Super Bowl XLVIII Game Probability

The game probability for Super Bowl XLVIII is now available at the New York Times. This week I take a look at why the efficiency model may differ from some other models and the public consensus.

...Some other analytical models, along with the consensus odds, give Denver a small advantage. I suspect the disagreement can be attributed to two factors. First, I doubt the strength-of-schedule effect is fully appreciated by wider audiences. And second, recent outcomes are often overweighted both by quantitative models (by design) and by fans and analysts (often unwittingly). Focusing on recent games would tend to favor Denver, which has appeared to be winning in easier fashion lately...

Podcast Episode 18 - Brian Burke

Brian Burke returns to the show for the final podcast of the season. He and Dave kick off the episode with a NFL rules brainstorming session. They discuss some of Brian's (and readers') ideas for creative rule changes the league could implement to make the game more interesting and fun.

Brian then dives into an explanation of his latest article on the value of a time out. He describes his process for analyzing the win probability ramifications of "burning" time outs, and why sometimes it's better for a team to make any choice rather than use a valuable resource debating the optimum choice.

Dave and Brian discuss Brian's win prediction model for the Superbowl, and why it looks to be a very close match-up. To wrap up the episode they use the Franchise Season Visualization tool to take a look back at the 2013 season.

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Thomas Bayes Would Approve of Seattle's Defensive Tactics

The following is a guest article by Gary Montry, a professional applied mathematician. Editor's note: Gary uses net yardage as the measure of utility, and we might prefer something like EP or WP, I think the general point of the article stands, and its strength is in the construction and solution to the problem. It's also a great refresher on conditional probabilities and Bayes' theorem.   

Last week a WSJ article about the Seahawks' defensive backs claimed that they "obstruct and foul opposing receivers on practically every play."  I took a deeper look in to the numbers and found that as long as referees are reluctant to throw flags on the defense in pass coverage (as claimed in the article), holding the receiver is a very efficient defensive strategy despite the risk of being penalized.

The following is an analysis using the concepts of expected utility, expected cost, and bayesian statistics.

The reason defensive holding is an optimal strategy comes down to one word. Economics. The referee's reluctance to call penalties on the defensive secondary is analogous to a market inefficiency. The variance in talent on NFL rosters, coaching staffs, and front offices between the best and worst teams in the league is probably very small. Successful teams win within a small margin. Seattle has found a way to exploit a relaxation in marginal constraints within the way the game is called that their competitors have not, and turned it into a competitive advantage.

If you think about committing a penalty in the same way as committing a crime, the expected utility is essentially the same. The expected utility (EU) for defensive holding is (opponent loss of down due to incomplete pass - probability of being penalized x cost of penalty). In other words, EU is the benefit of an incomplete pass minus the cost of the penalty times the probability of getting caught.

Advanced Stat Breakdown for Super Bowl 48

Instead of reading a bunch of words about the Super Bowl matchup, where each phase is trying its hardest to express some sort of numerical evaluation, wouldn't you prefer to see the numbers themselves collected into one giant eye chart? Well, if that appeals to you, you'll enjoy the SEA-DEN Matchup page.

NFL Overtime Modeled as a Markov Chain

by Ben Zauzmer. Ben is a junior majoring in Applied Math at Harvard University and is a member of the Harvard Sports Analysis Collective. This article was originally published at

In 2012, the NFL created new overtime rules designed to make the game fairer. The league switched from a sudden death setup to an arrangement that allows both teams to have a chance at scoring, unless the first team to receive scores a touchdown. Even with this change, it would seem that a coach should still always elect to receive if he wins the coin toss at the start of overtime, since an opening touchdown drive wins the game.

However, earlier this year, for the first time under the new rules, a coach made exactly the opposite decision. Bill Belichick, the three-time Super Bowl-winning coach of the New England Patriots, made the gutsy call to kick at the start of overtime. Many considered the main factor behind this decision to be the heavy winds at Gillette Stadium (if a team defers the choice of kicking or receiving, it may choose which direction to face). However, kicking first may also give a team better field position on offense and may actually benefit teams with strong defenses.

