Game Probabilities - Week 17

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also discuss home field advantage when a dome team visits a cold climate.

The 2009 All-WPA Team

The day after the Pro Bowl rosters are announced there are the obligatory "snub" articles in local papers around the country. In the DC area, the annual London Fletcher snub article is simply reprinted from last year's Post. So what about those Vincent Jacksons and Cedric Bensons who were unfairly left off the roster in favor of big name stars who may not have had a particularly good year? Who really earned their ticket to Miami?

I'll compare players using two different stats. Win Probability Added (WPA) measures each play's increase or decrease in a team's chances of winning. For every play that a player is mentioned in the play-by-play description, including penalties, turnovers and everything else, the WPA is tallied in his name. WPA is a narrative stat. It tells the story of what happened and is very context-dependent. It measures performance when it matters most. It has limited applications in terms of predicting future player performance, but it my mind it's perfect for comparing Pro Bowl and MVP contenders--even Hall of Fame candidates once there's enough data.

Request: Who Are The Pro Bowl Snubs?

I'm working on a comparison of players who were either selected for or snubbed from the Pro Bowl rosters. I'm tabulating each player's Win Probability Added (WPA) and Expected Points Added (EPA). In the comments here, list the players you think were legitimate all-pros but weren't picked. "Fantasy" positions only please (QB, RB, WR, TE). Except in rare cases, I can only analyze the positions that get run with, catch, or throw the ball.

Thanks!

Andy Reid Is No Longer My Hero

Note: This post was taken from a series of comments on the recent Games of Week post. Thanks to all who contributed to the discussion.

About a month ago Eagles head coach Andy Reid was my hero of the week for his daring, and smart, onside kick to open the game against the Redskins. Although it failed and gave up 7 points, he got them back by going for it on 4th down inside field goal range, succeeding, and getting the touchdown.

This past week, however, Reid is again the goat. With 3 minutes left in a tie game against the Broncos, the Eagles faced a 4th and 1 from their own 49. The Eagles punted. This was a big mistake, and you don't even need fancy math or some win probability model to prove it. Worse, Reid made the exact same call a year ago in the infamous tie against the Bengals.

If you have a 4th and 1 at about the 50 and you go for it, the value of the two possible outcomes are exactly equal. In other words, either I have a 1st down at the 50, or my opponent has a 1st down at the 50. It's perfectly symmetrical. Now consider what punting means.

Team Playoff Probabilities - Week 17

Courtesy of NFL-Forecast.com, here are the latest playoff forecasts.

The NFC teams are locked up. Only the seeds are left to be settled. The AFC wildcard contenders keep losing. Only the Jets and Ravens control their own destinies this Sunday.

Run-Pass Imbalance on 2nd and 3rd Downs

I've recently been looking at the imbalance in the payoffs for running and passing on first downs. The results suggested that most teams should generally pass more often outside the red zone and run more often inside the 10-yard line. What about 2nd and 3rd downs?

Game theory tells us that when the payoffs for two strategy options are unequal, the strategy option with the higher payoff should be selected more often. As the opponent adjusts to counter the new mix of strategies, the payoff of the favored option will decline while the unfavored option becomes more lucrative. Eventually, the payoffs for both options equalize, and at this point the overall payoffs are optimum. In two-player zero-sum games this is known as the minimax, or more generally as the Nash Equilibrium.

I used Expected Points (EP) to value the payoff of each play. Expected Points measures the net point advantage that the play result gives to an offense. It captures the value of yardage gained and lost, first downs, sacks, penalties, turnovers, and everything else in terms of equivalent point value. The change in EP resulting from a play is called Expected Points Added (EPA).

One of the things EP does not measure is the time value of a play. In situations when a team has a significant lead, the true value of a run includes the time burned off the clock. To a team behind late in a game, pass attempts have more value because they are more likely to stop the clock. For this reason I only include plays in the first and third quarters and when the score is within 10 points. This excludes trash-time plays and plays affected by the clock.

Team Efficiency Rankings - Week 17

It looks like the Bengals really are frauds, as Rodney Harrison kindly called them last Sunday night. Well, maybe not frauds, but they are an average team posing as a dominant division winner. Anything can happen in a single elimination tournament like the NFL playoffs, but I wouldn't count on them going very far.

It's no surprise the Jaguars have fallen apart down the stretch. They have been a slightly below-average team for most of the year.

