Sunday, April 27, 2014

Win Probability Added and the Four Factors

Having a terrifying mascot is not
one of the four factors
I have a new feature up on my win probability box scores. For each game, I breakdown team win probability according to the "four factors" of basketball success. The four factors are: field goal shooting, getting free throw attempts (and converting them), rebounding the ball, and turnovers. The four factors were first identified (and named) by Dean Oliver, pioneer of basketball statistical analysis.

Most everything that is important to winning and losing basketball games can be attributed to one of the four factors. Similarly, nearly every shift in win probability that takes place in a game can be assigned to field goal shooting (FG), free throws (FT), rebounds (RB), or turnovers (TO). What now emerges in the box score is a unique fingerprint for each game; an accounting of how each phase of the game contributed to the final outcome.

Because a winning team starts with 0.5 win probability and ends with 1.0, the difference between the victor's win probability added for the four factors combined should be 0.50 more than the losing team's total. It rarely works out exactly though due to plays that are not attributable to one of the four factors (e.g. end of quarter plays that don't result in a field goal attempt). But for most games, it is fairly close to a 0.5 difference.

For most games, the field goal WPA tends to be the difference maker, in line with the general consensus that field goal shooting is the most important of the four factors. Take game 4 of the Hawks-Pacers series. The Pacers held a 0.77 WPA advantage in field goal shooting, enough on its own to secure victory. The Hawks however, had a 0.44 edge in free throw shooting. Rebounding was a draw, but the Hawks lost the turnover battle by a margin of -0.28 in WPA.

And check out the FG WPA totals for game 3 of Spurs-Mavs. A game that was won and lost several times over on the floor.

An exciting first round, so far

The general consensus seems to be that this first round of NBA playoff games have been particularly good, featuring plenty of dramatic, closely contested games.

The excitement index from my win probability graphs supports this as well. The excitement index measures how far the win probability graph "travels" over the course of the game. For the 2013-14 NBA regular season, the average excitement index of a game was 5.9. So far, the average excitement index of the playoff games has been 7.1, more than a full win's worth of extra probability swings.

There have been plenty of good series, but most would agree that Portland-Houston has been the best. The table below summarizes the average excitement index of each series. As expected, Portland-Houston is on top. Also not surprising is Charlotte-Miami at the bottom.

series excitement
Trailblazers - Rockets 10.1
Grizzlies - Thunder 8.5
Wizards - Bulls 8.3
Nets - Raptors 6.8
Mavericks - Spurs 6.7
Warriors - Clippers 6.1
Hawks - Pacers 5.5
Bobcats - Heat 4.7

The top game of the playoffs so far has been Portland's 122-120 overtime victory over Houston in game 1 of the series, with an excitement index of 13.5 (it ranks eighth over regular season and playoff games combined for 2013-14).

Saturday, April 19, 2014

That stubborn final minute of regulation

As a follow up to my post on the realtime length of each minute of NBA gametime (thanks to Tom Haberstroh and Kyle Wagner for spreading the word), here is a deeper look into that final minute.

5.4 minutes on average

It's a common complaint that the last "minute" of NBA regulation is anything but. Using time stamp data from, I found that the last 60 seconds lasts about five and a half minutes on average. However, as many have pointed out, there is a lot of variance around that average. Close games, featuring lots of fouls, free throws, and timeouts should take longer than a blowout in its dying throes. The chart below summarizes average length of the final minute by how close the game was going into that minute.

Tuesday, April 15, 2014

The Pacers' path to the top seed

Because I'm waiting for the lunar eclipse here on the West Coast....

With the Heat's loss to the Wizards tonight, the Pacers have officially clinched the top seed in the Eastern Conference playoffs. In the East, the race for the number one seed has been a two horse contest for much of the regular season.