To calculate which strategy coaches should prefer, we will model NFL overtime as a Markov Chain. We will define our states as the set of possible point differentials, from the perspective of the team that receives the opening kickoff, in overtime: -6, -3, -2, 0, 2, 3, 6. This model inherently assumes that state-to-state probabilities are not conditional, and that the probability of the score differential being 5 or 9 – both technically possible under the new rules – is negligible.

We will let be the transition matrix for the receiving team’s first offensive possession, be the receiving team’s first defensive possession, be every subsequent receiving team offensive drive, and be every subsequent receiving team defensive drive. The first row/column of each matrix represents the receiving team at a -6 scoring difference, and so on until the last row/column is the receiving team at a +6 scoring difference.

The matrices have the following forms:

Momentum Part 5 - Series Level Analysis

This is the final part of my series on momentum in a football game. Is momentum a causative property that a team can gain or lose, or is it only something our minds project to explain streaks of outcomes that don't alternate as much as we expect? It's been a couple months since I began this series, so as a refresher, here is what I've looked at so far:

Part 1 examined the possibility that momentum exists by measuring whether teams that obtain the ball in momentum-swinging ways go on to score more frequently than teams that obtained the ball by regular means.

Part 2 looked at whether teams that gained possession following momentous plays went on to win more often than we would otherwise expect.

Part 3 focused on drive success following a turnover on downs, which is often cited by coaches and analysts as a reason not to go by the numbers when making strategic decisions.

Part 4 applied a different method of examining momentum by using the runs test so see the degree to which team performance is streakier than random, independent trials.

In this part, I'll apply the runs test at the series level, to see if teams convert first downs (or fail to convert them) more consecutively than random independence would suggest. But first, I'll tie up some loose ends left hanging from part 4. Specifically, I'll redo the play-level runs test to eliminate potential confusion caused by a team with disparate performance from their offensive and defensive squads.

Franchise Season Plots Updated

Check out how your favorite team's fortunes have evolved over the past 14 seasons. The Franchise Season visualization has been updated with 2013's data. It's a fun snapshot of each team's "identity" from year to year, plotting Expected Points Added per Game.

You can examine how SEA has completed its circle of life with its 2013 campaign, covering all possible combinations of good&bad offense&defense. See how DEN's offensive production changed with the arrival of Peyton Manning (or check out IND's 2011 year in the wilderness).

The reigning champions are always the default selections for all our charts and tables at ANS, so this is will be the last week as the default for my hometown team. To me it's interesting to see that they've spent most of their franchise's existence along one axis, ranging from all-world defense/terrible offense to above-average offense/average defense, and won the Lombardi Trophy on both extremes of the axis.

It's rare for a team to sustain above-average production on both sides of the ball for beyond a season or two at a time, even for perennial contenders like NE and IND. PIT might be the best counter-example, with seasons that cluster in the upper-right quadrant consistently through the recent era. Even their "down" years were decent. For example, 2013 saw the Steelers finish 8-8, falling perfectly at the average/average intersection in the plot.

CHI's plot is a really interesting one. They should feature it on Sesame Street. One of these years is not like the other...

It's interesting to see how the average line can appear to be something like the sound barrier to some squads. ATL just can't seem to put together an above average defense, and BUF can barely break the average-barrier on offense.

A smaller version is included below, but the permanent full-size version is available via the Tools | Visualizations menu.

As always, up and to the right is good. Down and to the left is bad. My thanks to Chase Stuart who suggested the idea for this a couple years ago.

Podcast Episode 17 - Kevin Quealy

Kevin Quealy, graphics editor at the New York Times, comes on the show to discuss data visualizations. An expert in using data to tell visual stories, Kevin walks Dave through the process he and the graphics department use to tell news-worthy stories with data and graphics. 

Kevin describes some of his recent sports work, including a graph of longest QB start streaks, the 4th Down Bot and his NFL draft success chart. He talks about how he and his team begin their work process by looking for interesting stories and data-sets, and how those stories go through a variety of iterations before they are turned into visually striking charts. Kevin explains his criteria for what makes for a great visualization and provides some helpful tips for aspiring information designers.

