Weekly Game Probabilities

Game probabilities for week 15 are up at the New York Times' Fifth Down.

This week I examine how some outlier teams can break the model, including this season's NE Patriots.

...Malcolm Gladwell’s book “Outliers” popularized the term in his title, but the exceptional people he featured in his best-seller were not actual outliers. If I spend five hours trying to learn to play the violin, I’ll stink. But if someone else spends 10,000 hours practicing violin, we would of course expect that person to be great. That’s entirely predictable and fits our model of practice makes perfect. A true outlier would be someone who spent only a few hours practicing, yet was still a violin prodigy.

Sometimes teams come along and break my model, and the 2012 Patriots are one of those teams...

When to Intentionally Allow a Touchdown, Part 5

This is the fifth and final part of the series on when a defense would prefer an intentionally allowed TD to forcing a FG. The previous four parts laid out the analysis and assumptions, computed the time remaining when the defense would regain possession, estimated the probability of a failed FG attempt, and estimated the probabilities of the team on defense responding with its own score. Now it's time to put all the parts together and present the results.

Putting It All Together

Taking a step back, the goal is to compare two strategies for the defense. The first is to play conventionally and force a stop and a FG attempt, hoping it will either fail or that there is enough time to match it with a counter-score. The second is to intentionally allow a TD immediately and use the time remaining to respond with a counter-TD.

So far, we have estimates for the key inputs:

-When the team on defense would get the ball back
-The probability of failure on the FG attempt
-The probability of responding to a made FG with a score
-The probability of responding to an allowed TD with a TD

When to Intentionally Allow a Touchdown, Part 4

This is the fourth part of a five part series on when a defense would prefer an intentionally allowed TD to forcing a FG. The previous three installments laid out the analysis and assumptions, computed the time remaining when the defense would regain possession, and estimated the probability of a failed FG attempt. This part will estimate the probabilities of the team on defense responding with its own score.

The Probability of Responding to a Successful FG

If the defense plays conventionally, and the opponent's FG is successful, a score will be needed to win. Either a FG or TD will do. We can assume that the drive will began at or very near the offense's own 20-yard line for a couple reasons. First, the average starting field position for all drives is the 22. And second, it's very likely that, with time at a premium, the offense would prefer a touchback so that no time expires on the kickoff.

For this estimate, I looked at all game situations in which an offense needed a score to survive and had a 1st down at or very near its own 20. Success is defined as any drive that results in a TD or FG.

The blue line is the raw success rate as a function of seconds remaining at the 1st down snap. The red line is the smoothed estimate of the probability of scoring based on a local regression. Because there were several bins of data with very few cases (which caused the large noisy swings in the raw averages), I used a regression method that weighted each case by how often it appeared. In other words, if there were 10 cases where a team gained possession with around 50 seconds to play and 20 with around 60 seconds to play, the regression weighted each bin of cases proportionately.

Team Efficiency Rankings - Week 15

NE moves up a couple spots and HOU slips a couple spots after Monday night's blowout. CAR and BAL remain the two big curiosities. Is CAR really the 3rd best team in the league? Well probably not, but they are the 3rd most efficient and definitely much better than their record indicates. Is BAL really the 21st best team? Again, probably not but they certainly are the 21st most efficient. They've dropped two straight games for the first time in the Harbaugh-Flacco era and are now 9-4. They face DEN, NYG, and CIN to finish the regular season, and all three opponents are playing much better than BAL lately. It's plausible that the once 9-2 BAL finishes the season losing six straight games, five regular season losses to finish 9-7 but squeaking into the playoffs to lose in the wildcard round. Unlikely but plausible.

Here are the rankings headed into week 15. Click on the headers to sort. Raw efficiency stats are in the second table below.

When to Intentionally Allow a Touchdown, Part 3

This is the third part of a five-part post on when an intentionally allowed TD is preferable to forcing a FG in the endgame. The first two parts of the post laid out the analysis and assumptions, and estimated the time remaining when the team on defense would get back possession. This installment looks at the probability of an unsuccessful FG attempt to take the lead.

