Recently I explored how shot types change during the final two minutes of a game. However, that only gave snapshots based on certain timeframes that I chose. Looking at how those shot types change, second by second, is much more enlightening. That is what I will be doing today. For each shot type, I will calculate the total amount of attempts from every game this year for each second.
Let’s start with three-pointers. From the last study, we saw that three-point attempts increase dramatically relative to other shot attempts in the last two minutes. Is that a late-game surge only or do three-point attempts increase progressively throughout the game? Here’s the data:
Outliers (which occurred at the end of each quarter) were removed from the graph for the sake of clarity. As you can see, there’s a significant increase in attempts as the game goes on. We also see a very rapid increase at the end of the game. I won’t speculate as to why this happens, but it certainly is interesting.
In the last two minutes, three-point attempts increase mostly at the expense of midrange/post attempts. Is this only a late-game trend, or does it gradually occur during all 48 minutes? Let’s look at midrange attempts:
Two-point shots away from the basket appear to do the opposite of three-pointers. They start at their highest frequency and gradually decrease as the game goes on. In the final moments the decline slows, but that is because all shot attempts, regardless of shot type, increase in the final seconds.
Layups are the third shot type with a large enough sample size at each second in the game to make some sense of it:
Layups decline ever so slightly as the game progresses. At the start of the game the trendline is at around 17, and by the end it is just above 15. This difference is very small and can possibly be explained by one other change as the game progresses: fouls. How do shooting fouls change over the course of a game?
These fouls rise by about 2.5 during the 48 minutes, so it may be that layups just go down because shooting fouls (which will not show the shot type in the play-by-play) go up. We don’t know that most shooting fouls are on layup attempts, but outside shooters are rarely fouled and dunks, tips, and putbacks are infrequent enough to not be much of a factor.
What about those dunks, tips, and putbacks? I’ve put together graphs on all three shot types, but good luck making any sense of them:
In conclusion, teams don’t move away from midrange/post and towards three-point shots only in the last two minutes. This appears to be a phenomenon that occurs from the very start of the game. Also, layups go down as the game progresses, but this may just be because of an increase in shooting fouls.
Although this information is interesting at the league-wide level, it may be even more helpful on a team-by-team basis. If you knew how a certain team changes its style as the game progresses, it would be easier to game plan for them. This is something I will look into studying in the future.
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there is one problem with your graphs for three pointers, midrange, and layups. there is so much data on these graphs that one could draw just about any trendline on them.
Can you publish the R-squared numbers? Drawing a simple linear correlation is not enough. Accepting the result as causality is statistically wrong. The biggest phenomenon that occurs in this article is how easily misinterpreted numbers can be when put into wrong hands.
“there is one problem with your graphs for three pointers, midrange, and layups. there is so much data on these graphs that one could draw just about any trendline on them.”
I personally didn’t draw the trendline (a computer did), but yes, there is obviously a ton of variability. The exact slope of the line to me isn’t important. What matters is that for at least two of the graphs (midrange shots and three-pointers) there appears to be a definite trend just by eyeballing the data.
“Can you publish the R-squared numbers? Drawing a simple linear correlation is not enough. Accepting the result as causality is statistically wrong. The biggest phenomenon that occurs in this article is how easily misinterpreted numbers can be when put into wrong hands.”
I don’t think I ever assumed causality. I just explained how there’s a correlation between time elapsed and the amount of attempts of certain shots. I’ve alluded to what could be real causes (defenses tightening up, teams being forced to make up large deficits at the end of games, etc.), but I’ve never tried to explain why exactly these trends are happening. Like I said at one point:
“As you can see, there’s a significant increase in attempts as the game goes on. We also see a very rapid increase at the end of the game. I won’t speculate as to why this happens, but it certainly is interesting.”
The R^2′s are obviously very low (we’re talking less than .1), but I’m ok with that. I wouldn’t dare try to predict how many three-pointers a team would take based on the time of the game. I’d much rather know the players, the coach, the situation of the game, etc. However, for example, there IS a significant positive linear relationship between three-point attempts and time elapsed at the .00000…01 level.
If you don’t have enough data to make sense of a plot, just lump the points into 5-second blocks or something like that (aka 0:00-0:05, 0:06-0:10, 0:11-0:15, etc.) You should be able to get a more reasonable correlation.
What I would like to see is some P-values for the regression coefficients, i.e., the statistical significance of the observed trends or correlations.
Basically, if the R^2s are less than 0.1, the coefficients of linear correlation should be around 0.3 or less. Depending on the number of observations, this may be statistically significant or merely a result of random variation.
By the way, the number of shooting fouls should increase during each quarter due to the accumulation of team fouls.
The p-values are essentially zero for three-pointers, midrange shots, and layups. See three comments above.
Shooting fouls are fouls committed during a shooting attempt, so they have nothing to do with team fouls. Fouls in the bonus do not count as shooting fouls.