Nylon Calculus: Is fourth-quarter scoring overvalued in the NBA?

Do NBA players that score a greater percentage of their points in the fourth quarter get paid more handsomely? How should we value fourth-quarter scoring relative to scoring overall?

Many of the most memorable NBA moments have come in the fourth quarter of close games. Players that make big shots in these situations are revered as being “clutch”, controlling their emotions to deliver under pressure. Those that fall short are “chokers” and their reputations can suffer.

But when contextualizing these labels in the broader perspective of winning basketball games, a stark delineation in player value based on one-quarter of the game can be folly. The scorekeeper doesn’t award additional points if a basket barely beats a buzzer or comes through in the final moments of a closely contested game. The shot taken at the start of the second quarter offers the same opportunistic value as the shot taken at the end of the fourth, all else equal.

And yet we as fans subconsciously assign greater weight to these end-of-game feats, even if the scoreboard doesn’t. If a Portland Trail Blazers fan is queried to share their favorite Lillard fourth-quarter buzzer-beater, they’ll likely have multiple moments to pick from in their memory bank. But if asked to recall, say, their favorite Lillard first-quarter shot, they might draw a blank.

This is due to our human capacity to assign contextual meaning to events we witness — what is categorically referred to as empirical data — when they offer some degree of novelty. In contrast, we’re rather poor at cataloging prosaic observations.

I would argue that fourth-quarter scoring is the most abundantly available form of novelty in today’s NBA (or at least a close second to highlight dunks from some of the world’s best athletes). If you watch a slate of games on any given night, you’ll likely witness some fourth-quarter shotmaking.

It’s impossible to remove this human element from sports, and I would argue we shouldn’t want to. The NBA is fun because of breath-taking moments; last-second buzzer-beaters and highlight-reel finishes. If basketball was played in an efficient and lifeless fashion there would be no drama and limited fan interest.

But there is a difference between individual play that is exciting and that which is valuable. Players that show strong defensive “help” principles or set properly-angled screens won’t be highlighted on Twitter or SportsCenter, but they do help their teams win games in hopes of securing a championship.

As such, the average fan probably doesn’t want their favorite team’s front office succumbing to this innate human desire for novelty at the expense of signing “mundane” players that might offer a better opportunity to win basketball games.

Are NBA players with reputations as clutch scorers overvalued?

So do players who provide greater novelty (or “novelty alpha”) in the form of above-average fourth-quarter scoring draw more interest from team decision-makers? And if so, do they realize greater earnings in free agency from their performance in the fourth quarter?

To answer these questions, I compiled a data set of nearly 3,000 regular-season scoring campaigns, with metrics from the 1999-00 through 2016-17 seasons. To increase the difficulty of this analysis, I had to determine how to tie a player’s performance to his pay, since his current contract is indicative only of performance up until the point he signed it.

As a proxy, I used a rule of thumb average contract length of four years (which is the current NBA average) to measure the relationship between play and pay. For example, to estimate the degree to which a player was paid for their play in 2009-10, I used his 2013-14 season salary (adjusted to 2021 United States Dollars to account for inflation).

I also removed players from the sample that averaged the equivalent of 5 points per game or less over an 82 game period — equal to 410 points per season — since these seasons could result in disproportionate fourth-quarter ratings from a smaller overall scoring figure.

We can begin by confirming if, as we would expect, there is a positive relationship between scoring overall (regardless of when it occurred during the game) and a player’s salary four seasons later.

The correlation coefficient for these two variables is roughly 0.5, meaning that almost half of the variance in a player’s salary in this sample would be attributable to his scoring performance four seasons prior.

This relationship is largely expected, and probably indicative of the financial decisions made by NBA teams, given that individual scoring is still the most coveted skill across the league. Even players that haven’t garnered large contracts relying on superior offensive ability, like Rudy Gobert, have displayed a requisite level of offensive prowess. In short, it’s highly improbable a player receives a large contract if they can’t score the ball.

Knowing that there is a positive relationship between scoring and salary, we can next analyze the relationship between fourth-quarter scoring and salary. To measure the incremental impact of baskets scored in the last quarter, I computed each player’s fourth-quarter scoring rate as a percentage of his overall scoring rate. In this case, a player with a rating of 0.25 has an exactly equal scoring distribution across all four periods.

However, what we find is that the distribution is skewed slightly to the left of the 25 percent mark, showing that the majority of players in this sample scored a slightly higher percentage of their points in the first three-quarters of games played.

Maybe then we can hypothesize that fourth-quarter scoring in the modern NBA is a scarce commodity, and thus more valuable.

But, that’s not the relationship we see for this sample.

Before drawing any conclusions from these data, I would first caution that attempting to align player performance with a contract value in the future using a rule of thumb measure is too abstract for our purposes. When forming hypotheses, it’s best to reserve certainty for data that can be measured with precise mechanisms.

Still, if we temporarily assume the sample data accurately captures the observed scoring phenomena and corresponding salary figures across the NBA, there are a couple of considerations that make these results less surprising.

First, the sample contains a subset of exceptional outliers that drove the negative relationship between salary and the percentage of points scored in the fourth. Alec Burks‘s 2012-13 campaign was the highest fourth-quarter scoring rate captured (at 56 percent!), and in turn, he received a fairly lucrative contract four years later with an annual salary of $10 million.

But the next twenty-seven players with the highest fourth-quarter scoring rates all received less than $10 million per year four seasons later. Among them, Travis Best, Jordan Farmer, Keyon Dooling, Eddie House, and Royal Ivey all made near league-minimum contracts while scoring 44 percent or more of their points in the final period.

Second, we should remember that each player has a different preplanned rest schedule throughout the course of a game. Particularly as the adoption of rest and recovery measures has become more prominent across the league over the last decade, so too has the likelihood of players resting during fourth quarters increased. Since we are only analyzing regular-season scoring metrics,  there is a higher likelihood that many of the players in our sample rested regularly during fourth quarters, which would cause their fourth-quarter scoring rates to naturally decrease.

Aggregate scoring is a fairly poor indication of a given player’s offensive value, which is why most offensive metrics are measured by the amount scored over the opportunity taken, either individual shots attempted or team possessions. The most widely adopted efficiency measure is per 100 possessions because it attempts to normalize contextual performance by accounting for changes in league rules, playing styles, and individual team playbooks (among others).

So, how well are players rewarded for efficient fourth-quarter scoring?

As expected, efficient scoring is highly indicative of a player’s future pay.

On an unrelated but interesting note, many of the greatest individual offensive seasons of the last fifteen years are on the far-right side of the above plot. Russell Westbrook, Steph Curry, and LeBron James all went on to win the MVP award in the highlighted seasons. This visualization also puts into perspective the meager contract Isaiah Thomas was playing on during his peak with the Boston Celtics.

Overall, we can conclude that NBA decision-makers have compiled a decent track record of accurately paying for performance over the last 20 seasons, mainly by not succumbing to novelty bias in the fourth quarter. Rather than overpaying players that receive notoriety from scoring in the clutch, individual offensive performances are rewarded for being efficient and exceptional, irrespective of when they occur during a game.

Although we have completely ignored half of a player’s performance in this analysis, the numbers would suggest scoring is the most highly commoditized skill in the NBA. So the next time a mid-level role player is given a larger-than-expected contract, it may be worth investigating their scoring rate just a few seasons prior.

And when we do witness the next memorable game-winning shot, we should remember that these feats alone don’t cut a player’s paycheck. Instead, the zeal driven by our fandom and our novelty-hungry brains is contextualizing player value less objectively.