Just before halftime in last year's Super Bowl, on first and goal from the one, Kurt Warner threw the ball directly into the arms of James Harrison who rumbled 100 yards for a touchdown. With so little time left in the half, passing was the obvious call, but that play highlights the dangers of passing so close to the goal line.
Game theory tells us that when payoffs for strategies are unequal, the strategy with the higher payoff should be chosen more often. We've seen that between the 20 yard lines payoffs for passes are consistently higher than for runs on 1st down, but inside the 20 running becomes more lucrative. Now let's take a look at the red zone in more detail, where the stakes get higher and the field gets shorter. On 1st downs in the red zone, should offenses run or pass more often, or do they already strike the right balance?
The methodology and data are identical to that used for the previous article on 1st down run-pass balance. Every down-distance-yard line situation can be expected to lead to a certain future net point advantage. For example, a 1st and 10 at midfield is typically worth 2.0 EP. A 2nd and 5 at an opponent's 45 is worth 2.2 EP. So a 5-yard gain on 1st down at midfield would produce +0.2 Expected Points Added (EPA). This method factors in risks such as sacks, fumbles, interceptions, incompletions, penalties, safeties and everything else. This analysis is limited to 'normal' football situations, when the score is relatively close and time is not a factor.
Unfortunately, the data becomes relatively thin as the field position approaches the goal line. There are fewer and fewer plays, and the data can become noisy. Drives often stall outside the red zone, or they score from beyond 20 yards out. The data for passes are particularly thin because offenses rely heavily on runs. In the previous article I grouped field positions in 10-yard bins, but inside the red zone I want to see the numbers with better resolution, so I'll use 3-yard bins. This trade-off accepts a higher degree of noise but lets us see what's going on near the goal line.
The graph below charts the EPA for 1st downs by play type inside the 20.
As you can tell, the numbers for passes are rather noisy inside the 10. The run numbers are far more reliable in this region. Still, if we use a really fat crayon, we can see that passes become less lucrative than runs inside the 10.
I think there are two or three mechanisms at work here. First, the compression of the field makes the defense's, and particularly the secondary's, job easier. I would suspect passes are affected by the short field more than runs. Further, inside the 10, teams no longer need a full 10 yards to be successful. Runs are typically low-variance plays in which an offense is more assured of a modest gain. If an offense is relatively assured of say, a 1 to 2-yard gain on a run, then it would have little problem scoring on 1st and goal from the 4 or 5. Lastly, turnovers become slightly more costly as a team approaches the goal line. Because passes are more susceptible to a turnover, running should be more preferred.
These effects may be true, but the real question is whether play callers are properly adjusting their play selection to account for them. Here is a graph of the proportion of play types on 1st down inside the red zone.
If you get out your ruler, you might see that the proportion of runs increases relatively steeply from the 20 to the 7-9 yard bin, then it shallows from there in to the goal line. I think the EPA imbalance suggests that the proportion of runs should continue to increase at a steeper rate inside the 10. Perhaps it should reach 85% or more at the goal line, instead of 75%.
This result is consistent with other findings that teams are passing too often in short yardage situations. In terms of conversion success and in terms of EP, runs on 3rd and short tend to be more successful.
As always, the usual caveats apply. This is a baseline for the league as a whole. Play calling is never as simple as just run or pass. There are many different types of each, but it can be useful to look play types as a whole. Additionally, there is some amount of bias in the data. Teams that are good in passing would be expected to pass more often, and teams good in running would be expected to run more often.