrap yourself into a self-consistent opponent adjustment. Here is the description (link):

"To adjust for opponent strength, I could adjust each team efficiency stat according to the average opponents’ corresponding stat. In other words, I could adjust the Cardinals’ passing efficiency according to their opponents’ average defensive efficiency. I’d have to do that for all the stats in the model, which would be insanely complex. But I have a simpler method that produces the same results.

Peyton Manning - Colts Defensive MVP??

by Steven Buzzard

A growing sentiment that has started to crop up with a lot of the talking heads in the league is that the Colts would be pretty terrible if Peyton Manning was playing because the defense has been so atrocious. These same people love to state the obvious and point out that Peyton Manning doesn’t make tackles. However, a lot of stats analysts have known over the years that the Colts offense has actually helped the Colts defense in 3 key ways.

1) They stay on the field a long time and limit the total number of drives per game
2) By staying on the field they give the defense great field position despite terrible special teams
3) By getting leads the defense can force more turnovers

MRE - Measure of Random Events through week 5

by Bruce D

MRE = (good luck points)-(bad luck points), so positive numbers are the luckiest teams.

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

If random events can't be repeated, then past points due to MRE can NOT be considered as being due to skill. Likewise, past performance due to MRE can't be included in analyzing future performance. In a nutshell, "lucky" teams can't be expected to be so "lucky", and "unlucky" teams are better than we may think.

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

MRE is valued as follows:

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

NFL QBR Differential after week 5

by Jeff Anderton

After reading several articles about Passer Rating Differential being the most relevant stat correlated to winning NFL football games, I decided to see what the current year to date QBR Differentials were for the NFL. For those that don't know, QBR is the "new" rating that ESPN developed and introduced this summer(2011). ESPN was looking to build off the "traditional" passer rating formula and take into account specific things that happen during a play.

For example, a QB makes a bad pass on a 5 yard "out route" but the receiver makes amazing catch, the Defensive Back falls down, and the receiver then turns it up field for a 30 yard gain. Under the QBR system the QB would not get as many "points" for this play since he made a bad throw, the DB fell down, there were a lot of yards after the catch, and the receiver made an amazing catch. There are also factors that figure out how to differentiate between "garbage time" and clutch scenarios, taking into account the current score, time left in the game, type of defense being used(prevent defense dink and dumps score low), etc.

So with that quick background behind us, lets take a look at what I did to compile these numbers. I took the individual QBR rating for each teams opponent for every week of the year, then simply added them up and divided by games played. I then took the team's own QBR rating(what their man under center scored for the year so far) and subtracted what they "got" from what they "gave up". Nothing major here in terms of math, just some down and dirty research.

For games that involved teams who used 2 QB's I simply added both ratings together for that game and divided by 2. I realize there could be some flaws with this method if we look at it from a "weighted performance perspective", but it would be such a small variance I don't think it much matters.

Not a whole lot of suprises as most of the good teams are at the top and the bad teams are at the bottome, but still interesting to see where a few teams fell. I was surprised that the Texans and Eagles were this high, and also surprised that the Jets, Bears, Falcons and Redskins were this low. These numbers are through and including week 5 and account for teams that had a bye week already.


Team by Team QBR Differential through and including week 5 of the 2011 NFL Season

Team	QB Differential
Cowboys	47.56
Packers	43.48
Titans	42.2
Saints	37.96
Bills	32.48
Texans	30.84
Lions	30.12
Patriots	29.76
Chargers	29.37
Panthers	24.12
Eagles	22.52
Giants	19.78
Broncos	18.79
Ravens	14.27
Steelers	13.62
Raiders	12.36
Chiefs	10.84
49ers	10.32
Falcons	9.2
Bucs	6.72
Browns	2.54
Redskins	2.02
Bengals	0.95
Jets	-4.22
Vikings	-5.12
Seahawks	-6.73
Bears	-8.14
Cardinals	-15.24
Jaguars	-15.78
Dolphins	-18.8
Colts	-28
Rams	-35.98

Joe's numbers, and the moral of the story

Appreciating how the Old Ones played. Or: Joe Namath in the 2000s. Part III -- by Jim Glass.

Part I explained what is going on here and why. Part II presented the statistical background behind this comparison of the 1970s and 2000s.

Namath in the 2000s

"Namath's numbers were shockingly bad. You tend to remember Namath as this seminal figure, and of course he was, and then you see those stats and just go: 'Yuck.'" -- Joe Posnanski, Sports Illustrated.

This has become a popular notion among many football fans who never saw Namath play, and who have a little knowledge of football statistics - but not enough.

