## Introduction

I am an enthusiast of unrepentant gunners, regardless of actual efficacy or basketball skill. However, only the fun, manic kind (JJ Redick, Nick Young, etc.), not the slow, sad kind (Carmelo, Wiggins, etc.) peaks my interest. With my insatiable lust for threes chucked without conscience, I often find myself repeating “shooters gotta shoot” when my current fixation starts a game 0-for-7. Now that I have a platform, I can take a look at that saying and see if it holds up. For those unfamiliar with the saying, the implication is that a shooter needs to just keep hoisting shots and eventually they will fall.

One common misconception is that if a good shooter goes 0-for-6 from three in the first half, they are likely to go 4-for-4 in the second half due to reversion to the mean. One of my favorite definitions of reversion to the mean comes courtesy of Wolfram MathWorld. Of note, that an extreme event (low probability) is likely to be followed by a less extreme (higher probability) event does that mean that someone is “due” for any specific outcome. All we mean is that assuming independence, events with higher probabilities are more likely to occur than those with low probabilities, no matter what occurred previously.

Reversion does not imply that one extreme negative event (0-for-6) is likely to be followed by an extreme positive event (4-for-4), just that a less extreme (higher probability) event is more likely. With that in mind, I wanted to look at how an NBA shooter’s start might impact his finish over the course of a game. In short, if you see that your main shooter is 0-for-4 to start the game, is he likely to continue shooting poorly or improve?

## Methodology

I decided to use JJ Redick for this little look, as he’s an established excellent career 3-point shooter and also takes a high volume, about eight attempts per game this season. He also takes about six two-point field goals a game. I settled upon taking his first four (about half of total attempts per game) 3PT attempts and first four 2PT attempts of each game, then trying to relate the field goal percentages over the four attempts to the field goal percentages of his remaining 3PT and 2PT attempts.

## Results

### 3-Point Shooting

First, here’s a look at all of JJ’s 3PT attempts, excluding heaves.

Next, let’s look at his shooting in terms of area FG% by each quarter. These are not perfectly applicable to the area of investigation, but I think are useful anyway.

Now, we can take a look at a graph that probably crosses the line of being too complex, but does contain a fair amount of useful information. The x-axis in this case is the FG% based on his first four 3PT attempts in each game this season. There is some horizontal jitter to allow for readability, but obviously a shooter could only shoot 0-for-4, 1-for-4, 2-for-4, 3-for-4, or 4-for-4. JJ did not start a game this year 4-for-4 from three.

The y-axis is the FG% of the remaining 3PT attempts over the course of the rest of the game. The color of the point refers to the overall 3PT% in that game, and the number refers to the number of total 3PT attempts. For example, if we look at the point in the top left of the chart, we can see that he went 0-for-4 to start the game and then finished the remainder of the game 1-for-1. That gives him five total attempts and a 3PT% of 20%.

Next, let’s look at a much simpler version of this plot with a linear regression line thrown in as well. The regression is the 3PT% on the first four attempts vs. the 3PT% of remaining attempts.

Welp. Looks like there is essentially no relationship, and the statistical information bears that out. While we did not account for context (lineup data, opponent, etc.), this does appear to be strong-ish evidence that how the first four 3PT attempts of a game go does not assist with predicting the remainder of JJ’s 3PT attempts.

### Two-Point Shooting

## Conclusion

Aside from accidentally figuring out that JJ shoots a much better 2PT% from the left side of the court than the right, this was a moderately convincing case (to me) that there is no predictive ability on a large scale for the first few shots of a game and the percentage of shots through the remainder of the game. However, no contextual information about gameplay or situation was included, and in particular, no distinction between jumpers and shots at the rim was made for 2PT field goals.

As always, let me know if you have ideas for further pieces or questions in the comments below.