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.
I did not account for this scenario in my analysis. The reason was that timeouts on offensive final drives did not have a discernible effect on scoring success. In fact, the number of timeouts available to the offense appeared to have a slightly negative effect. I believe this is an artifact of sample error, but the fact remains that I can't estimate the value of an offensive timeout with the current data. For that reason, I said teams would always use their timeouts while on defense, which definitely does show to have measurable value. (An alternative approach would be to notionally add time to the game clock for each timeout available to the offense.)
The graph below indicates how much time will be on the clock at kickoff (vertical axis) based on the time remaining at the 1st down snap (horizontal axis). This assumes the offense will attempt to keep the clock running on 1st, 2nd and 3rd downs, and the defense will use its timeouts whenever a play does not span the two-minute warning. It also assumes the offense will consume 39 seconds between plays whenever the clock is allowed to run and that the duration of each play is 6 seconds.
Each color represents a number of timeouts remaining to the defense. The sharp vertical segments indicate the effect of the two-minute warning.
Here are two examples to help understand this chart. Suppose the defense has two timeouts and the 1st down will occur with 1:40 (100 seconds) to play. On the horizontal axis find the 100 mark and move upward until you hit the green (2 timeouts) line. Look directly leftward from that point to the vertical axis to see that there will be 37 seconds remaining. Here's the breakdown from the algorithm for this example:
1st down snap: 100
2nd down snap: 94
3rd down snap: 88
4th down snap: 43
Get ball back at: 37
Timeouts left: 0
Now suppose the defense has one timeout and the 1st down will occur with 2:10 (130 seconds) to play. On the horizontal axis find the 130 mark and move upward until you hit the red (1 timeout) line. Look directly leftward from that point to the vertical axis to see that there will be 67 seconds remaining. Here is that breakdown:
1st down snap: 130
2nd down snap: 124
Two minute warning
3rd down snap: 118
4th down snap: 73
Get ball back at: 67
Timeouts left: 0
These numbers are critical to the analysis because they will largely determine likelihood of scoring in response to either a forced FG or an allowed TD, which in turn will determine which is the better option.
The next three installments will estimate the probability of a failed FG attempt (part 3), estimate the probabilities of the team on defense responding with its own score (part 4), and present the results (part 5).