In this post I will lay out an approach for measuring clutch play in the NBA, using my win probability model as the underlying framework.

Clutch play, much like the hot hand or momentum, is something that many casual fans and color commentators assume is real, but the typical "stat geek" (for lack of a better term) may regard with skepticism or outright derision. Peter Keating addressed the topic of clutch play in a recent article for ESPN Insider. The piece was also included in ESPN The Magazine's March "Analytics Issue", which I still can't believe is an actual thing. Keating attempts to bridge the gap between the traditionalist view of clutch play and the stathead view, with sound advice for both sides.

Go right ahead and appreciate game-changing plays. But define your terms so that clutch doesn't mean one thing on Monday and another on Thursday just so you can defend your favorite player. Likewise, measure clutch performance with smart tools like Win Probability Added, but don't expect to predict it.
For the stat geeks among us:
Respect clutch achievement, even if it's not predictable. Don't be killjoys.
With that in mind, I come here not to bury clutch play, but to measure it.

### Using the Win Probability Model to Measure "Clutch"

NBA.com has a "Player Clutch" section in which they define clutch as the last five minutes of a game in which the point differential is 5 or less. While this is a straightforward and reasonable definition of clutch situations, it can clearly be improved. A three point basket with your team down by two and five seconds to play is far more clutch than a two pointer with 3:50 on the clock and up by three.

As Keating mentions in his article, clutch play is best measured with tools like Win Probability Added. I already summarize player win probability added for each game as well as season totals by player. It's tempting to define clutch as Win Probability Added and call it a day. But WPA, while giving more credit to a player for big plays, is, at best, an imperfect measure of clutch. Lebron James and Kevin Durant dominate the total WPA numbers this season because they are good at basketball pretty much all the time. It is possible they may also step up in clutch situations, but WPA by itself doesn't necessarily tell you that. There's some chaff that we need to strip out before we get to the wheat.

What we need to strip away are the win probability contributions one would expect under average (or normal) basketball conditions. Let's take one of the most famous clutch shots in recent memory: Ray Allen's game tying three pointer from game 6 of the 2013 Finals. That shot was worth +35% in win probability added. On average, three point shots are worth +4.6% in WPA. So, one way to breakdown Ray Allen's WPA for that shot is that about 5% is "normal basketball" WPA and 30% is "clutch WPA".

Clutch can also go the other way, with a player failing to step up in big situations. About 30 seconds prior to Ray Allen's shot, Lebron James turned the ball over with 0:39 on the clock and the Heat down by 2. That turnover, coming late in the game with a chance to tie or take the lead, cost -15% in WPA. On average, a turnover is worth -2% in WPA. So, Lebron's "clutch WPA" in that case would be a negative 13% (=15%-2%).

We can calculate the expected WPA (eWPA) contributions for every type of play that contributes to Win Probability Added. I have summarized those results in the table below (these numbers come from the 2012-2013 NBA season).

play typeeWPA
turnover-2.0%
missed field goal-1.5%
missed free throw-1.6%
getting 1 foul shot+1.6%
getting 2 foul shots+1.5%
getting 3 foul shots+3.3%
make 2 point shot+2.2%
make 3 point shot+4.6%
defensive rebound+0.8%
offensive rebound+1.5%

While this table is a means to an end, I find it interesting in its own right. It converts the various box score stats into a common currency we can all understand: wins. One note on the eWPA for getting one foul shot: It probably looks odd that 1 foul shot is worth more than 2 foul shots. The reason for this is that 1 foul shot is invariably an "and one" situation. Embedded within the "2 foul shots" eWPA is a likely burning of a team's possession (this is also embedded in the made field goal eWPAs). In contrast, the "1 foul shot" eWPA is, in the parlance of professional statisticians, "just gravy". Also note that while rebounds aren't a part of my official WPA stat, I'm including their eWPA values here for completeness.

Armed with these values, we can then breakdown a player's WPA into two components: "expected WPA" (eWPA) and "clutch WPA" (clWPA). Or, in equation form: WPA = eWPA + clWPA.

While this is a big step forward, we're not quite done. As currently defined, this approach will credit a player for clutch WPA in situations where most would agree don't really belong in a definition of clutch play. For example...

### The Clutch / Garbage Time Decomposition

My examples above (Ray Allen's three pointer and Lebron's turnover) are both clear cases of positive clutch play (Ray) and negative clutch play (Lebron). But let's take another example from a game with far less drama: Game 2 of the NBA Finals in which the Spurs were blown out by the Heat by a score of 103-84.  With 6:24 left in the fourth quarter and his team up 94-69, Dwyane Wade missed a 14 foot jump shot. The WPA for this miss was literally 0%. The Heat's win probability was already 100%, and a miss at that point in the game was not going to move the needle. But how would my clutch definition above score this play?

From the table above, the eWPA is -1.5% for a missed field goal, and we already know the total WPA was 0%. To make the equation balance, I need to assign Wade plus 1.5% in clutch WPA for missing a shot. Granted, if you're going to miss a shot, that would have been the time to do it, but that's not really an example of clutch play. Similarly, if Wayne had made that shot, he would have been penalized 1.5% in clutch WPA, simply because he made a shot at a point in the game when it had no impact on his team's chances.

