## Sunday, January 12, 2014

### New Feature: NBA Win Probability Added Totals by Player

 DeAndre Jordan attempts a free throw
The purpose of this post is to announce that Win Probability totals at the player level are now available for the 2013-2014 season. But before getting to that, I wanted to add some historical context to a recent improbable comeback by the Cleveland Cavaliers.

### A Magical Collapse

A few weeks back, I began publishing win probability graphs and box scores for the 2013-2014 NBA season, based on my win probability model. Not even a week into publishing these, the Cavaliers did their best to break the model. Down by 9 points against the Magic with 1:03 to go in the fourth, my model pronounced the Cavaliers dead, their win probability flatlining at 0.0%. Somewhat embarrassingly for me, the Cavaliers defied those odds, and were able to force overtime, ultimately winning the game by a score of 87-81. See Yahoo Sports' Dan Devine's blog post for a more thorough breakdown of the Magic's collapse (with an assist from the inpredictable win probability model).

My model is based on historical results, so victories by teams that were trailing by 9 points with a minute to go should be exceedingly rare. Officially, the model had the Cavs chances at about 0.02%, or 1 in 5000. The dataset I used to calculate the probabilities includes 8 seasons of NBA games (2004-2011). From that dataset:

• 1:00 to 1:09 to go: There were 207 games in which a team started a possession down 9 with between 1:00 and 1:10 left on the clock. That team lost all 207 times.
• 1:10 to 1:19 to go: There were 175 games in which a team started a possession down 9 with between 1:10 and 1:19 left on the clock. That team lost all 175 times.
• 1:20 to 1:29 to go: There were 164 games in which a team started a possession down 9 with between 1:20 and 1:29 left on the clock. That team won once out of those 164 times (0.6%).
• 1:30 to 1:39 to go: There were 210 games in which a team started a possession down 9 with between 1:30 and 1:39 left on the clock. That team won once out of those 210 games (0.5%)

So, 0.02% may be underselling the Cavaliers chances somewhat, but it seems like a reasonable extrapolation from the raw data. Given the number of NBA games that are played each day, and the number of plays within each game that I am evaluating probabilities, these types of "anomalies" are to be expected from time to time, which I'm sure is very comforting to fans of the Magic.

### Getting to the Point

With that out of the way, here is the actual purpose of this post: a new feature which summarizes player Win Probability contributions (or withdrawals in some cases) summed over the entire season (available for just the current season now, with plans to add prior seasons at a later date). Here is the link: NBA Player Win Probability

Win Probability Added, or WPA, is based on a concept I first picked up from Advanced NFL Stats; it measures how each player's contributions added or subtracted to their team's chances of winning. WPA deliberately allocates more credit to a player for clutch shots, and penalizes them more for failing to come through when the game is on the line (e.g. missing a shot late in the game with your team trailing by 1 point). My win probability graphs already display the best and worst WPA players for each individual game (Most Valuable Player and Least Valuable Player). We can now take measure of the MVP's and LVP's of the season.

### WPA Isn't Everything (and it's not even the only thing)

I laid out the definition of my official WPA metric in this post: NBA Win Probability Added (see here as well). Win Probability Added, as I've defined it, sums the win probability contributions of each player's missed shots, made shots, turnovers, and free throws. It does not include WPA added via other traditional box score stats such as rebounds, assists, blocks, and steals. That's not to say I don't think those stats are important. Rather, I was aiming for stats where it is easy to assign both credit and blame for what a player does with his team's possessions. It's easy enough to credit a player for grabbing a rebound, but how do you debit a player for not grabbing one? How do you hear the dog that doesn't bark?

So, the new player page summarizes these additional player WPA contributions as a supplement to, but not a component of, official WPA. I suppose there are ways one could try to blend these numbers into a single master stat, but I don't think it's worth it. There's something to be said for tracking a multitude of simply defined stats rather than a single, murky concoction of all of them. The stats may contradict themselves. They are large, they contain multitudes.

Case in point: this season's "Least" Valuable Player (through January 11) is Minnesota's Ricky Rubio, with a WPA of -1.71 (see here, all columns are sortable, just click). But that -1.71 explicitly ignores Rubio's +7.30 in Assist WPA (6th in the league) and his +1.92 in Steal WPA (3rd in the league). Rubio clearly excels at feeding his teammates and creating additional possessions for them on defense, but when it comes to shooting the ball and not turning the ball over, he is clearly not helping the Timberwolves win games.

### Other Leaders (in which DeAndre Jordan is featured prominently)

The WPA leader (through January 11) is journeyman role player Lebron James with a total of 5.19 win probability added, and that doesn't even count his 2.36 in rebound WPA, 7.21 assist WPA (#8 in the league), and 1.24 steal WPA (#20 in the league). The next two spots are occupied by Rip City teammates Damian Lillard and Wesley Matthews, both of whom have hit their share of clutch shots this season.

And here are the leaders in the other WPA stats:
These supplemental stat rankings probably do not differ much from standard measures like counting assists, rebounds, etc. (aka the easy way). They're just given common units (wins) and weighted by game context.