If you're interested in learning more about data visualizations, check out the rest of Kevin's work here and his post about the process of creating the QB streak graphic. While you're at it, take a look at Jennifer Daniel's terrific 4th down Bot sketches.

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The Value of a Timeout - Part 2

In the first part of this article, I made a rough first approximation of the value of a timeout. Using a selected subsample of 2nd half situations, it appeared that a timeout's value was on the order of magnitude of .05 Win Probability (WP). In other words, if a team with 3 timeouts had a .70 WP, another identical team in the same situation but with only 2 timeouts would have about a .65 WP.

In this part, I'll apply a more rigorous analysis and get a better approximation. We'll also be able to repeat the methodology and build a generalized model of timeout values for any combination of score, time, and field position.


For my purposes here, I used a logit regression. (Do not try to build a general WP model using logit regression. It won't work. The sport is too complex to capture the interactions properly.) Logit regression is suitable in this exercise because we're only going to look at regions of the game with fairly linear WP curves. I'm also only interested in the coefficient of the timeout variables, the relative values of timeout states, and not the full prediction of the model.

I specified the model with winning {0,1} as the outcome variable, and with yard line, score difference, time remaining, and timeouts for the offense and defense as predictors. The sample was restricted to 1st downs in the 3rd quarter near midfield, with the offense ahead by 0 to 7 points.


Thoughts on the Extra Point

Roger Goodell is considering elimination of the extra point. I've been whining for 5 years now, advocating some kind of change to the XP. I just hope the league doesn't mess it up, like they did with overtime.

I realize quoting myself is not in good taste, but then again I've never been accused of good taste. Here are some of my thoughts.

Kicking field goals is such a peculiar and specialized thing. It has almost nothing to do with the rest of the sport but can be so decisive. It would be like getting extra runs in baseball by lacing up some skates and slapping a shoot-out shot after every home run.

Here's an excerpt from a diatribe in my old Washington Post column.

The extra point is something left over from gridiron football’s evolution from rugby. Originally, the ‘touchdown’ in rugby was less important than the ensuing free kick, and the points given for the touchdown and the ‘point after try’ varied during football’s early history. Today’s extra point is a vestige of football’s rugby roots. It’s football’s appendix–inconsequential, its original purpose uncertain...and safe to remove.

It's easy to see that XPs are pretty pointless, but it's harder to come up with some good ways to fix them or replace them. Here are some of my favorite ideas (and plenty more in the comments):

The Value of a Timeout - A First Approximation

During the NFC Championship Game the other day, we saw a familiar situation. Down by 4 with 14 minutes left in the game, the Seahawks were confronted with a decision. It was 4th and 7 on the SF 37. Should they go for it, punt, or even try a long FG to maybe make it a 1-point game? Pete Carroll ended up making what was the right decision according to the numbers, but not before calling a timeout to think it over.

As I noted in my game commentary, if you need to call a timeout to think over your options, the situation is probably not far from the point of indifference where the options are nearly equal in value. And timeouts have significant value, particularly in situations like this example--late in the game and trailing by less than a TD--because you'll very likely need to stop the clock in the end-game, either to get the ball back or during a final offensive drive. Would Carroll have been better off making a quick but sub-optimum choice, rather than make the optimum choice but by burning a timeout along the way?

Here's another common situation. A team trails by one score in the third quarter. It's 3rd and 1 near midfield and the play clock is near zero. Instead of taking the delay of game penalty and facing a 3rd and 6, the head coach or QB calls a timeout. Was that the best choice, or would the team be better off facing 3rd and 6 but keeping all of its timeouts?

Both questions hinge on the value of a timeout, which has been something of a white whale of mine for a while. Knowing the value of a timeout would help coaches make better game management decisions, including clock management and replay challenges.

In this article, I'll estimate the value of a timeout by looking at how often teams win based on how many timeouts they have remaining. It's an exceptionally complex problem, so I'll simplify things by looking at a cross section of game situations--3rd quarter, one-score lead, first down at near midfield. First, I'll walk through a relatively crude but common-sense analysis, then I'll report the results of a more sophisticated method and see how both approaches compare.

