Sunday, April 19, 2015

Spurs' "Hotness" Entering NBA Playoffs

The San Antonio Spurs, owner of five NBA titles including last year's, were floundering for much of the current season, at least relative to their high standards. A four-game losing streak in late February put San Antonio at 34-23. Perhaps having the oldest roster in the NBA was starting to catch up with the Spurs. From that point on, however, Coach Gregg Popovich's crew went 21-4 to finish with a regular-season record of 55-27. And it wasn't just quantity of wins, but also quality, as the Spurs' hot streak included a March 22 win at Atlanta, an April 5 home win over Golden State, and a sweep of an April 8/10 home-and-home match-up vs. Houston.

Baseball-statistics maven Bill James has a statistic he calls "temperature" to assess how hot or cold an individual or team is at the moment. According to this article, the formula adds a standard value to a team's temperature for each win in a streak, regardless of the quality of opposition and other possible features of each win (e.g., home/away, margin of victory). James's temperature for individual baseball players' hotness puts greater weight on recent than distant performance, but it's not clear his team formulas do the same.

I started thinking about a temperature statistic for basketball teams, incorporating quality of opposition (with additional factors such as those listed above possibly being added later). The core concepts are that, against a tough opponent, a win should raise a team's temperature a lot, but a loss shouldn't hurt too much. Conversely, against a weak opponent, a loss should be damaging, but a win not very rewarding.

In my system, a team starts at the neutral point of 1.00. Then, after each game, the previous value is multiplied by an update factor. The multiplier after a win is (1 + opponent's winning percentage), so that the better the opponent, the larger the rise in temperature. The multiplier after a loss is just the opponent's winning percentage, which will drop the temperature (multiplying anything by a number greater than 1.00 increases value, whereas multiplying something by a number between 0.00-1.00 decreases value). The following graphic (on which you can click to enlarge) provides some examples.

The opponent's winning percentage (right before you've played them) appears on the horizontal axis, the red and blue lines are used after a win or loss, respectively, and the multiplier after a game appears on the vertical axis. As one example, suppose your opponent enters the game with a .750 winning percentage and you beat this opponent. The previous value of your "temperature" is then multiplied by 1.750; this is a bigger increase than if you beat a .600 team (which would result in a multiplier of 1.600). Conversely, losing to a .400 teams requires you to multiply your previous temperature by .400, cutting value by more than half (e.g., a previous value of 10 would become 4). Losing to a .800 team, in contrast, doesn't hurt as much (multiplying the previous value by .800).

In order for a win and a loss to cancel each other out and return a team to the neutral point of 1.00, a more dramatic win, such as beating a .750 team, would be offset by losing to a not-quite-as-good team, in this case with a pre-game .571 win percentage, and vice-versa (1.750 x .571 = 1.00, within rounding). The following graph provides a general characterization of the relationship between win and loss multipliers in order to restore a team to 1.00 (neutrality), plus another example.

Enough formulas, let's get to some basketball! First, we see the Spurs' hotness for the final 10 games of each of the past four regular seasons (I think you'll need to click on this chart!).

San Antonio's hotness over its last 10 games of the 2014-15 season is 28.47, obtained by multiplying the automatic start value of 1.00 x 1.685 (for the win over Memphis) x 1.466 (for the win over Miami), and so forth. The season-ending loss to New Orleans (which entered the game with a .543 winning percentage) essentially halved the Spurs' hotness value (i.e., multiplying by .543) in one fell swoop.

The fact that the Spurs' hotness was right around the neutral point of 1.00 in both 2013-14, when they won the NBA championship, and in 2012-13, when only a statistically unlikely comeback by Miami in Game 6 of the finals prevented a San Antonio title, suggests hotness over the final 10 games is not important.Similar findings have been obtained for baseball.

In the lockout-shortened 2011-12 season, however, the Spurs followed up their 10-game winning streak to end the regular season (hotness = 46.75) with 10 straight wins to begin the playoffs, before being eliminated. San Antonio didn't win the title in 2011-12, but a 20-game winning streak spanning the regular season and playoffs is pretty good!

Let's look at some other teams that were hot over their final 10 regular-season games in recent years.

As shown in the top row, the Spurs' opponent in the opening round of this year's playoffs (getting underway tonight), the Los Angeles Clippers, are pretty hot at the moment, too. Both teams are 9-1 over their final 10 regular-season games, but San Antonio (28.47) is hotter than L.A. (18.47), due to the Spurs' higher-quality opposition. For what it's worth, however, the Clippers' 18.47 hotness exceeds the 2012-13 NBA champion Miami Heat's 15.14 in also going 9-1 over its final 10 regular-season games (second row).

Looking at teams with 8-2 records over their final 10 regular-season games this year, the Golden State Warriors, who had far-and-away the NBA's best record (67-15), had a hotness value of 9.76 (third row), and the Boston Celtics, who needed a feverish run just to make the playoffs, had a hotness of 9.65 (last row).

As I noted above, other factors could be added to the mix. Perhaps a team's hotness could be multiplied by bonus adjustment factors of 1.05 or 1.10 (or something else) for each road win or blowout win, or could be multiplied by a deflationary factor of .95 or .90 for a home loss. Recency of performance, which I don't think was a big issue here due to the focus just on teams' final 10 games, could also be taken into account by multiplying newer wins by greater enhancement factors than older wins. Finally, teams' records toward the end of the regular season can be misleading due to resting of players. That's another factor for which adjustments would be helpful. Please share any ideas you have for further refinements, in the Comments section.

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