"Joe Namath is in the Hall of Fame because of his celebrity - getting a big contract, winning one famous game, being the first pro football player to wear pantythose in public - not for achievements on the football field." - comment at Football Outsiders.

Appreciating how the Old Ones played. Or: Joe Namath in the 2000s, continuing...

by Jim Glass

If you haven't read Part I of this, you probably should to get the context and some details about the numbers being used here.

[] Passing game changes, 1970s to 2000s. These numbers for passing statistic averages and standard deviations show how passing norms have changed since the 1970s.

("SD%" = the standard deviation divided by the average for the stat. For instance, for yards-per-completion the SD% of .128 for is the SD of 1.47 divided by the average of 11.53)

The bulk of the difference between eras results from rule changes. In 1978 the NFL adopted major rule changes to favor the passing game (see "The Top Ten Things that Changed the Game") and has steadily followed up on them since. The result has been shorter, safer, higher-percentage passing, and more of it.

Appreciating how the Old Ones played. Or: Joe Namath in the 2000s.

by Jim Glass

The way NFL football is played has changed over the decades. Statistics in part reflect this, as seen in the steady inflation of passer rating.

But more importantly, what wins games has changed – and this is not reflected in commonly used rating and ranking stats. So even using "inflation adjusted" ratings leads to mistaken conclusions about players of the past when the ratings are based on performance measures that matter the most to us today – but not the ones that mattered most to them.

This article opens with a little rant, then presents the results of multivariate regressions run for the periods 1971-5 and 2006-10 to identify changes in performance measures that matter most to winning.

To illustrate how big these changes have been, it ends by translating Joe Namath's passing numbers – particularly for his 1972 season - into 2010 terms.

MRE - Measure of Random Events through week 4

by Bruce D

MRE = (good luck points)-(bad luck points), so positive numbers are the luckiest teams.

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

If random events can't be repeated, then past points due to MRE can NOT be considered as being due to skill. Likewise, past performance due to MRE can't be included in analyzing future performance. In a nutshell, "lucky" teams can't be expected to be so "lucky", and "unlucky" teams are better than we may think.

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

MRE is valued as follows:

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

Luck points through week 3

by Bruce D.

Team luck points = (good luck points)-(bad luck points), so positive numbers are the luckiest teams. Please note that this is change from previous posts where negative numbers were used for the luckiest teams.

Please note: In a predictive situation, past "good luck" can be bad for a team in the future, and past "bad luck" can be good(luck is NOT repeatable).

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

Luck is tracked to help analyze a team's true ability and to 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.

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

Luck Points for the New Season

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.

Nearly Impossible to Pick the RAVENS PLAYER OF THE GAME

by Borat
Before yesterday, JOE FLACCO was 2-6 against the Steelers — 0-6 when Ben Roethlisberger has played and 0-2 in the playoffs — with a 53 percent completion rate, seven touchdowns and eight interceptions. Against all other teams, his W/L record is 34-13 — 4-1 in the playoffs — with a 65 percent completion rate, and he has twice as many touchdowns as interceptions, 54-27. Also he had lost five fumbles against the Steelers in 8 games, and only five total against everyone else in 47 games. Yesterday Flacco passed for 224 yards including 3 TDs was sacked only once and did not fumble. His Passer rating was 117.6.

Dispatches From the Anti-League: #1

by James Sinclair

My fantasy football league consists entirely of guys in their mid-to-late 20s who have excess quantities of both free time and snarkiness, so it was only a matter of time before six of us started a separate "Anti-League", in which the goal is to compile the worst team possible.

Assuming we weren't exactly breaking new ground, I looked around online for write-ups of similar leagues and, sure enough, found a handful of efforts, but none that go into any real depth about rules, settings, tactics, and in general how to create a league that actually works. So I'm going to (try to) do just that. I'll check back in after tonight's draft, and probably a few more times during the season with updates, observations, and tales of strategy decisions gone hilariously awry. For now, here's an overview of how the Anti-League is set up:

Rosters
Nobody in this league is the sort of NFL fan who can name, say, the Bengals' No. 3 receiver. But, without taking a formal poll, I'd bet at least half of us can name the Bengals' quarterback. (Incidentally, I wonder if Andy Dalton can name the Bengals' No.3 receiver?) Point is, unlike running backs and receivers, quarterbacks often become household names merely by virtue of being less skilled than their peers, even if they aren't egregiously overpaid or facing criminal charges (though it doesn't hurt). So, we're going with two starting QBs, but only one RB and one WR.

Completing Short Passes in Playoffs

by Denis O'Regan

A picture's worth a thousand words,so here's a few pictures and not too much waffle.

