What is clutch time?

NBA Clutch Time: Closer than 5 points with less than 5 minutes to play.

The NBA's definition of clutch time is well defined and implemented at Stats.NBA.com. This link for example, shows that Russel Westbrook has taken the most clutch time shots this season and, in an indictment of his play, is only shooting 38% in these situations. Teammate Carmelo Anthony is shooting 30% and Paul George is shooting 40.1%, so better options are not forthcoming. One wonders however, how did the NBA arrive at this definition, and are there better options for measurement if not for clutch shooters on OKC.

While the definition presented lends itself well to common sense. I'll see if I can disprove or lend weight to the NBA's stats gurus.

Clutch

How can we quantify a "critical situation in which the outcome of [the game] is at stake?" This is our challenge.

Approach

The clutch definition can be broken down into two important parts. First, when is the game at stake? Second, when is it a critical situation?

The game is at stake when a winner is unclear. This is not particular to clutch situations however, as the winner is unclear at a games start. As a certain team pulls away however, and a winner becomes obvious, we are entirely out of clutch territory. The crucial part of the clutch definition is a "critical situation" which can be interpreted as a moment when a made or missed shot can have a drastic impact on the result.

Taken together, our two definitions can be represented using a win probability model which tells us what the win probability is at any given moment, and how the probability would change given a made shot. A game hanging in the balance is easy to interpret - let's say p(win) << 100%. A critical moment is when Δp(win) >> 0 for a made shot. We'll get more scientific about this, but let's start by taking a look at these values.

Win Probability = Probability of Home Team Winning the game

Δp(win) is a bit trickier to define as a basket can be worth different amounts of points and can be scored by either team. Let's create a metric called "potential" which is the difference in Win Probability if the away team scores compared to if the home team scores. We'll value a score at 2 points for simplicities sake. I.e. if the home team is currently up by 3 (Points Needed to Win[PNtW] = -3) we'll look at the win probability of being up by 5 vs. the win probabilty of being up by 1 to determine the "potential" of a made shot to change the outcome of the game.

Potential = Δp(win) from PNtW - 2 to PNtW + 2

The following chart uses my bayesian prediction model allows you to see win probability and potential based on time left in the game and Points Needed to Win (PNtW). Drag along the top slider to adjust time left and along the x axis to adust PNtW. The intermediat sliders you cannot interact width but will show you the movement of Winning Probability and Potential as you play with time left and PNtW.

Putting it together

Now that we've got a quantitative system for measuring just how clutch a moment is, let's arbitrarily say that "clutch time" is when a moment is in the top ten percentiles for it's potential to swing a game. Below I've got a chart where you can visualize where these moments sit and even drag your cutoff % to see how it changes the data.

Playing with the data above, you'll be able to see that the NBA's definition of clutch approximates to moments in the game in the top 5-10% percentile for potential. Taking a strict approach, their definition should extend the definition of clutch to close games outside of 5 minutes and tighten the defenition of close games to those with less than 4 points difference. However, all good metrics favor explainabity over strict adherence to the data. We've derived a fair representation of clutch time and should be quite satisfied with the NBA's statisticians

What about this analysis should be better?

The Probability Model

My probability model for who'll win a given game is certainly not the most advanced. By getting a more accurate guess at a team's win probability at any moment, we can get a better idea of how much a made basket can swing a game. Read more about my probability model at Bayesian Win Probability, but it's very simplistic.

Defining Potential

Our definition of potential determines the probability impact of a made basket in either direction (a 4 point swing). However, an alternative definition would only include a made basket in the most impactful direction. I.e. a basket moving a team from down 3 to down 1 would make more impact than from up 3 to up 5. Spending more time thinking about Expected Value of a Shot (normally around 1), 3 pointers, and other types of scoring might also effect our definition of potential.

Signing Off

Thanks for joining me on this meandering discussion of clutch time in the NBA. I hope you learned something. Feel free to reach out to me at