NFCCG SF-SEA Observations

As expected, this was a real defensive slugfest. The winning QB had -3.4 EPA. Kaepernick posted -0.28 WPA and 2.2 AYPA. Both offensive lines were beaten soundly. SF's notched -5.4 EPA and SEA's had -2.6 EPA.

Unlike the AFC game, this one was all about 4th downs. HUGE leverage throughout the game. I know I can be a broken record on this stuff, but this game really hinged on some very interesting strategic decisions.

-SF 4th and 2 on the SEA 7, 1st qtr. They punted. Probably should have gone for it.

-SF 4th and goal on the SEA 1. They went for it. Great call.

-SF 4th and 6 on the SEA 46, 1st qtr. They punted. Probably should have gone for it.

-SEA 4th and 6 on SF 38, 26 sec in 2nd qtr. They went for it, converted then kicked a FG to end the half.

-SEA 4th and 7 on the SF 35, 4th qtr 14 min to play, down by 4. They went for it. Great call except SEA burned a timeout that they were reasonably likely to need in order to think things over. Here's the thing: Timeouts are very valuable. If you can't decide between going for it or kicking or punting, you're probably very close to the point of indifference anyway. You may be better off making any quick decision and saving the timeout than you are making an optimum decision but wasting a timeout.

-SEA 4th and goal from the 1, 4th qtr 8:39 to play, up by 1. The went for it. Great call. Why? First, because they'll probably make it and virtually put the game away. And if they don't they're likely to leave the ball on the SF 1-yd line. That's not exactly a good place to be for an offense. I heard someone say that despite the math you can't take a chance like that against the SF defense. But as I noted last week, over the past 2 seasons SF has faced 15 (now 17) plays from the 1-yd line and allowed TDs on 10 of them. That's worse than league average. Don't get me wrong. I'm not saying that the SF defense is below average. Instead, the point is that good and bad teams aren't that different on any one given play. It's just that good or bad teams show up that way after accumulating very small advantages over several dozen individual plays in a game.

-Here's a weird one. SEA 4th and 11 on the SF 29, 4th qtr 3:43 to play, up by 3. My numbers say...punt? Yes, punt. Here's why:

AFCCG NE-DEN Observations

I thought the big story of the game wasn't how easily DEN moved the ball. We all expected that. The big story was DEN's defense, which held NE to just 3 points in the 1st half and 10 points through 55 minutes. Brady was held to -0.02 WPA. He did notch +8.3 EPA, but a lot of that was after the game was mostly decided.

NE was going to need some fluky things to go their way to win--turnovers, a special teams play, or some terrible call by the refs. It never came.

Manning and the DEN passing game did have a fantastic day. Manning: +.48 WPA, +17.9 EPA, 9.3 AYPA, no turnovers, no sacks.

I, and the NYT 4th Down Bot--(funny how you never see the two of us together at the same time), agreed with every 4th down call during the game. Belichick knows what he's doing. I was disappointed to see DEN burn a timeout just prior to NE's 4th down conversion attempt. Teams should be better prepared for a 4th down attempt, particularly in situations like this: a 4th and short in or near the red zone. In a high-leverage situation like that, it's ok for a team with a significant lead to use a timeout, but in a closer game, it would be much more costly. (I'm working on a project to value timeouts in terms of WP now, and without any spoilers--they are very precious in the 2nd half.)

Live Super Bowl Probabilities

They're back. Details here.


Game Probabilities - Conference Round

Game probabilities for the conference round are available at the New York Times. This week I explain why the Patriots' recent success running the ball is not so recent at all.

But to followers of advanced metrics, that is far from a surprise, as the Patriots have been mercilessly efficient on the ground for the past several years. Using success rate to measure running effectiveness provides a much more accurate picture of how the Patriots win with the run than traditional measures like total yards or even yards per carry...

...What the Patriots have figured out is how to use the running game effectively. They do not use it as a bludgeon on most first and second downs, as other teams do...