I've looked at every individual passing attempt by every quarterback in the playoffs since 2006 and I've noted both the distance traveled by the ball through the air and if the pass was completed or not. I've then produced a regression equation for air yards thrown and completion rate and plotted this curve for every post season quarterback. Below is a plot for five of the most prominent passers over the period. To illustrate how to use the graph when passing to targets five yards behind the line of scrimmage, Brady, Manning(P), Roethlisberger and Rodgers are all completing at around 85%, while Rivers is down around 70%.

Fixing the ELO ratings system

by Tom Baldwin

Back in 2008 Brian covered a well known ratings system first conceived by the man whose name it now bears, that article offers a great insight into both the good and bad points of Elo ratings, and is certainly worth a read in preparation for this article.

Recently I got thinking about Elo ratings again, and realized their limitations, that they do not consider the score of games, can be overcome. When a game's outcome is considered by the original ELO ratings system it is done so on the basis that the game ends with a binary result, a win or a loss, but that is not all of the information available. As we have seen, a team like last year's Falcons can appear far stronger than they truly are when only their win-loss record is considered, and that is because they were on the right end of luck. Close wins are much more about luck than they are skill, winning by ten points is a lot more of an indication of one team's supremacy than winning by one, but how can we quantify this? Well, we need to know the answer to quite a simple question: when two completely equal teams play each other, what is the chance that, by luck alone, team A beats team B by X or more points? In this instance it will always be by luck alone, since both teams are technically equal, their levels of 'skill' completely cancel each other out.

Balanced teams have higher EPA and win more games

by Jim Glass

Should NFL teams invest the most in offense or defense?

Previously, discussing diminishing returns to passing, I noted that marginal return analysis says investment resources - including NFL salary cap money - should be allocated among different investments to produce the largest return at the margin.


In plain English about football, this means that if your team has two all-pro wide receivers and zero competent linebackers, and you have a choice between adding a third all-pro receiver or an all-pro linebacker, you'd better go for the linebacker. Adding your first good linebacker will give more net points to your team than adding a third top receiver.

This is true even if you believe offense is more important to winning games than defense. Whatever their relative importance in the big scheme of things, you are best off making salary cap investments that produce equal returns at the margin, so that your next million cap dollars invested in offense produces the same net return as the next invested in defense. With diminishing returns to additional investments, if you overinvest in offense you will receive fewer net points than from making that last investment in defense – that third good receiver gives you fewer net points than a first good linebacker. Overinvesting in defense is the same mistake in reverse.

Defense wins Championships ...

... that might be true in Soccer, Hockey, Baseball, Basketball, Handball, Deep Sea Fishing or whatever, but not in Pro Football (nor Cycling).

by Karl Berthold

Pundits like Easterbrook, Prisco, TV Commentators and - Coaches tell us year in and year out that "Offense sells tickets but Defense wins Championships". But is that true, or is it a myth?

Many studies about Superbowl Champions were done by Brian Burke and others based solely on Regular Season Statistics which showed us, the smart readers of "Advanced NFL-Stats", that "Offensive-Teams" (read "Passing-Teams") have the edge to win the final Game of the Season.

But nobody has yet done a study of Playoff - Statistics of Superbowl Winners based on the (up to four) Playoff Games they had to win before winning the Lombardi Trophy. That means the above mentioned "Experts" could still say Playoff-Football is different and in cold January you need a good running game and great Defense to prevail in the end.

Well... no longer can that be said.

Packers and Steelers fans, enjoy this Sunday

-- because "We'll be back next year" isn't so likely any more.
by Jim Glass

Once upon a time, way back before 1998, a team playing in the Super Bowl could reasonably expect to be in the thick of the competition for the Lombardi Trophy again the following year.

From 1970 through 1997 the Super Bowl team conference champions won an average 79% of their regular season games, and during the following year won 69%. In the follow-up seasons they compiled 47 winning records against only six losing and three .500 records. As 69% is 11 wins in a 16-game season, the teams could feel confident that they'd be in the playoffs again.

Then in 1999 the defending Super Bowl champion Broncos and runner-up Falcons, after going a combined 28-4 during 1998, fell to 6-10 and 5-11 respectively.

From then on, defending conference champions not named "Patriots" have had only 10 winning records in 20 seasons, against nine losing and one .500 record. All 24 Super Bowl participants including the Patriots have compiled a following-year average 56% winning record, a tad below 9-7.

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

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.

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.

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.

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.

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 touchdownlate in the game.

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?

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.

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?

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.

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.

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.

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.

"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.

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

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.

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."