The charts need some explanation. They plot how many timeouts a team has left during the second half based on time and score. Each facet represents a score difference. For example the top left plot is for when the team with the ball is down by 21 points. Each facet's horizontal axis represents game minutes remaining, from 30 to 0. The vertical axis is the average number of timeouts left. So as the half expires, teams obviously have fewer timeouts remaining.
The first chart shows the defense's number of timeouts left throughout the second half based on the offense's current lead. I realize that's a little confusing, but I always think of game state from the perspective of the offense. For example, the green facet titled "-7" is for a defense that's leading by 7. You can notice that defenses ahead naturally use fewer timeouts than those that trail, as indicated by comparison to the "7" facet in blue. (Click to enlarge.)
The second chart is for offenses. In this case, each facet indicates the offense's number of timeouts left based on time and score.
One of the things that stands out to me is that there are really only a couple patterns at play. Teams that trail all seem to use their timeouts in the same pattern (in the shape of Florida apparently) no matter the score margin. And teams with leads seem to use them in the same manner.
No matter what the situation, teams burn half a timeout on average in the second half at some point prior to the endgame, when timeouts can have a big impact. These are typically to save a delay of game, due to a failed challenge, or to think over a high-leverage play.
I realize the coloring of the charts is gratuitous, but it's harder to turn off than leave it. And there isn't an immediately obvious difference between offense and defense. But there is a slight difference, especially in the endgame, which is when it really impacts the model (and the game itself).
This last chart might be of more interest. This is the average number of timeouts left for a trailing defense. There's a clear inflection point at the 5-minute mark.
I should note that the data were grouped by minute, so the apparent full timeout remaining at the 0-minute mark is a little misleading. By the final second of the game, the average gets down to about 0.7 timeouts left for a trailing defense.
One last interesting tidbit is that coaches don't seem to manage timeouts differently when trailing by less than one score as they do when trailing by more than one score. The plot is nearly identical, with the exception that coaches trailing by more than one score start using their timeouts about 30 seconds sooner than they do when trailing by one score or less.
I am always perplexed when a team calls a timeout a few seconds before the two minute warning. Unless the play following the 2mW gets a time stoppage, e.g. incomplete pass, etc. the team is often forced to use a second timeout. Is the timeout a few before the 2mW worth it ?
A timeout at 2:03 makes sense if you predict the offense will run a play that does not stop the clock. For example, if you know for certain the offense will do a 5-second running play that leaves the clock running, calling a timeout at 2:03 saves three seconds.
Scenario A: TO #1 at 2:03, Two minute warning at 1:58, TO #2 at 1:53.
Scenario B: Two minutes warning at 2:00, TO #1 at 1:55, TO #2 at 1:50.
The difference is if the offense might run a play that does not stop the clock. Or if the freedom at 2:03 to run a play even though it might stop the clock substantially increases the offense's potential yards gained (they can throw the ball because if it's incomplete, the clock would stop anyway at the two minute warning).
Although slightly off topic, I have been thinking about timeouts in a bit different light which I'll share here in the hopes it might trigger other thoughts.
Timeouts are a type of currency. They have no intrinsic value but they can be exchanged (by an offense) for either yardage, the avoidance of a five yard penalty: or they can be exchanged for the opportunity to have up to about 3 more plays, the number of plays which can reasonably be held in the 40 second maximum between plays. Finally they can be exchanged to avoid a perceived mismatch between personnel groupings or play/defense calls.
They can also be bet on a replay review, but this bet in essence is bet for yardage.
When a timeout is called to allow a team to better consider its options or reset its personnel, the TO is basically avoiding the 5 yard penalty which would be called if the time to make the decision or change were simply taken.
The yardage trade-off produces a simple and straightforward way to value TO's. The value is WP (at yard line) - WP (at yard line-5). The change in value over the time in the game would be captured by the WP change over time (given down and distance.)
The opportunity cost valuation is more subtle. What is the value of an extra play or two? How do you know the team that called a TO improved its chances as a result of the play?
It seems that the yardage valuation provides a base line and the opportunity cost might be captured by comparing the play or two following the TO vs some measure of average expected improvement in WP. The opportunity cost valuation becomes a metric for coaches.
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