The reigning champion Steelers are still a very good team, but are a long-shot for the playoffs. Had Roethlisberger been able to play in the the first game against Baltimore, which was lost in overtime, the wildcard situation might be very different right now. That was a division and conference game, which would come in very handy in a tie-breaker.

The Jets had a relatively small chance to make the playoffs through most of the season despite their 3-0 start. That all changed in the 3rd quarter against the Colts. On the first series without Manning and their other starters, the Colts gave up a sack, a fumble, a touchdown, the lead, and a perfect record. They also handed the Jets a very strong hand going into the final week. Colts fans are upset at losing the shot at perfection, but maybe the fans who should be most upset are those of the Broncos, Steelers, Jaguars, Texans, and Dolphins.

Games of the Week

Tonight's game notwithstanding, the game of the week was the Denver-Philadelphia game. What started to look like a blowout turned into a barnburner. Down big early, the Broncos came back to tie before surrendering a late field goal. DEN 27 PHI 30 (EI 4.9).

The runner up was the Baltimore-Pittsburgh game (4.0 EI). The Ravens were down by 10 at the half but came back to tie in the 3rd quarter. They had multiple opportunities to win the game, but imploded with penalties. BAL 20 PIT 23.

The comeback of the week was also the upset of the week. New Orleans gave up a commanding lead over Tampa Bay, and ultimately lost in overtime. TB 20 NO 17. At their low-point in the game the Buccaneers had a 3% chance of winning (CBF 33).

Game Probabilities - Week 16

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also look at just how big a blowout Monday night's Giants-Redskins game was using the WP model.

Troy Polamalu and 'WPA Plus/Minus'

Troy Polamalu is one of my favorite players in the league. As a Ravens fan whose heart despises everything that is black and gold, I'm compelled to say that he is truly spectacular. (The picture to the left is his interception return for a touchdown that saved the AFC Championship game for Pittsburgh last year.) He's also a classy and selfless player who never showboats, a breath of fresh air in today's NFL. Unfortunately for Steelers fans, his injury this season has revealed just how great a player he is.

Polamalu has played in five games this season and has missed nine. Using the Win Probability (WP) model, we can calculate the Win Probability Added for any play (WPA). We can also sum WPA for any team, squad, or player to estimate the context-dependent contribution of that player to his team's chances of winning.

WPA for defensive players is particularly problematic. If a running back evades all ten other defenders but is tracked down 60 yards later at the 5-yard line by the eleventh, it's the tackler that will show up in the play-by-play and be charged with the loss in WP. That doesn't make sense.

But Polamalu's 2009 season provides us with a special opportunity. We can measure the WPA of the entire Steelers defense when Polamalu is playing and compare it to the WPA of the Steelers defense when he's not.

Team Playoff Probabilities - Week 16

Courtesy of NFL-Forecast.com, here are the latest playoff forecasts.

The Ravens have further strengthened their position in the AFC, while the battle in the NFC continues to be a battle between the Giants and Cowboys. The Cowboys currently have the upper hand, but the Packers' loss last week has made them vulnerable. The Ravens' weekend was miraculous. They won, while the Jaguars, Jets, Dolphins and Broncos all lost. Except for the Steelers, who still only have a small chance of making the playoffs, every single other competitor for the AFC wildcard lost ground. The Ravens went from the 'outside looking in' to the #5 seed.

Team Efficiency Rankings - Week 16

The team rankings below are in terms of generic win probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

Desperation Graphed

[Note: I can't remember if I already posted this or not. I did this back over the summer and saved it for the season. But I don't think I ever clicked 'publish.' ]

How desperate do NFL coaches have to be before they start going for it on 4th down?

Recently I've shown that, as a rule, teams should be going for it on 4th down far more often than they currently do. But what is 'currently do?' How far do coaches let themselves get backed up against the wall before they start actually doing what's best for their chances of winning?

Games of the Week

Tonight's game notwithstanding, the game of the week was the Oakland upset over Denver (6.2 EI). The runner up was the Green Bay-Pittsburgh barnburner (5.8 EI), which was also the comeback of the week (33 CBF).

Unlike last week, there was a good number of competitive games, including:
CLV 41 KC 34
CIN 24 SD 27
IND 35 JAX 31
MIN 7 CAR 26 (which despite the score was very close until the 4th qtr).

