By Brian Burke
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.