Go For Two!

Photo by Keith Allison

While most New England fans are still recoiling from today's loss to the Jets, I thought I would take a moment to draw your attention to a huge error by coach Belichick that significantly reduced our chance to win the game.


With less than two minutes left in the game, the Patriots scored a touchdown and kicked the extra point, to bring themselves within 7 points of the Jets.

Before the score, the Patriots were down 31-17. It's pretty clear at this point in the game that the only way the Patriots could win is to score two touchdowns while preventing the Jets from scoring.

So, any assessment of the correct strategy should assume that the Pats will score two touchdowns while holding New York scoreless.

The league average success rate for 2-point conversions is 47.9%. Using this rate, it doesn't make sense to "go for 2" if you can tie the game by kicking the extra point. Here's a quick example of how the math works out in that situation (when the trailing team is behind by just 1 point after scoring the touchdown, but before the point-after):

(PAT success is 98.7%):

1) Team scores touchdown to bring score within 1 point. Team kicks extra point.

Chance of leading after this score: 0%.
Chance of being tied after this score: 98.7%.
Chance of trailing after this score: 1.3%.

2) Team scores touchdown to bring score within 1 point. Team goes for two.

Chance of leading after this score: 47.9%.
Chance of being tied after this score: 0%.
Chance of trailing after this score: 52.1%.

A team that ends the game in the lead wins that game. If they end the game trailing on the scoreboard, they lose. All things being equal, a team that ends the game tied has a 50% chance of winning that game.

So, we can award 1.0 wins for a result that puts the team in the lead; 0.5 wins for a result that ties the game; and 0.0 wins for a result after which the scoring team is still trailing.

Using those values, kicking the extra point produces 0.4935 wins but going for two results in only 0.4790 wins.

However, if the trailing team needs *two* touchdowns, the math is totally different.

1) Team trails by 14 points and scores two touchdowns. Team never goes for two:

Chance of leading after both scores: 0%.
Chance of being tied after both scores: 97.42%.
Chance of trailing after both scores: 2.58%.

2) Team trails by 14 points and goes for two after the first touchdown:

Chance of pulling within 6 points: 47.9%.
Chance of pulling within 7 points: 0%.
Chance of pulling within 8 points: 52.1%.

Then, when the team scores a 2nd time, they kick the extra point *if it would give them the lead*. If the team scored 8 points with the first touchdown, they have already tied the game before kicking the extra point.

2a) Team trails by 6 points before the touchdown, and kicks the extra point:

Chance of leading after both scores: 98.7%.
Chance of being tied after both scores: 1.3%.
Chance of trailing after both scores: 0.0%.

If the two-point conversion failed on the first touchdown, the team has to go for two in an attempt to just tie the game:

2b) Team trails by 8 points before the touchdown, and goes for two:

Chance of leading after this score: 0.0%.
Chance of being tied after this score: 47.9%.
Chance of trailing after this score: 52.1%.

To see the overall chance of winning the game with this strategy (going for two after the first touchdown), we have to combine the odds from 2a and 2b:

2) Team trails by 14 points and goes for two after the first touchdown

Chance of leading after both scores: 47.28%.
Chance of being tied after both scores: 25.58%.
Chance of trailing after both scores: 27.14%.

Assuming a 50% chance of winning tie games, here's what we get:

Going for two after the first score: .6007 wins
Kicking the extra point after the first score: .4866 wins

Going for two after the first score increases the chance to win the game by 23.4%. That's a huge difference (and one that Belichick shouldn't have passed up).

The key is that when you know that you need *two* touchdowns, you can make the decision whether to go for 2 on the second touchdown, *already knowing whether you had a successful conversion on the first touchdown*. If you weren't successful, then you need to go for two to tie the game. But if you succeeded on the first touchdown, you can just kick the extra point on the second touchdown, and win the game by 1 point.

2010 Offensive Line Rankings

Based on stats from the last 12 seasons (yes, Matt Birk has been in the league since 1998), here are ratings for the current offensive lines for all 32 NFL teams.

Rank	Team	Overall	Run Blocking	Pass Blocking
1	New Orleans Saints	95	95	93
2	Tennessee Titans	94	95	92
3	New York Jets	92	94	89
4	Carolina Panthers	92	94	88
5	New England Patriots	91	84	97
6	Atlanta Falcons	90	85	93
7	Baltimore Ravens	89	94	83
8	Miami Dolphins	88	93	82
9	Dallas Cowboys	88	91	86
10	Minnesota Vikings	87	92	83
11	Arizona Cardinals	87	81	93
12	Indianapolis Colts	86	75	97
13	New York Giants	86	82	89
14	Denver Broncos	85	81	89
15	Cleveland Browns	84	81	88
16	Cincinnati Bengals	84	80	88
17	Jacksonville Jaguars	82	91	72
18	San Francisco 49ers	81	83	79
19	San Diego Chargers	81	72	91
20	Houston Texans	80	71	90
21	Philadelphia Eagles	80	81	79
22	Green Bay Packers	79	92	67
23	Kansas City Chiefs	79	85	72
24	Chicago Bears	78	69	88
25	Tampa Bay Buccaneers	77	72	83
26	Buffalo Bills	76	85	68
27	Pittsburgh Steelers	75	81	67
28	Detroit Lions	75	76	74
29	Oakland Raiders	74	79	69
30	Seattle Seahawks	73	72	74
31	St. Louis Rams	73	75	71
32	Washington Redskins	72	74	69

For more information on each offensive lineman, check out the individual ratings in Football Mogul.