Explanations for Excitement Index (EI) and Comeback Factor (CBF) can be found here.

Was the Steelers' Onside Kick Smart?

Up by 2 points with 3:58 left against the Packers, Steelers head coach Mike Tomlin called for an onside kick. Was this a good decision?

When onside kicks are expected, they are successful only about 20% of the time. But unexpected onside kicks are successful a surprising 60% of the time. I think we can say this particular kick was certainly unexpected. And surprise onside kicks can be the most beneficial when a team is ahead late in the game. Possession is critical.

Roundup 12/19

If you're snowed in like me this Saturday afternoon, you've got plenty of time on your hands. Early season college basketball doesn't really grab my attention. Neither does the apparently sponsor-less "New Mexico Bowl." (Actually, I often root for Fresno State due to being stationed nearby at Naval Air Station Lemoore, CA for many years.) Here are some links to help pass the snowy Saturday.

Chase Stuart from PFR looks at Steven Jackson's huge year for the struggling Rams. That's very unusual for a RB to have such a big year on a losing team. In a contribution to the Fifth Down Blog, Chase looks at the five least likely playoff teams in history based on their early season struggles.

Are Teams Going For It More In 2009?

Is it me, or do I sense that teams are going for it more often on 4th down this year? And maybe I'm imagining things, but I also get the feeling that teams have been even more daring since the Belichick 4th down decision against the Colts.

The three graphs below tell the story. The top two graphs depict the proportion of 4th down decisions by field position. The first graph is for the 2000-2008 seasons, and the second is for the 2009 season. The third graph isolates just the proportion of conversion attempts by field position so we can better compare the previous seasons with the current season.

Game Probabilities - Week 15

Weekly game probabilities are available now at the nytimes.com Fifth Down.

Team Playoff Probabilities - Week 15

Courtesy of NFL-Forecast.com, here are the latest playoff forecasts. The tables below do not include results from this week's Thursday game.

The Ravens have strengthened their position in the AFC, while the battle in the NFC appears to be between the Giants and Cowboys.

Expected Point Values

Lately I've been using the concept of 'Expected Points' (EP) as a measure of success for football plays. It's been the foundation of much of my analysis of fourth down decisions, onside kicks, run-pass balance, and even touchbacks.

Every down-distance-field position combination has an average net point advantage. For example, when an offense has a first and goal at their opponent's 1-yard line, they can expect about a 6-point advantage over their opponent in the long run. A first and 10 at midfield is worth about 2 EP.

Expected Points on first downs are easy to compute because there are so darn many 1st and 10s compared to any other down and distance combination. Here is the EP chart for 1st and 10 (or goal) from my fourth down study earlier this season.

Team Efficiency Rankings - Week 15

The team rankings below are in terms of generic win probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

Games of the Week

Some weeks can have a lot of really exciting games. Week 14 wasn't one of them. This week's most exciting game was (technically) BUF 16 KC 10 (5.5 EI). True, this wasn't a shootout between two playoff contenders, but if you really cared about who won, this was exciting. Leads of 6 points often produce exciting games because a TD at any time can tip the balance.

The runner up actually had playoff implications.

The comeback of the week wasn't terribly thrilling either. NE had about a 1 in 6 chance of winning (a CBF of 6) late in the second quarter as CAR drove into scoring position with a 7-point lead. NE ultimately won, NE 20 CAR 10.

Run-Pass Imbalance by Year

I've been chronicling the imbalance in the payoffs of runs and passes on first down in several recent articles. One of the possible explanations for the imbalance is that coaches are too slow to adapt to the NFL rules that seem to become friendlier to the pass year after year. If so, maybe the adaptation to the new realities can be seen in a decrease in the payoff imbalance over recent years.

The graph below charts the difference in payoffs between passes and runs by year. As with my previous posts, data are limited to 'normal' football situations--when the score is close and when time is not yet a factor. As you can see, there may be a slight decreasing trend in the imbalance, suggesting coaches might be catching up.

Team Playoff Probabilities - Week 14

Courtesy of NFL-Forecast.com, here are the latest playoff forecasts. The tables below do not include results from the Thursday games.

The Jaguars and Broncos have strengthened their positions in the AFC, while the Giants, Eagles, and Packers have improved their chances in the NFC.


