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February 2, 2012
Growing Importance
The Value of Threes

by Kevin Pelton

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Let's talk about three-pointers. I've been thinking about the topic lately because two of this season's biggest disappointments can be traced, in large part, to the three-point line. I wrote all about the Los Angeles Lakers' shooting woes a couple of weeks ago, then noted in this week's New York Knicks roundtable that the Knicks' poor performance from downtown explains a lot of their offensive issues.

I've also been curious about the historical aspect. I'm pleased with the change to WARP last season that provides extra credit for floor spacing based on the percentage of players' usage devoted to three attempts, but have found the adjustment less effective in the '90s. Low-percentage three-point shooters like Mookie Blaylock end up looking like superstars, while interior players might take too much of a hit. It stands to reason that three-point shooting may have grown in importance over time.

The last question on my mind is the relative importance of three-point attempts and accuracy. At the individual level, after accounting for everything that was already factored into WARP, merely attempting additional threes showed the most benefit to the team. That may not carry over at the team level, but in a column several years ago, I found great value to three attempts.

So, I ran some studies. I dumped team performance by year into a spreadsheet and looked at the correlation, for each season, between three-point percentage and three attempt percentage and Offensive Rating. Here's a chart of what that looks like:

As a reminder, correlation measures the strength of the relationship between two variables. If they move in concert, the correlation (or r) will be 1.0, or -1.0 if they move in opposite directions. A correlation of 0 means no connection between the two variables. In this case, we see that the relationship is generally positive--the more threes a team takes, and the higher percentage of them they make, the better that team's offense performs.

This wasn't always the case. For a few seasons after the three-pointer was first introduced in 1979-80, teams that shot more threes performed worse. There a few plausible explanations for this. Bad teams might have been more willing to embrace the experiment that was the triple at that point, and since so few threes were shot around the league, teams that took a lot to try to catch up from a deficit probably skew the numbers.

Since about 1985-86, the time Larry Bird had become the first superstar to truly embrace the three-point shot (he led the league in both makes and attempts that season), better shooting teams have been better offensive teams. Over time, the strength of this relationship is growing. During 2009-10, we saw the strongest correlation on record between three-point percentage and Offensive Rating--0.772. The r^2 that season was .60, which can roughly be translated as indicating that 60 percent of the variation in teams' per-possession scoring is explained by their three-point shooting. That, obviously, is a massive amount.

It makes sense why three-point shooting would become more important over time. Teams have progressively increased the number of shots taken from beyond the arc, although that number seems to have plateaued the last four seasons right around 17 percent of all plays. Additionally, the game has evolved in a way that spacing the floor for both post players and pick-and-roll plays is critically important.

As for the relationship between three attempts and three-point accuracy, the numbers generally come down squarely on the side of three-point percentage. For a few scattered seasons, three attempt percentage has been as important or even more so, but for the most part accuracy does a better job of explaining how teams perform on offense.

This becomes even clearer when we combine the two numbers into a multiple regression, which accounts for the fact that good shooting teams usually also take more threes than poor-shooting ones. Focusing on the last five seasons, we find that combining three-point percentage and three attempt percentage explains about 38.5 percent of the variation in teams' Offensive Ratings. Most of that comes from accuracy. In 2010-11, for example, the difference between the best shooting team and the worst was estimated to make a difference of about 7.5 points per 100 possessions. The difference between the team with the most attempts and the least was about 2.9 points per 100 possessions. So accuracy appears to be about three times as important as attempts.

Coming back to this season, the interesting aspect is these same conclusions no longer hold. Maybe it's because we're still barely a month in, or possibly because the compressed post-lockout schedule has depressed shooting percentages, but there has been virtually no connection between three-point attempts and offensive performance (r=0.08). The number hasn't been that low since 1982-83. The Chicago Bulls and Philadelphia 76ers are the league's two best teams despite shooting fewer threes than average, while the three most prolific teams (the New Jersey Nets, the Orlando Magic and the Knicks) have all disappointed.

As teams like the Knicks and the Lakers can testify, there is a relationship between three-point percentage and Offensive Rating (r=0.49), but it too is on the low side compared to other recent seasons. Before the year, my research into the last lockout campaign in 1998-99 suggested that teams that relied on hot shooting from the field would struggle. To some extent, that does seem to be the case. Nonetheless, it remains true that if struggling offenses want to get better in a hurry, adding shooting is the easiest and cheapest way to do so.

Kevin Pelton is an author of Basketball Prospectus. You can contact Kevin by clicking here or click here to see Kevin's other articles.

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