Fixing Overtime In The NFL (Revisited)

We already have a great solution to the problem of the coin flip in overtime games. Nevertheless, it has been almost four years, and we're still stuck with the old system.

After the Vikings-Saints NFC Championship game (and the Colts' failed attempt to go 16-0) the argument for this change to the rules is even more compelling. If this rule had been implemented, both the Saints and the Colts would have still had something to play for in the last month of the season.

To summarize, we can fix the following two problems with one rule change:

1) The coin-flip winner has an unfair advantage in overtime.
2) Teams like the 13-0 Saints and 14-0 Colts have no incentive to win after they have clinched the top playoff spot.

The solution is elegantly simple: automatically award the coin flip to the home team.

In addition to eliminating the coin flip, there are a number of other positive effects:

1) This increases the importance of home field advantage in the playoffs. If a team like the Colts go 14-2, they get an edge if a playoff game goes to overtime (just as the home team in baseball has a strategic advantage).

2) We now know who the "home team" is in the Super Bowl. And it matters. This would have been pivotal this season: the Colts and Saints would continue to play hard, knowing that if they met in the Super Bowl, home-field advantage would be determined by their regular-season record. Instead, we got five unwatchable games by two teams that had nothing to play for.

3) It adds drama to the final minutes of a game, and clarifies strategy for coaches. If you're the away team, and you're up against a good offense, you want to play for the win, not the tie, in any last-minute play calls. You go for two if you have the chance. And you go for the touchdown instead of the field goal on 4th down. More excitement, and less overtime (which tends to run into the next game, which doesn't make most football fans happy).

4) It increases attendance. As the NFL becomes more fun to watch on TV, ticket sales are suffering. Giving the home team a bigger advantage increases the likelihood that a home-team fan will have a great experience at the stadium (by getting to see his or her team win).

Wes Welker For MVP

Photo by Mike Gil 

Peyton Manning was announced two days ago as the MVP for the 2009 NFL season. But yesterday, without even leaving Bob Kraft's luxury box, Wes Welker proved that he was the one who should have received the award.

With Welker on the roster, the Pats were 7-0 at home this season. Without Welker, they lost in Foxboro to the Ravens, 33-14. It seems silly to pin a 19-point loss on an injury to one guy. But the evidence shows that Wes Welker turns Tom Brady from a "very good" quarterback into "the best quarterback ever".

Brady's career Passer Rating with Welker: 108.1. That's easily the best Passer Rating ever. It's not even close. According to Football Mogul, Steve Young has a career Passer Rating of 96.8. Peyton Manning and his vaunted four MVPs: just 95.2. Take Welker away from Brady and his career Passer Rating drops to 88.7, more than two points behind Chad Pennington!

The difference is just as stark in the playoffs. Brady's Passer Rating in playoff games with Welker is 97.1, including an amazing 70.6% overall completion rate. Without Welker, Brady's playoff Passer Rating is a mediocre 83.2. And the icing on this shit cake is a 49.1 Passer Rating in Sunday's game versus the Ravens.

Julian Edelman caught two touchdowns in Brady's first home playoff loss. But he didn't move the chains like Welker. And he didn't free up Moss to go deep. Brady spent a lot of time holding the ball and getting pressured, because he didn't have Wes to go to when he needed to.

For some final perspective, note that Matt Cassel's season with the Patriots (and with Welker) in 2008 was better than four of Brady's seasons without Welker. But it was worse than the seasons that Brady has had with Welker. So, Brady is better than Cassel. But Wes is better than both of them.

So, my vote for 2009 NFL MVP goes to Wesley Carter Welker. Without Wes, the Patriots may not have even made the playoffs this year. Tell Peyton to give back that trophy!

Coke Is It! Three In A Row

We can now be fairly confident that the United States has elected three consecutive presidents that have used cocaine.

Maybe this isn't a big deal. In theory, personal experience with illegal drugs should aid in understanding and fixing the drug problem in America (although it is worth noting that Clinton and Bush 34 did little to change the status quo).

The interesting thing is that the U.N. says 7.6% of American adults have tried cocaine. This means that if you picked 3 adults at random from the U.S. population, the chance of all three having tried cocaine is about 1 in 2300. Three presidents is a small sample size, but those odds are long enough that's it's fair to acknowledge the positive correlation between cocaine use and presidency.
The odds of electing 10 male presidents in a row, if presidents were picked at random from the population, is about 1 in 1000. Of course, we all know that there is a causal connection between gender and political success, so that doesn't surprise us. But the cocaine use is surprising. We certainly have enough evidence to think there is a connection between cocaine use and being elected as leader of the "free world". I have a couple ideas:

1) Politics is tough work, and participants feel they need strong stimulants to survive the physical and emotional toll.