Game Probabilities - Week 14

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also lead-in with a discussion of the luckiest and unluckiest teams so far this season.

Luckiest and Unluckiest Teams - Week 14

For some reason this is my favorite stat.

I estimate team "luck" by using my efficiency regression model to calculate each team's expected wins--how many wins a team can normally expect, on average, given their actual performance in offensive and defensive running, passing, turnovers, and penalties. The difference between the expected wins and actual wins is what I loosely call team luck.


What do I mean by luck?

In my own life, I'm a big believer in hard work, preparation, focus, execution and everything else that isn't luck. Coaches and players can't let themselves think any other way for a single second. But once we account for all those things, what do we call what's left over? Statisticians call it "residual," and a substantial portion of any residual is due to random effect, including sample error and what I call "bunching." In a bounded and meticulously measured system like sports, a vast amount of the residual from any decent model will be due to randomness. A season of 16 games simply isn't long enough for the breaks to even out.

Team Efficiency Rankings - Week 14

The team rankings below are in terms of generic win probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

Games of the Week

Game of the Week: OAK 27 at PIT 24 (6.7 Excitement Index)
Runner Up: NE 21 at MIA 22 (6.2 EI)

Comeback of the week: NO 33 at WAS 30 (100 Comeback Factor)

Defensive Run-Pass Balance

I've been writing a lot about offensive run-pass balance lately, recommending that most teams should pass more often. So far I've ignored half of the equation--Defensive strategies matter too.

Unlike offensive play choices which are discrete defined options (such as either run or pass), defenses have a continuum of options ranging from a prevent defense to a goal-line stand. Defenses don't have to commit to one or the other. Instead, they can bias their strategy anywhere from 100% pass to 100% run.

With play-by-play data, we know what option an offense chose. Unfortunately, without coach's film of every game and an intimate knowledge of a teams' defensive schemes and intentions, it's nearly impossible to know where on the continuum a defense stood on any given play.

Still, it may be useful to see how often a team was run against or passed against, and see how successful each play type was. The table below lists each defense's proportion of passes faced on first downs. Also listed is the average success of each type of play as measured by Expected Points Added (EPA). The difference in average success between passes-against and runs-against roughly measures the imbalance in play selection.

MVP Candidates Through the Lens of WPA

One of the cool things to do with a Win Probability model is to look at the total Win Probability Added (WPA) of a player. Each play in a game changes a team's chances of winning either positively or negatively, and the WPA for the plays in which a player takes part can be tallied. WPA discounts 'trash-time' performance, and emphasizes 'clutch' performance. The result roughly measures the past value of a player in terms of what matters most--winning games.

WPA is a narrative statistic. It tells the story of how a player performed, but it does not predict how he'll likely play in the future. It includes all the flukes, miracles, and everything else that makes football unpredictable and fun to watch. In essence, WPA is what the MVP award is all about.

I've tallied the WPA for the notable MVP candidates through Week 12 of the 2009 season. The table below lists various players and their WPA expressed a few different ways. There is total WPA, which is simply a raw sum. There is also WPA per game and WPA per play, which tell a slightly different story.

2009 Team-Specific Run-Pass Balance

Recently I've been looking at run-pass balance on first downs based on a principle of game theory. When strategy mixes are optimized, the two strategies will ideally produce equal payoffs. If they aren't equal, then the better strategy should be selected until the opponent responds with his own counter-strategy. Results suggested that, in the NFL overall, the gains by passing on first down exceed those by running. In turn, this suggests that offenses should pass more often than they currently do.

However, every team has its own relative ability between passing and running. You can't just tell the 2009 Raiders to start passing more often. Their running game may actually be superior to their passing game in terms of expected payoffs, so while most teams should be passing more frequently, it's possible a minority of teams should be running more often.

Team Playoff Probabilities - Week 13

Courtesy of NFL-Forecast.com, here are the latest playoff forecasts. The tables below do not include results from the Thursday games.

It looks like the AFC wildcard picture has changed with the Jaguars' and Texans' losses, and the Ravens' win over the Steelers. Although the Ravens currently hold the 6th seed (I think), they're projected to have a 40% chance of holding on to it.

The NFC wildcard picture has changed too. The Packers' and 49ers' chances have improved while the Giants' and Falcons' chances have taken a hit.

Game Probabilities - Week 13

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also discuss the playoff prospects for the Jets and Giants, and why they may seem pessimistic to most fans.