...Running backs like Adrian Peterson or Chris Johnson who are known for their occasional 80-yard breakaway touchdowns might be first-round draft picks in your fantasy league, but in the real world, I’ll take the Patriots’ running game any day.

Obligatory Manning-Brady Post...But This One Is Cool, I Promise

The risk of injury aside, it's inevitable we'll see either Manning or Brady in this season's Super Bowl. These two great players will be linked for all of football history. Even advanced stats aren't going to separate their performance from their teams'--the numbers are only the start of the conversation, not the end. But as long as the conversation is going to happen, we might as well start with the best numbers.

The interactive visualization below chart's each player's career. It's a special version of the QB viz I update weekly throughout the season. In this edition, I've selected only Manning and Brady for comparison, plus I've included postseason data.

The viz offers two unique and innovative ways of looking at each player, unashamedly stolen from the best baseball analytics site on the Web, Fangraphs. First, there is a plot of career cumulative Win Probability Added (WPA) from each QB's first year through his most recent year. It's an interesting way to compare the career trajectories of top passers because it's a cumulative chart.

Second, there is an "Nth best season" Expected Points Added (EPA) chart, which takes some thinking to understand because it's not plotted in chronological order. It plots each QB's season in order from his best EPA season through worst EPA season. It's not cumulative and because it appears to trend downward does not mean the QBs are declining. I like it because re-ordering each season makes the separation between each player's performance clear to see.

Podcast Episode 16 - Keith Goldner

Keith Goldner is back on the podcast to discuss this past weekend's divisional round playoff games. Keith is the chief analyst at Numberfire and also a regular contributor to Advanced NFL Stats. Dave and Keith begin by discussing some of the key decisions from the past weekend's playoff games, including whether Marshawn Lynch should've gone down at the one yard line at the end of the Seattle/New Orleans game, Riverboat Ron's goal line strategies and what to do when a punt is botched and the snap ends up in the end zone.

Keith reviews his lists of the regular season's most efficient quarterbacks and running backs and explains the differences between high efficiency and high success rate player performance. Dave and Keith round out the episode by previewing this weekend's AFC and NFC championship games, and Keith predicts which teams he expects to see playing for a ring in New York this February.

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If you thought this weekend's games lacked excitement and were one of the least interesting division rounds in recent memory, you'd be correct. I don't expect the NFL to provide heart-pounding, mind-bending drama every week, but it would be nice to have one of the four games in what is supposed to be the best weekend of football be in doubt  past the 2nd quarter. Maybe we were due for a letdown after a couple weeks of great games.

The Excitement Index (explained here) lets us measure how riveting a game was. Here are the average EIs for the division round games by year since 2001.

Seahawks Should Not Have Scored

I'm not going to touch Sean Payton's late field goal attempt, down eight, into the wind, with only one timeout remaining. After the miss, on the ensuing Seahawks drive, Marshawn Lynch tore down the left sideline and it appeared he was let into the end zone by the Saints. The question is, did the Saints make the right decision letting him score once the first down was achieved - and should Lynch have gone down at the 1-yard line? The answer to both of these will always be the same, and in this case, it's yes.

Lynch scored with 2:48 remaining in the game. Up by 15, kicking off to the Saints, the Seahawks had about a 99% chance of winning. The Saints would need to score, recover an onside kick, and score again just to tie.

Update: Lynch actually scored with 2:40 remaining, not 2:48 as originally listed in the play-by-play. That means that the Seahawks could have milked the entire clock as listed at the very bottom of this article.

But, what if Lynch had gone down at the one? Using the time calculator, we can see how much time the Saints would have had following a chip shot (99.7%) field goal from the 1-yard line. The Saints had no timeouts left, so we are looking at the blue line.

Game Probabilities - Division Round

Game probabilities for the division round are available at the New York Times. This week I take a look at the role of luck in the composition of the playoff field.

...the luckiest may be the Indianapolis Colts. Not only did they survive a 28-point second-half deficit in the wild-card round, but they were also the team that most overperformed statistical expectations in the regular season.