2) Presidential races attract "alpha" personalities. People who are cocky and overconfident -- enough to think that they can use cocaine without getting addicted. Cocaine also has a "brand identity" that matches people with these kinds of personalities.

I prefer theory #2. However, I'm not sure how to test it.

Belichick Made The Right Call

Photo by Keith Allison

Last night, near the end of an important game against the Indianapolis Colts in Week 10, the New England Patriots faced 4th-and-2 on their own 28-yard-line. The Patriots were ahead by 6 points, with 2 minutes and 8 seconds left on the clock. Conventional wisdom said the Patriots should punt the ball, to force Manning to try to drive the length of the field for a game-winning score. Instead, the Patriots went for it and failed to convert. The Colts went on to win.

Commentators are already arguing about whether Coach Belichick showed too little faith in his defense, or too much faith in his offense. It has nothing do with faith. It's all about giving your team the best chance of winning. And the numbers say that Belichick made the right call.

To assess whether Belichick chose wisely, I used Football Mogul to simulate the situation that the Patriots faced. Football Mogul had access to every detail of the game, including current rosters and playbooks for each team. It even takes into account the weather and wind, and the fatigue level of the New England defense.

Specifically, I simulated the remainder of the game exactly 20,000 times. For 10,000 of these simulations, the Patriots went for it on 4th-on-2. For the other 10,000 simulations, the Patriots punted.

We could look at this simply in terms of what chance the Colts had to drive down the field and score, depending on whether or not the Patriots punted. However, that doesn't take into account all of the things that can happen during a football game. For example, in some of the simulations when the Patriots went for it, the Colts got an interception return for a touchdown. This gave Indy the lead, but also gave Brady two minutes to drive down the field for a game-winning field goal. Similarly, the "safe" choice to punt sometimes resulted in a blocked punt and an instant touchdown for the Colts.

Thus, the only way to accurately find the best call is to simulate the exact game situation thousands of times, taking into account all of the different possible results that can happen in an NFL game.

The verdict: Belichick made the right call.

Breaking down the numbers, we see that when the Patriots went for it, they got the first down in 55.2% of all the simulations. After the first down, they won the game 94.3% of the time (the Colts' one timeout gives them the chance to get the ball back and still score a last-second touchdown, which they were able to do about 1 time in 20, even when the Patriots got the first down).

When the Patriots went for it and didn't convert, the Colts won the game 76.1% of the time. Most of these were because Peyton drove the ball 28 yards for the score. But sometimes the Colts won for another reason. For example, the Colts might score a quick touchdown, leaving Brady enough time to get a winning field goal, but still have enough time to score on the following kickoff return (leading to the Colts winning 42-37).

All-in-all, Belichick's call to go for it gave the Patriots a 62.8% chance of winning the game.

On the flip side, punting the ball only gave the Patriots a 41.3% chance of winning the game. That's right; the Colts won the game 58.7% of the time when the Patriots punted.

So, not only did Belichick make the right call. It wasn't even close. He made the call that increased his team's chance of winning by more than 50% (from 41.3% to 62.8%).

The End Of The 50-Yard Field Goal

Stephen Gostkowski, the kicker for the New England Patriots, has one of the strongest legs in the NFL. Most of his kickoffs go into the opponent's end zone -- many of them for touchbacks.

But he doesn't have any 50-yard field goals this year. That's because Coach Belichick hasn't asked him to try any. Gostkowski has a 93% success rate on kicks less than 50 yards. But no attempts beyond that distance.

This stat is part of a larger trend in the NFL.

In 1994, the NFL changed the rules for missed field goals, so that the team taking possession got the ball at the point of the kick -- not at the previous line of scrimmage. This is only a 7-yard difference. But it's enough to shift the odds away from the decision to try long field goals.

This rule helped create a "no man's land" near the opponent's 35-yard line. On 4th down, it doesn't make sense to punt from within 40 yards of the end zone -- there's a good chance you'll kick too far and end up with a touchback, and a net gain of only 15-20 yards.

But a field goal attempt doesn't make much sense either. Let's assume the average kicker has a 50% success rate on 52-yard field goal attempt (this is a kick from the opponent's 35-yard line). Half the time, you get 3 points. The other half of the time, the other team gets the ball with good field position -- at their own 42-yard line. Getting the ball at your 42-yard line is worth, on average, about 1.8 points.

So, half the time you get 3 points; but the rest of the time you lose 1.8 points. This means that a field goal attempt from the opponent's 35-yard line is worth less than a point (0.6 to be more exact).

By contrast, having the ball at your opponent's 30-yard line is worth about 4 points. So even if you have less than a 50% chance of getting the 1st down, it frequently makes sense to go for it instead of trying to kick the field goal.

Although kickers continue to get stronger and more accurate, we'll see fewer and fewer long field goals as more coaches continue to realize that 50-yard field goal attempts are bad bets.