NFC Playoff Picture: Wildcards

Chris Cox from NFL-Forecast.com, who computes team playoff chances using his Monte Carlo simulation, provides the current playoff breakdown in the NFC. His AFC breakdown is here.

Yesterday, I posted a summary of the AFC playoff race. Today I turn my attention to the NFC. As a reminder, my approach is to tentatively declare Cowboys, Vikings, Saints, and Cardinals as division champs so that I can focus on the wild card races. The NFC East, and to a lesser extent the NFC West, are still up for grabs, but this assumption greatly simplifies the analysis.

Team Efficiency Rankings - Week 13

The team rankings below are in terms of generic win probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

JaMarcus Russell: Concorde of the NFL

With Jamarcus Russel’s recent benching, there’s been a lot of talk about when it’s time for a team to cut its losses on a failed quarterback. I don’t have hard numbers at my fingertips, but I’d be fairly certain that if a QB isn’t playing above average football or there hasn’t been steady improvement, by the end of his second year, it’s time to move on. [Edit: Here's a good look at that very question at PFR.] There’s no question teams tend to stick with struggling QBs well beyond their expiration date, even when better alternatives exist. The real question is, why?

Let’s say you’re an out-of-town Bills fan, and before the season began you were understandably optimistic about the team’s prospects. You bought prime tickets to the January 3rd game hosting the Colts, including parking and a hotel room. Altogether the bill comes to $400. In August, this feels like a great deal.

As the season wears on, it becomes clear the Bills aren’t contenders. The coach is fired, and the upcoming Colts game is not looking promising, as the Colts appear likely be playing for home field advantage in the playoffs. Everything points toward a humiliating blowout. What’s worse, as the game approaches the weather isn’t looking good. Bills fans are always the hardy type, but the foercast is beyond bad—snow, wind, freezing rain, and bitter cold. You’re not exactly excited about the prospect of going to the game.

AFC Playoff Picture: Wildcards

Chris from NFL-Forecast.com has done an excellent break down of the AFC playoff picture. Enjoy.

With 5 weeks remaining in the season, there are clear leaders in seven of the eight divisions. The NFC East division champ is very much up for grabs but in each of the other divisions there is one team that has an 80% chance or better of winning the division. The Cowboys have the inside track to the NFC East title, and even if the Eagles or Giants ultimately win that division, the Cowboys are likely to claim one of the wildcard spots. For the moment, if we designate the Patriots, Bengals, Colts, Chargers, Cowboys, Vikings, Saints, and Cardinals as division champs, we can focus on the wild card races. In this article, I will focus on the AFC wild card race.

(Much) More on 1st and 10 Run-Pass Balance

In a recent article I presented evidence that offenses should generally pass more often on first down. Accounting for both the potential gains and the potential risks of each type of play, passing tends to lead to a greater net point advantage than does running. The analysis was based on a concept known as Expected Points, which measures the average point advantage an offense can expect given a down-distance-field position situation.

Expected Points incorporates all the various factors such as turnovers, yardage gains, sacks, incompletions, first down conversions, scoring, and so on. But I thought it would be helpful to dig deeper to investigate how and why passing appears more advantageous. In this article, I'll present a series of graphs comparing running and passing on first down, each one looking at a different facet of the game.

Sunday Night 4th Down

Down by 3 with a little more than 3 minutes left in the game, Ravens head coach John Harbaugh faced a decision with a 4th and 5 at his own 48. Harbaugh decided to go for the first down. Both Al Michaels and Chris Collinsworth agreed Baltimore had no choice but to punt. Was it a good call?

Punts from the 46 net an average of 34 yards, which would put the Steelers at their own 20. In that situation, teams win 83% of the time. A punt gives the Ravens a 0.17 win probability (WP).

Conversion attempts for 4th and 5 situations outside the red zone are successful 48% of the time. An unsuccessful attempt leaves the Steelers with a first down at the Ravens' 46. Teams win 87% of the time from there, leaving the Ravens with a 0.13 WP. A successful conversion would, at worst, give the Ravens a first down at the Steelers 49, worth a 0.37 WP. On net, the conversion attempt is worth:

Andy Reid: Hero

Reid was my goat of the year for 2008 for the season's single worst 4th down decision, but today he's my hero of the day (or at least for the 1st quarter of the 1 pm games). Reid started the game with an unexpected onside kick, which is an underused but very worthwhile tactic. This time it didn't work out, but the Eagles recovered nicely, and now lead 10 - 7.