The chart below summarizes how the top seed probability has sloshed back and forth between the Heat and the Pacers. Miami opened the season as the favorite, with a 74% probability. Thanks to a very strong start, the Pacers quickly supplanted the Heat as the prospective top seed favorite. They maintained that frontrunner status from early December on through to the All Star break. And then the Pacers chances, once as high as 97%, began to crumble.

By April 7, with just a week and half of games left, the Heat had recaptured their pre-season status as the Eastern Conference favorite, with an 81% probability of achieving that top seed. But the Heat found it just as difficult to stay on top, and in the past four days saw their chances drop from 69% to 0%.

Sunday, April 13, 2014

How long is each minute of NBA gametime?

In a recent post for FiveThirtyEight, Carl Bialik took a look at the length of college basketball games, particularly the grueling slog that the last minute of game time often becomes. The NCAA currently does not track game length as an official stat, so Carl had to rely on some nice work from Regressing (a Deadspin blog) for the raw data. He also contrasted the length of NCAA basketball games to those of other major sports, noting that the NBA, in contrast to the NCAA, does maintain official stats on game length.

Having been snooping around the Stats section of recently, I noticed that not only does the NBA track game length, it also provides a timestamp for every play. So, not only can we see how long that last minute of regulation drags on, we can do the same for every minute of game time. The chart below summarizes that data for the 2013-14 NBA season.

Monday, April 7, 2014

New Stats for Box Scores and Player Pages

I've had some updates to the win probability box scores and player totals waiting in the wings for some time. With the NBA taking the night off for the NCAA Men's Final, now seemed to be a good time to push through the changes. A brief summary:

  • Clutch and Garbage Time WPA: These stats (as defined in this post) are now a standard part of both the box scores and the player totals. As of April 7, James Harden is still the league leader in Clutch WPA.
  • "Hero" and "Goat": In addition to the MVP and LVP designations, which specify the players with the highest and lowest win probability added (WPA), "Hero" and "Goat" does the same for Clutch WPA. More often than not, the MVP and Hero will be the same player, but not always. Take last Friday's double OT thriller between the Heat and the Timberwolves. Chase Budinger was the MVP, due to solid production throughout the game. But Chris Bosh receives the Hero tag (in a losing effort) because of his contributions in clutch situations (see here, here, here, and here).
  • True Shooting Percentage: In the box scores, I have replaced Effective Field Goal Percentage (eFG%) with True Shooting Percentage (TS%), as that is more closely aligned with the component of WPA I am comparing it to (it includes both field goals as well as foul shots).

More updates to come.

Sunday, April 6, 2014

Shooting Performance - Clutch vs. Garbage Time

James Harden Rockets croppedIn this recent post, I laid out an approach for measuring clutch play in the NBA, using my win probability model as the underlying framework. In that post, I broke down a players win probability added (WPA) contributions into three components: expected WPA, clutch WPA, and garbage time WPA. The clutch WPA component measures the "excess" win probability added (or subtracted) a player has amassed due to performance in clutch situations.

Under that definition, I found that the Rockets' James Harden has the most clutch WPA so far this season. However, for this post, I will take a different approach to measuring clutch play. Rather than focus on aggregate WPA contributions, I will measure shooting performance (i.e. eFG%) in both clutch and garbage time situations, and see how they vary for each player. Are there players that "elevate their game" when the stakes are higher?

Defining Clutch and Garbage Time

Previous attempts to define clutch play have been a bit on the kludge-y side (see's "last five minutes, within five points" definition). A win probability model allows for a less arbitrary determination of when a game is in a clutch or garbage time situation (although it is still not without its own drawbacks).

Wednesday, April 2, 2014

Playoff Seed Motion Chart - Updated Daily(ish)

Here is an update to the Playoff Seed probability motion chart I first published at the All Star break. I use my team rankings to simulate the remainder of the regular season and then apply the seed tiebreaker rules. The simulations are run daily and archived. The motion chart takes this archive and displays how each team's seed probabilities have evolved over the course of the season. I'll try to keep this updated on a daily basis for the remainder of the regular season, just check back here.