Field Goal Success Probability

The simplest way to win for a defense caught in the field goal choke hold is to pray for an unsuccessful FG attempt. This is a mostly straightforward calculation but has a couple wrinkles. The success rates here include all possible causes of a FG ultimately being unsuccessful. That includes blocks, botched snaps, and even penalties that force longer attempts which turn out unsuccessful.

Also, as mentioned previously, an estimate of the expected field position on 4th down is required. For now, I will say that the offense will gain 5 yards during its 1st, 2nd and 3rd down plays. This is essentially a plausible placeholder for now, and a more detailed analysis can be done to confirm or adjust this.

The graph below shows three things. The jagged blue line is the actual raw FG success rate by line of scrimmage. (Add 17 or 18 yards for the commonly used 'kick distance'.) The red line is the estimated true probability of success. This estimate was computed non-parametrically, using locally weighted regression. The green line is the same curve as the red line, but offset 5 yards closer to the uprights. (Inside the 10, the 5 yards are progressively curtailed.)

When to Intentionally Allow a Touchdown, Part 2

This is the second part of a five-part series on when a defense would prefer an intentionally allowed TD to forcing a FG. The first part laid out the analysis and assumptions. This part explains how to estimate the time remaining when the defense would regain possession following a forced FG attempt by the offense.

Time Remaining Following a Forced FG

The first task of the analysis was to create an algorithm to compute the time on the clock when the team on defense would get the ball back following a forced FG. This is a function of current time and time outs remaining for the defense. For example, suppose the offense has just converted a series so that the 1st down snap will happen at 1:20, and the defense has two timeouts. The offense will run three times, you'll call both timeouts, and following a FG, you'll probably get the ball back with 17 seconds remaining. The two-minute warning is factored in, which is more challenging than it might seem.

The time-you-get-the-ball-back algorithm assumes that the defense will use its timeouts at every immediate opportunity. The only exception will be when the play itself spans the 2-minute warning. For example, if there is 2:10 on the clock at the snap and the play duration is 6 seconds, the defense will call a timeout at 2:04 rather than allow the clock to wind down to the 2-minute warning.

However, there is a special case where the defense may want to allow the clock to run down to the two-minute warning rather than use all its timeouts. For example, if there is 2:10 remaining between 2nd and 3rd down and a team has 2 timeouts remaining, it may chose to allow the clock to wind down to 2:00. The third down snap would occur following the two minute warning, and the defense would call its 2nd timeout between 3rd and 4th down, at around 1:54. This would allow the defense to save one timeout for use on offense.

Sunday's Numbers Have Been Crunched

Sunday's numbers are now available, including advanced stat box scores, top players of the week, team stats, and season leader boards.

• Advanced stat box scores
• Top QBs of the week
• Top RBs of the week
• Top WRs of the week
• Top TEs of the week
• Top Defenders of the week
• Advanced team stats
• Offensive player season leaders
• Defender season leaders
• Team Viz
• QB Viz
• RB Viz

When to Intentionally Allow a Touchdown

This study examines a team's chances of winning at the end of the game when an opponent is in potentially game-winning FG range. It's a dire situation for the team on defense because the offense could run enough time off the clock before its FG attempt so that there is no time to respond.

The Field Goal Choke Hold situation looks like this:  The defense has a lead of 1 or 2 points with less than 3 minutes to play. The opposing offense has just converted a first down inside FG (attempt) range. Through week 13 this season there have been 12 games that qualify, which makes this situation about as common as overtime. (There were 12 more games with similar circumstances except the game was tied, a situation nearly identical but that requires some slightly different math.)

Two strategies are compared. The first is playing for the stop and forcing the FG attempt. This may be dangerous due to the ability of the offense to burn clock. The second strategy is to allow an immediate TD. This strategy forfeits points to the opponent in exchange for enough time to respond with a game-winning TD drive.

There is no guarantee the offense will take the bait and score a TD. If the offense is cognizant of the strategy, they may take a knee close to the goal line. So strictly speaking, this analysis merely estimates which combinations of circumstances make an immediate TD preferable to forcing a FG attempt. Even if all offenses were prepared for this contingency and were inclined to take a knee, this analysis lays out when that would be the smart move.