http://www.nytimes.com/newsgraphics/2013/11/28/fourth-downs/post.html
How Coaches and the NYT 4th Down Bot Compare
By BRIAN BURKE and KEVIN QUEALY
Even the boldest N.F.L. coaches can turn timid on fourth down. When a team fails to pick up enough yards on third down, coaches are faced with a few options. They can decide to kick the ball (by either punting or attempting a field goal) or they can decide to go for it. Going for it is risky – if they fail, they risk ridicule by every TV analyst, armchair quarterback and cabdriver in the country. Kicking is the safe, more conventional choice.
But is it the right one?
That’s where NYT 4th Down Bot comes in. It evaluates whether an N.F.L. team should punt, attempt a field goal or go for it on fourth down, in any situation. To make its decision, NYT 4th Down Bot uses a model developed by Brian Burke, founder of
AdvancedNFLStats.com. According to the model (and thus, according to NYT 4th Down Bot), coaches are much more conservative than they should be.
NYT 4th Down Bot works on the premise that for most of the game, a coach should be trying to maximize the point spread between his team and his opponent – that is, scoring as many points as possible while suppressing his opponent’s opportunities for points. Later in the game, other factors come into play (more details on that below), but when the score is reasonably close in the first three quarters and early in the fourth, point maximization is the name of the game.
Here is a comparison of how a coach who truly maximizes points would behave on any fourth down anywhere on the field. On the right, the same chart showing how coaches have actually behaved since 2002.
WHAT NYT 4TH DOWN BOT RECOMMENDS ON 4TH DOWN
4th & 14th & 24th & 34th & 44th & 54th & 64th & 74th & 84th & 94th & 104th & 114th & 124th & 134th & 144th & 15PuntField goalGo for itGoal1020304050403020102030405040302010Goal
WHAT N.F.L. COACHES DO MOST OFTEN
4th & 14th & 24th & 34th & 44th & 54th & 64th & 74th & 84th & 94th & 104th & 114th & 124th & 134th & 144th & 15Goal1020304050403020102030405040302010GoalPuntField goalGo for it
The bot’s recommendations may seem aggressive, but they are the results of an analysis of N.F.L. games since 2000, including the success rate of fourth-down attempts and the value of having the ball at different places on the field.
The difference is stark: coaches are much more conservative than they should be if they are truly trying to score as many points as possible. Too often, coaches forfeit the ball through a punt, for instance, when they have a solid chance to make a first down. The field position they gain from the punt is often not worth the missed opportunity to keep a drive going.
Perhaps the most common mistake coaches make is punting or kicking a field goal on fourth and only a few yards. Recent football history suggests teams should often go for it on fourth and short even deep inside their own half of the field. By punting, they guarantee the other team will have the ball with good field position. By going for it, they are risking giving their opponents fabulous field position – but with the potential reward of keeping the ball.
Obviously, the best strategy varies, depending on a team's strengths and weaknesses. But the overall pattern seems clear: coaches are far too conservative.
HOW DOES NYT 4TH DOWN BOT DECIDE?
NYT 4th Down Bot uses thousands of N.F.L. plays since 2000 to calculate the average number of points each situation is worth, a measure called
expected points. (Expected points and its application to fourth downs is not new. It was
created in 1971 by former N.F.L. quarterback Virgil Carter and Robert E. Machol and has been improved and refined in various ways since, notably with the book “
The Hidden Game of Football” and David H. Romer's
signature 2002 paper. NYT 4th Down Bot's model is similar to Mr. Romer’s, but has more seasons of data behind it.)
With about 10 minutes left in the fourth quarter, NYT 4th Down Bot switches from maximizing points to maximizing
win percentage. Win percentage measures how often teams who punted, attempted a field goal or went for a first down won the game. (This measure is more useful later in the game because it is easier to measure the impact of a single play on a game’s outcome.)UM, EXPECTED POINTS?
The measure assigns a single point value to any game situation, based on how likely a team is to score from that field position. Below is a chart of expected points on an average first down, depending on where on the field the first down is.
Goal102030405040302010Goal-1.00+1.0+2.0+3.0+4.0+5.0+6.0EXPECTED POINTS ON 1ST AND 10
The chart is straightforward: the closer to the opponent’s end zone, the likelier it is a team will score. Near your own goal line, the expected points dips below zero: from that far back, your opponent is more likely to score next than you are. As you approach your opponent’s end zone, the expected points approach 7, the value of a touchdown and extra point.HOW ABOUT AN EXAMPLE?
Consider a hypothetical situation of fourth-and-10 on your opponent’s 38-yard line.
