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.
Unfortunately, there aren't nearly as many examples of 2nd and 3rd downs plays for each to-go distance as there are 1st down and 10s. For example, since 2000, between an offense's own 30 and 40 yard lines, there were 4,459 runs on 1st and 10 but only 166 runs on 2nd and 9. For this reason, to get a statistically reliable estimate of the values of 2nd and 3rd down plays, I had to make a couple compromises. I did not break out plays in terms of field position like I did for first downs. Instead, I grouped plays as either inside the red zone, between the 20s, or inside a team's own 20. In this post, I'll focus on plays between the 20s. I also grouped to-go distances as very long, 10 yards to go, long, mid, short, and 1 yard to go.
The tables below list each distance to go for 2nd and 3rd downs. For each combination of down and distance the table lists the proportion of pass plays, the EPA for runs, the EPA for passes, and the difference between the EPA for passing and running. Positive numbers for the EPA difference indicate an advantage for passing, and negative numbers indicate an advantage for running.
|2nd down &...||Pass %||Pass EPA||Run EPA||EPA Diff|
|13, 12, 11||72%||0.06||0.00||0.06|
|9, 8, 7||63%||0.11||0.01||0.10|
|6, 5, 4||45%||0.00||-0.10||0.11|
For second downs between the 20s, passes have been more lucrative. Except for 2nd and 1 plays, which indicate an advantage for neither play type, an offense can currently expect about 0.1 more points for a pass than for a run.
One interesting thing to note from the 2nd down table is the relatively low proportion of passes on 2nd and 10. Notice that for 2nd and 'very long' teams pass 72% of the time, and for 2nd and 'long' teams pass 63% of the time. But for 2nd and 10, teams pass only 48% of the time. Note also that 2nd and 10 indicates the biggest advantage for passing at 0.16 EPA.
This is a curious result, and it's is almost certainly due to the inability of some coaches to randomize. When attempting to be unpredictable , most people (including football coaches apparently) tend to alternate rather than be truly random. Random sequences are far less alternating than most people think. Because 2nd and 10s usually result from incomplete pass attempts on 1st and 10, offenses tend to run more often than the situation calls for. It appears defenses may be be aware of this and are scheming against the run on 2nd and 10.
The next table outlines the differences in payoffs for passing and running on 3rd downs.
|3rd down &...||Pass %||Pass EPA||Run EPA||EPA Diff|
|13, 12, 11||92%||0.01||0.32||-0.31|
|9, 8, 7||92%||-0.02||0.19||-0.22|
|6, 5, 4||88%||-0.02||0.19||-0.22|
For 3rd downs we see the opposite result. Runs are more lucrative in nearly all cases by about 0.2 points per play. This is big, really big. Think of it this way: An offense can expect to improve its net point advantage over an opponent by 0.2 points simply by choosing a certain type of play...a single play. This essentially measures the value of a play before we learn the actual result, and only measures the play choice itself. According to these numbers offenses should run more often on 3rd down. This is roughly consistent with my initial look at 3rd down playcalling over a year ago.
Note again the results for 10 yards to go. Although there is no discrepancy in the proportion of passes vs. runs, the advantage for running disappears, and there is a slight advantage for passing. This could be due to the 'alternation' effect that I mentioned for 2nd and 10, or it could be due to some other cause.
The other thing that stands out to me is the very large EPA for runs on 3rd and very long. The bulk of the advantage from running in this situation comes in the 20 to 40-yard line region of opponent territory. I think this result suggests most teams are better off playing it safe, running for better field goal range rather than passing and risking a sack, which might knock an offense out of FG range, or an interception, which would be even more costly.
Even better, coaches should almost always think of this region of the field as 4-down territory. On 3rd and very long an offense could run for an easy 6 or more yards, then set up for a manageable 4th down conversion attempt. Once defenses respond by playing tougher against the run on 3rd and very long, passes become less predictable making sacks and turnovers less likely.
Just like on first down, runs are more lucrative inside the red zone for 2nd and 3rd downs for nearly every to-go distance. I intend to post full results for the red zone in a future article, but for today I'll just say that the numbers suggest offenses should run on 2nd and 3rd down more often inside the 20-yard line, and inside the 10-yard line in particular.