These types of situations, where both good and bad plays have little to no impact are what is commonly referred to as "garbage time". And I can use my win probability framework to come up with a simple and intuitive definition of garbage time plays. I put together the table below to illustrate when I count a play as "clutch" and when I count it as "garbage time". Feel free to sing along in your head:

playtimeWPA is:play type
Right PlayRight Time> eWPA and > 0Clutch(+)
Right PlayWrong Time< eWPA and > 0Garbage(+)
Wrong PlayRight Time> eWPA and < 0Garbage(-)
Wrong PlayWrong Time< eWPA and < 0Clutch(-)

Or, to put it simply, clutch plays are when a play (either positive or negative) has a greater than average impact on win probability, and garbage time is when a play has a lower than average impact.

So, here is the final result, where I can now breakdown a player's WPA contributions into three numbers:
• expected WPA (eWPA): the win probability added one would expect from just looking at a player's box score stats
• clutch WPA (clWPA): excess WPA (either plus or minus) due to WPA contributions during crucial game situations
• garbage time WPA (gbWPA): WPA a player would have been credited with had their contributions come at more meaningful points in the game
And here is the equation:

WPA = eWPA + clWPA - gbWPA

The sign convention for garbage time WPA (gbWPA) is going to be confusing no mater what, but I have chosen to define garbage time WPA such that a player that amasses a lot of "good" stats during garbage time will have a positive gbWPA. A player with high gbWPA might be referred to, fairly or not, as a "stat padder".

### Season Leaders in Clutch WPA

In the near future, I plan on adding these new clutch stats to my NBA box scores and player total pages, but until I do, here are the totals for this season. The table below shows the top ten players by total "clutch WPA".

Top 10 Clutch Players 2013-2014 Season
Rank Player WPA eWPA clWPA gbWPA
1 James Harden 7.20 3 4.53 8 3.09 0.42 77
2 LeBron James 8.43 2 6.92 2 2.80 1.30 3
3 Anthony Davis 5.75 7 4.25 12 2.38 0.89 19
4 Damian Lillard 5.41 10 4.40 9 2.22 1.20 4
5 Blake Griffin 6.33 4 4.81 7 1.95 0.43 73
6 Stephen Curry 5.00 11 4.29 10 1.87 1.16 6
7 Chris Bosh 5.74 8 4.26 11 1.81 0.33 109
8 Wesley Matthews 5.98 6 5.15 6 1.72 0.88 20
9 Kevin Durant 9.30 1 9.02 1 1.66 1.38 1
10 Thaddeus Young 3.36 23 2.22 55 1.65 0.51 55

Thanks to plays like this, James Harden sits atop the clutch WPA rankings this season. Everything here is in the same units of win probability. Lebron's 2.80 in clutch WPA means that his actual WPA exceeds what one would expect his WPA to be based on his box score stats by 2.86 wins. This table also explains why James and Durant have been running neck and neck for the season WPA lead, but Durant has been the clear consensus MVP for some time. Durant holds a commanding lead in eWPA (expected WPA), which is basically a box score based, context-independent version of WPA. James makes up a lot of that gap by accumulating more clutch WPA.

So what about the chokers? Here is the bottom 10 in clutch WPA for the season:

Bottom 10 Clutch Players 2013-2014 Season
rank Player WPA eWPA clWPA gbWPA
1 Brandon Jennings -1.55 479 0.27 251 -1.22 0.60 35
2 Ricky Rubio -2.30 480 -1.31 480 -1.08 -0.09 399
3 Pau Gasol -0.07 376 1.44 107 -1.01 0.50 57
4 Carlos Boozer -1.16 473 -0.37 448 -0.99 -0.21 452
5 Raymond Felton -1.44 476 -0.65 472 -0.82 -0.03 346
6 Brandon Knight 0.54 197 1.44 106 -0.78 0.12 202
7 Kirk Hinrich -0.93 472 -0.32 440 -0.68 -0.07 384
8 Victor Oladipo -1.31 475 -0.34 445 -0.60 0.37 93
9 Rajon Rondo -0.88 471 -0.34 444 -0.58 -0.03 350
10 Jameer Nelson -0.16 407 0.85 165 -0.57 0.44 72

Season "leader" Brandon Jennings had a pretty brutal night on December 12 against the Pelicans, with about -0.50 of his negative -1.17 clutch WPA coming in that game (a combination of particularly poorly timed missed shots and turnovers late in the 4th and in overtime). I have acknowledged in a previous post that my WPA metric may be particularly harsh on point guards, due to its penalty for turnovers. So, I can also rank players just by just their clutch WPA due to field goals. For better or worse, clutch play is often synonymous with made or missed shots. Here is the table:

Bottom 10 Field Goal Clutch Players 2013-2014 Season
rank Player fgWPA efgWPA clfgWPA gbfgWPA
1 Kirk Hinrich 0.11 349 0.85 233 -0.58 0.16 262
2 Ersan Ilyasova -0.06 450 0.55 266 -0.48 0.13 284
3 Brandon Jennings 0.53 261 1.69 140 -0.46 0.71 40
4 Carlos Boozer 0.44 274 0.99 214 -0.34 0.22 229
5 Pau Gasol 1.32 172 2.25 98 -0.32 0.60 62
6 Carmelo Anthony 4.23 17 5.41 4 -0.29 0.88 18
7 Ricky Rubio -0.08 459 0.31 317 -0.28 0.11 304
8 Gerald Henderson 0.84 223 0.94 223 -0.27 -0.17 478
9 Brandon Bass 1.03 204 1.35 173 -0.27 0.05 358
10 Wilson Chandler 2.05 118 2.93 49 -0.24 0.65 49

In this wild triple overtime game between the Bulls and Pelicans, Kirk Hinrich missed a three point shot with 18 seconds left in the second overtime and his team trailing by 2. That missed shot accounts for -0.14 of his -0.58 league worst clutch field goal WPA. Note that I am not trying to tag Hinrich, or anybody else on this list, as a "choker" at this point. I have no idea whether clutch performance persists or is predictable, this is a "just the facts" post. I'll save the interpretations, predictions, and accusations for future posts.

### Clutch Performance at the Line

A player tagged with the "clutch" label is often presumed to be in possession of a certain mental fortitude. An ability to maintain a cool head in high pressure situations (think Joe Montana pointing out John Candy in the stands to his teammates, just prior to driving them to victory in Superbowl XXIII). A test of mental toughness particular to basketball is being put on the line late in the game with the outcome in doubt. You have some time to think, to stew in your own juices so to speak. And if you're on the road, you may have to deal with, um, distractions from the home crowd.

The framework I have established here can also be easily applied to just free throw shooting. The table below shows the top clutch free throw shooters this season:

Top 10 Clutch Free Throw Shooters 2013-2014 Season
rank Player WPA eWPA clWPA gbWPA
1 Isaiah Thomas 0.96 4 0.68 6 0.50 0.22 2
2 Stephen Curry 0.92 6 0.57 11 0.46 0.11 20
3 Carmelo Anthony 0.98 2 0.66 8 0.43 0.11 19
4 Kyrie Irving 0.97 3 0.59 9 0.43 0.05 58
5 Paul George 0.91 7 0.71 5 0.40 0.20 4
6 LaMarcus Aldridge 0.69 10 0.38 17 0.38 0.07 40
7 Nicolas Batum 0.57 15 0.23 47 0.35 0.01 190
8 Nick Young 0.52 16 0.31 29 0.33 0.11 17
9 Kevin Durant 1.40 1 1.33 1 0.33 0.26 1
10 Dirk Nowitzki 0.88 8 0.74 4 0.32 0.18 8

Isaiah Thomas tops the list with a solid half win's worth of clutch free throw shooting. And Carmelo Anthony redeems his shooting performance somewhat with a #4 ranking here. What about the bottom of the list? Here are the worst clutch free throw shooters this season:

Bottom 10 Clutch Free Throw Shooters 2013-2014 Season
rank Player WPA eWPA clWPA gbWPA
1 Dwight Howard -2.42 480 -2.48 480 -0.58 -0.64 480
2 Kevin Love 0.02 183 0.59 10 -0.41 0.16 9
3 Andre Drummond -1.51 478 -1.68 478 -0.34 -0.51 479
4 DeAndre Jordan -1.55 479 -1.70 479 -0.28 -0.43 478
5 Joakim Noah -0.37 465 -0.17 423 -0.18 0.02 133
6 Nene Hilario -0.80 476 -0.75 475 -0.17 -0.12 453
7 J.J. Hickson -1.09 477 -1.16 477 -0.16 -0.22 473
8 Amir Johnson -0.25 449 -0.14 403 -0.15 -0.04 391
9 Greg Monroe -0.63 474 -0.60 473 -0.15 -0.12 454
10 Brandon Jennings -0.16 424 0.04 141 -0.15 0.06 52

Dwight Howard's appearance at the top shouldn't be a surprise. He is a poor free throw shooter, but he is still kept in the game during crucial situations, presumably because his other skills outweigh his liabilities at the line. If you're not a Timberwolves fan, you may wonder how Kevin Love, an above average free throw shooter, made it on this list. In Minnesota, they know exactly why: with 2.2 seconds left to go in a January 4 contest against the Thunder, Love was fouled on a three point shot with his team down by two. Love missed all three shots, which is pretty much the definition of choking at the free throw line.

### Next Steps

I think there's plenty more that can be done within this framework. Look for these new stats to show up soon in the win probability graphs and player total pages. I'm also considering alternate definitions of clutch and garbage time, with perhaps a focus on just the more extreme situations on both sides (e.g. only count a play as clutch if it is in the top 25% percentile in WPA for that type of play, as opposed to just being above average).

The stats I've reported in this post have all been "volume" stats, just summing the clutch and garbage components of WPA. Another approach would be to look at success rates, or maybe eWPA per play, when split between clutch and garbage time. Which players have better production in clutch, or vice versa? And is that pattern random or persistent?

Thanks for making it this far, and, as always, feedback or suggestions are always welcome in the comments section.