The linchpin of the Eagles's 1st quarter TD drive was a successful 4th down conversion. With a 4th and 1 on the Redskins' 42, Reid went for it, made it, and went on to take the lead (for the moment).

Team Playoff Probabilities - Week 12

Courtesy of NFL-Forecast.com, here are the latest playoff forecasts. The tables below do not include results from the Thursday games.

It looks like the AFC teams remain relatively firm. As of now, the Colts, Bengals, Steelers, Patriots, Broncos, and Chargers are on the inside track. Baltimore, Jacksonville, and Houston are on the outside looking in.

Not much has changed for the NFC either. The top teams have a tight hold on playoff spots, but the wildcards are up for grabs. The Saints, Vikings, and Cardinals each have a good grip on their divisions if they keep playing well. The Cowboys are the class of the East at the moment, and have a good shot at a wildcard if they don't take the division. The other contenders include the Eagles, Giants, Packers, Falcons, and the 49ers.

Game Probabilities - Week 12

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also discuss the major shortcoming of a purely quantitative approach to game predictions.

Happy Thanksgiving, everyone!

Team Efficiency Rankings - Week 12

The team rankings below are in terms of generic win probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

Offenses Run Too Often On 1st Down

NFL offenses generally run too often on 1st down. Accounting for the relative gains of each play type, and accounting for the risks of turnovers, offenses should pass more. There is currently an imbalance, where teams are too often running directly into defenses that are expecting runs.

Game theory tells us that when there are two strategy options, like run and pass, the expected payoffs for both options should be equal. You really don't need game theory to intuitively understand this. If one option yields a better payoff, then it should be chosen until the opponent responds with a strategy change of his own. Eventually, as the opponent responds, the payoffs for the two options equalize. The point at which the strategy mix equalizes payoffs is known as the minimax, or sometimes called the Nash equilibrium. The resulting strategy mix, or run-pass balance in this case, produces the best overall, long-run payoff.

When there are two strategy options and one of them yields a much higher payoff, it tells us two things. In this case, passing is more lucrative than running on 1st down, and this tells us: 1) offenses should be passing more often, and 2) for now, defenses should continue to be more biased toward stopping the run.

Last Thoughts on the 4th and 2

At the risk of being accused of milking this thing, here are some final few thoughts on the topic. I watched the Football Night in America segment and a few things struck me.

Let me say I have a lot of respect for Coach Dungy. I also think that convincing someone skeptical is difficult, and we shouldn't expect someone to immediately come around. In general though, coaches (and former players/analysts) benefit from a perception that football is some unknowable mystery, and that they are the only priests that can divine the true answers.

From Dungy's perspective, he's enjoyed long career by doing it the conventional way. But the reason his way worked was because everyone else played the same way. To change his mind now might mean admitting, "I did it wrong all these years." That's a tough hurdle to overcome.

Team Playoff Probabilities - Week 11

Courtesy of Chris at NFL-Forecast.com, here are the latest playoff forecasts. The tables below do not include results from the Thursday night Dolphins-Panthers game.

It looks like the AFC teams are relatively firm. As of now, the Colts, Bengals, Steelers, Patriots, Broncos, and Chargers are on the inside track. Baltimore, Jacksonville, and Houston are on the outside looking in.

The top NFC teams have a tight hold on playoff spots, but the wildcards are up for grabs. The Saints, Vikings, and Cardinals each have a good grip on their divisions if they keep playing well. The Cowboys are the class of the East at the moment, and have a good shot at a wildcard if they don't take the division. The other contenders include the Eagles, Giants, Packers, Falcons, and even the 49ers.

ESPN Interview

ESPN's Sunday NFL Countdown will be doing a piece on 4th down decisions this weekend. The focus will center around Bill Belichick and his thoughts on the topic in an interview they did with him a few years ago. At the time, they also interviewed Dr. David Romer, author of 'Do Firms Maximize.' Yesterday, ESPN re-interviewed Romer, and interviewed me too. I'm anxious to see how it turns out.

I'm told it will probably air a few minutes before noon EST on Sunday. Set your DVRs now!