OPTION 1: FIELD GOAL ATTEMPTA field goal is worth 3 points, if it’s successful. But there is a catch: after scoring, you must kick off to your opponent, which, on average, will begin its drive on the 22-yard line. Judging from the chart above, a first-and-10 from your 22 is worth about 0.4 points. To NYT 4th Down Bot, a field goal is worth 3 points
minus the cost of kicking off: 3 - 0.4 = 2.6 points. (Similarly, a touchdown and extra point is worth 7 - 0.4 = 6.6 points.)
What if the kicker misses? It’s a long field goal, about 55 yards, and the success rate of 55-yard field goals is only about 40 percent.
If the kick is no good, the opponent takes over on its 45-yard line. From our chart above, a first-and-10 from there is worth about 1.8 points. In this case, however, it is a first down for your opponent, so the point value from your perspective is –1.8 points.
NYT 4th Down Bot uses the expected points from success, the expected points from failure and the likelihood of each outcome to compute the net value of a decision.
On average, a 55-yard field goal attempt is worth -0.02 points.
OPTION 2: GO FOR ITSay you go for it and get the first down, but just barely — advancing the ball to your opponent’s 28. From our chart above, that is worth about 3.5 points. But if you fail, say, with an incomplete pass, your opponent takes over on its 38. That’s worth about -1.3 points to you.
NYT 4th Down Bot’s best estimate of success is about 35 percent, so going for it on fourth-and-10 from your opponent’s 38 is worth 0.36 points.
OPTION 3: PUNTFinally, you could punt. Even though there are good punts, bad punts and botched punts, punting does not succeed or fail — the ball just moves down the field and the opponent takes over.
From the 38, the average net punt is about 24 yards, giving your opponent the ball at its own 14. From our chart above, that is worth +0.04 points for your opponent, or -0.04 points for you.HOW DO OUR CHOICES COMPARE?
NYT 4th Down Bot looks at all three options and gives its recommendation: Go for it!
OPTIONEXPECTED POINTS
Go for it+0.36 points
Punt–0.04 points
Field goal–0.10 points
Does that mean coaches should go for it every time they have a fourth-and-10 on their opponent’s 38? Not necessarily. If there is a strong tailwind, or the coach has a great kicker, he might adjust his estimate for making a field goal. If he has a Pro Bowl punter, the likelihood of pinning the opponent inside the 5-yard line might increase, which would boost the value of punting. But for an average fourth-and-10 from your opponent’s 38, NYT 4th Down Bot will recommend going for it every time.BUT WHAT ABOUT LATE IN THE GAME?
When might a team prefer a strategy
other than maximizing points? Certainly, as the end of the game nears, winning becomes more important than getting more points.
Here is another example: Say your team is down by 5 points with two minutes remaining. It is fourth-and-8 on the 50. Here is the table of expected points for that situation:
OPTIONEXPECTED POINTS
Punt–0.26 points
Go for it–0.30 points
Field goal–2.49 points
Punting and going for it are nearly equal options here, and if you only cared about point maximization, you might consider them as roughly equivalent. But in reality, if you do not score again, you lose. You need to go for it. NYT 4th Down Bot thinks so, too.
To calculate which decision gives a team the best shot at winning, it determines how often N.F.L. teams have won in relevant situations from several seasons’ worth of games. Obviously, some situations are rarer than others, so when the sample is too small to make a reasonable calculation, NYT 4th Down Bot broadens its search a little.
But at its core, win percentage is a measure of how often teams in a certain situation can expected to win the game if they punt, attempt a field goal or go for it.
Let’s look at the calculations for win percentage in this situation:
OPTIONEXPECTED POINTSTEAMS DOING THIS WOULD WIN...
Go for it–0.30 points17% of the time
Punt–0.26 points9% of the time
Field goal–2.49 points4% of the time
In general, things are not looking good for your team. You are probably going to lose. But going for it instead of punting nearly doubles the small chance you do have, to 17 percent from 9 percent.
Does NYT 4th Down Bot offer a rigid set of rules for how N.F.L. coaches should behave? No. It is, however, an argument that coaches could benefit from being bolder on fourth down.WHEN THE 4TH DOWN BOT CAN BE WRONG
The 4th Down Bot is, alas, not perfect. There are known situations that can confuse it. For example, the new overtime rules have not been in effect long enough for it to accumulate a large sample of past situations. At the moment, it bases all its recommendations in overtime using traditional sudden death rules.
NYT 4th Down Bot may also be in error when there is an extreme mismatch in team strength. The estimates used by the underlying model are a baseline for league-average teams.
Finally, on some occasions near the end of the first half, the value of kicking off is not as high, and the models may therefore undervalue the effect of scoring. Still, NYT 4th Down Bot can be relied on to make the best recommendations for the vast majority of situations.
The Math Behind the Robot
NYT Fourth Down Bot is based on a statistical model created from more than 10 years of data from real NFL plays.Read more
As usual, some of the tables didn't post correctly so you can use the link if interested.