Based on the core efficiencies of passing, running, turnovers and penalties, plus the Colts’ strength of schedule, my efficiency model expected them to have between seven and eight wins. But they finished with 11, which was 3.2 more than expected.

All but 2 of the 12 playoff teams were above average in terms of beating their statistical expectations, and all but one of the surviving eight beat expectations. Although you may at first think this pattern points to an obvious flaw in the efficiency model, it turns out this is exactly what the field of statistics predicts...

Podcast Episode 15 - Alok Pattani

Alok Pattani of ESPN Stats & Info joins Dave to discuss how ESPN uses analytics across its different platforms. He talks about how ESPN's use of advanced stats has evolved during his time at the company and explains the process of getting statistical concepts from research idea to broadcast.

Dave and Alok then look at some of ESPN Stats and Info's NFL research, including a new stat that quantifies pass protection and how that correlates to defensive and offensive pass efficiency. Alok reviews his research on the discrepancy between EPA and YPG for certain playoff teams, and how the story of a team's success (or failure) can be explained by different combinations of stats.

After a brief chat about the ways to quantify offensive pace, Alok outlines out an interesting parallel between two QB's playing against each other this weekend. To close out the show, Dave and Alok look at three divisional-round rematches, and attempt to tease out what can, and can't, be learned from when the same teams played earlier in the regular season.

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Would Auburn Have Been Better Off Not Scoring a Touchdown?

Slate asked me to take a look at the possibility that Auburn would have a higher win probability had they not scored on Tre Mason's go-ahead touchdown run, and instead taken a knee at the 1-yard line with 1:19 to play. It was a difficult analysis, and required some unsatisfying assumptions, but in the end the results confidently pointed toward one conclusion.

...Nevertheless, Auburn had about an 81 percent chance of winning after Mason’s score, as teams in Florida State’s position are able to score a touchdown about 19 percent of the time. (These numbers are based on analogous situations in the NFL, though I’ve made slight adjustments for the differences in pace between college and the pros, and to include the chance of a kick return for a touchdown.)

So, the question we’re evaluating is whether having a first down at the 1-yard line would have given Auburn more than an 81 percent chance of winning. It’s a tricky question because it needs to be analyzed backwards...

(What I didn't explain in the article is that it's easiest to work backwards because the Auburn WP on 3rd down is depending on the results of a potential 4th down. And the WP on 2nd down are dependent on the potential results of 3rd down, which in turn depend on 4th down. And so on.)

For the Slate articles, I can't get away as much math and equations as I like, so here's a table of the relevant probabilities I used. It was complicated because the deeper into the goal-line series Auburn went, the lower Auburn's chances of getting the TD went BUT the lower Florida State's chances of responding went too. This edition assumes Auburn goes for it on the 4th down on what would be a single make-or-break play for championship.

Peter King Podcast

I was on PK's podcast today. We talked about people shooting at me, my days as a young Colts fan, firing coaches, hiring coaches, what to do with Andy Dalton, and which surviving teams look strongest going into this weekend.

What if KC Had Just Kneeled Out the 2nd Half?

With 13:39 left in the 3rd quarter, KC led IND 38-10. Obviously, 3rd grade math tells us IND needed at least 4 touchdowns just to tie the game at this point. A little more arithmetic might illustrate just how badly KC bungled this game.

There were a total of 1,519 seconds left in the game. KC can burn 40 seconds between plays and 6 seconds during a typical play just by calling a super safe run (that stays in bounds) or even a kneel. Even if KC doesn't try to convert a single first down, they can burn 144 seconds on a series. However, IND can use its 3 timeouts to make one series only take 24 seconds off the game clock.

Because IND is due to receive the kickoff at 13:39 in the 3rd, KC was guaranteed to have at least three possessions--one between each theoretical IND TD. That means that just by kneeling, KC can burn a total of 456 seconds (7:36) off the game clock, which leaves a total of 1,207 seconds of game time (20:07) and no timeouts for IND to score 4 touchdowns.

Live Super Bowl Probability

It won't be nearly as much fun as the live playoff probability widget from last week, but I thought it would be interesting to put together a similar live Super Bowl probability widget for the games over the next couple weeks. It's now out of beta and ready for prime time. More notes below the widget.