ESPN also talked about my take on '4th-and-2-gate' on the Monday Night Football pre-game earlier this week. A lot of people were harsh on Matt Millen and Steve Young for their comments, but I think they asked exactly the right questions. Young said, 'Is that in context? I'd want to see that in context.' I presume he wants to know if the score and time remaining were considered. Millen asked, 'But does that take into account the Colts offense?' They were rightfully skeptical, but they zeroed in on the heart of the matter immediately. I have to give them a lot of credit.

'Patriots Lead Colts at Halftime' - The Onion

The guys at the Onion have previously made their opinions known about 4th down decisions. This time they take on the Patriots' 4th down call from Sunday night. Too funny for words.



Belichick told reporters..."The only time they've been able to stop us is on on short-yardage passing plays, so if we're careful to execute and avoid any situation where we give Peyton Manning excellent field position, I'm extremely confident we'll leave here with a 'W.'

Thanks to Justin for the pointer.

Game Probabilities - Week 11

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also look at what's plaguing the Jets, and how it affects their match-up against the Patriots this week.

Belichick 4th Down Follow-Up

Thanks to the commenters on the original post, all 200+ of you, for all the great criticisms and suggestions. The Internet is a big place, and although not every comment was helpful, I was pleased to see such a thoughtful and constructive debate. In this follow-up, I'll try to address some of the most common criticisms and questions. I suspect some skeptics will never be fully satisfied, but I feel many of the comments deserve a response.

1. You used 38 yds for the expected punt distance, the average punt distance for that region of the field. But Patriots punter Chris Hansen had averaged 4 punts for 44 yds. Why not use that distance instead?

Team Efficiency Rankings - Week 11

The team rankings below are in terms of generic win probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

Should the Patriots Have Let the Colts Score?

After the Patriots' failed 4th down conversion attempt in the now epic game against the Colts, they wound up facing a Colts offense with a 1st down on the Pats' own 14-yard line. With 1:20 on the clock, the Patriots could have allowed the Colts to score an easy touchdown, yielding a 1-point lead, but giving the Patriots a shot to take the lead back with a possible FG drive. Or, they could have played straight defense, hoping to keep the Colts out of the end zone.

I'll take a look at league-wide averages, and then we can make adjustments from there. Against a team needing a TD, playing straight defense yields a TD about 62% of the time. This means the Patriots would have a 0.38 Win Probability (WP).

The Two-Minute Drill

In my recent posts on the Maurice Jones-Drew kneel-down and the Belichick 4th down decision I cited a few stats about how likely an offense that needs a touchdown to tie or win is to score one with about 2 minutes remaining in the game. Normally I like to back up obscure stats like that with some firmer context, and I was finally able to get around to it for these numbers.

The chart below graphs the percentage of time a team that needs a TD, defined as being down by 4 through 8 points, gets a TD on its current drive given a 1st down at various field positions with 2:00 +/- 15 seconds left. (I know that's quite the run-on sentence, but I don't know how else to say it.)

MJD Taking a Knee

With just under two minutes remaining against the Jets, Jaguars RB Maurice Jones Drew broke free for a go-ahead TD. Instead of plunging into the end zone he took a knee at the one-yard line. This decision allowed the Jaguars to run out the clock before kicking a chip-shot FG for the win. A TD would have allowed the Jets almost two minutes to answer with a TD of their own. How important was MJD's decision?

The analysis was a little more complicated than I thought because had the Jaguars scored the TD, they would have gone for the 2-point conversion. With a single XP, a Jets TD wins. With a failed 2-pt conversion, a Jets TD also wins. But with a successful conversion, a Jets TD only ties, so there is nothing lost and a lot to gain for the Jags by going for the 2.

Belichick's 4th Down Decision vs the Colts

New England coach Bill Belichick is taking a lot of heat for his decision to attempt a 4th down conversion late in the game against the Colts. Indianapolis came back to win in dramatic fashion. Was the decision a good one?

With 2:00 left and the Colts with only one timeout, a successful conversion wins the game for all practical purposes. A 4th and 2 conversion would be successful 60% of the time. Historically, in a situation with 2:00 left and needing a TD to either win or tie, teams get the TD 53% of the time from that field position. The total WP for the 4th down conversion attempt would be:

Game Probabilities - Week 10

Weekly game probabilities are available now at the nytimes.com Fifth Down.