The chances each remaining team will make it to the SB and win it are tracked live as each game progresses. The probabilities take into account the current game's live win probability, weighted by pre-game estimates of team strength and home field advantage. It also accounts for all future permutations of remaining games, weighted according to their likelihood of occurring. Those future games are also weighted by team-strength and home field according to seed.

Worst Article about Football Analytics of 2013

I came across this article from a website called Trending Buffalo just yesterday. It's from September, but unfortunately it's one of the top 10 results if you google football analytics. Although the author is misinformed or uninformed or both, I sense that his feelings are shared by a large number of fans and traditional analysts in the media. So I thought I'd respond point by point.

From 'Trending Buffalo' Sep 13, 2013

Precise breakdowns of every player on every play of every game can be found on countless websites [countless?] but “Player X failed to execute his route” and “Player Y is responsible for the B gap” ring pretty hollow when you don’t know what the players were supposed to do. [The author doesn't understand what analytics is. It's not amateur scouting.] Remember when Doug Flutie discredited analysts because “You watch the game. We watch the film”? He should’ve added “and we know the play calls.” Without that crucial information, your analysis is a really, really in-depth GUESS. [Football analytics is a lot of different things, combining tools from several disciplines, but it's not about guessing assignments on plays. I suppose the author doesn't care for Pro Football Focus, which isn't strictly 'analytics' on its own. But I'd submit that even though PFF doesn't know 100% of the assignments, most can be easily inferred. It's far from perfect, but it's a big step forward for public player evaluation and a giant leap beyond traditional punditry.]

Can Late-Season Momentum Explain Playoff Upsets?

Outcome bias is a powerful habit in forming mainstream opinion, and one of the most common NFL-related ones entails "momentum."  It's easy to look at a team that wins the Super Bowl and point to a late-season three-game winning streak as a sign that the future champs "figured things out" or "got the ball rolling."  Fill in your favorite cliche and voila, instant storyline.

But how often does so-called momentum play a role in playoff success?  This isn't a new question, and many analysts and fans have realized that success at the end of the regular season is not a prerequisite for a deep postseason run.  Last season's Baltimore Ravens won it all despite losing four of their final five regular season games.

Game Probabilities - Wildcard Round

Game probabilities for the wildcard round are available at the New York Times. This week I take a look at the matchup between KC and IND.

When the Colts host the Chiefs on Saturday in the first of this weekend’s four wild-card games, each team will feel as if it is looking into the mirror. The two teams are nearly statistically identical and tend to play disciplined, low-risk, ball-control football while letting their opponents make mistakes...

The two opponents are even more similar on defense. Kansas City’s and Indianapolis’s net yards per pass attempt allowed are 6.4 and 6.2, both close to the average of 6.2. They both allow 4.5 yards per carry, a bit more than the league average of 4.1. Both teams have grabbed more than their share of interceptions, as the Chiefs intercept the ball on 3.3 percent of all pass plays and the Colts on 2.8 percent...

Special Playoff Team Viz

I put together a special version of the team stat visualization for the playoff field. It's a good, quick way to get a feel for how each contender compares on offense and defense, in the passing game and in the running game. The first three tabs depict the three key team stats: EPA, WPA, and SR. Two additional tabs break out run and pass EPA production.

What might be particularly useful is the week selector slider. It's handy for isolating recent trends or for isolating subsets of games, such as GB's games with and without a healthy Aaron Rodgers.

The dashed average lines for each stat represent the 2013 overall league average, not just the playoff field. Here's a version below, but a larger version can be found here.

Final Team Efficiency Rankings: Week 17

Since these are the final efficiency rankings of the season, I thought I'd take a look at not only where we are, but where we've come from.  Here is a link to an interactive chart displaying the progression of each team's standing in the rankings, which the HTML editor was not very happy with when I tried to embed it in this article.

Instead of focusing on a couple teams as usual, we'll be more broad in evaluating the final rankings.  Consider this a mega-version of the quick hits section that typically ends each write-up.