# Does Miami have a playoff gear?

— -- It began as mere suspicion, but soon became conventional wisdom. *Miami is coasting this season. *

*LeBron definitely looks like he's coasting, especially on defense. But the Heat'll turn it up a notch in the playoffs.*

It's a time-honored sports cliché: The weary, aging champion, angling to hold on to the crown, reserves its best effort for the postseason, when it really matters.

But is there any hard evidence that the 2013-14 Heat can turn up the quality of their play at will? Do they really have a playoff gear?

Short answer: So far this postseason, the Heat have *not* shown that they have an extra gear.

The longer, more interesting answers are below.

### Impact of shorter playoff rotations?

If the Heat really can turn it up at will, we should expect to find evidence in a comparison of their in-season versus postseason play. If Miami has a playoff gear, the team's overall statistical performance should increase significantly in the postseason, especially after we account for its tougher playoff schedule.

We can measure that by looking at the Heat's net efficiency: how well they are performing against their opponents, as measured by points scored and allowed per 100 minutes.

The analysis sounds easy enough, but there's an interesting wrinkle: Teams usually tighten up their rotations during the playoffs, giving more minutes to their starters and limited court time to guys at the end of the bench. Such rotational adjustments can greatly improve a team's overall play -- i.e., its net efficiency -- even if no one on the team plays any better (on a per-minute basis) than he did during the regular season.

So, before we can begin to figure out if Miami's players have truly turned it up a notch this postseason, we first need to account for the impact of the team's tightened playoff rotations. And there's a metric that's particularly well-suited to such an analysis: real plus-minus (RPM).

As previously described in this article, RPM is a mathematical estimate of each player's plus-minus impact, adjusting for the strength of on-court teammates and opponents and other factors like home-court advantage.

To get each team's power rating, which is its overall expected strength of play in terms of scoring margin, we simply add up the RPM ratings of the players on a minutes-weighted basis.

To see how we do it, look at the first two charts:

#### 2013-14 REGULAR SEASON

As shown in the first table, the weighted-average RPM value of a Miami player this season was about +1.5 (points per 100 possessions). And since there are always five players on the court, the team's cumulative RPM effect -- that is, the net efficiency advantage when facing a league-average opponent -- was 7.5 points per 100 possessions (7.5 is simply 1.5 multiplied by 5).

But, of course, Miami has tightened up its rotations for the playoffs. So the second table shows how the regular-season numbers change when based on the minutes allocated through the first two completed rounds:

#### 2013-14 POSTSEASON*

As shown, Miami gets a nice bump in efficiency simply by tightening its rotations -- an increase of roughly 3.5 points per 100 possessions (up from +7.5 in the regular season to +11.0 in the first two rounds of the playoffs). To put that increase in perspective: Over the course of an entire 82-game season, it would be worth about nine additional wins.

### Truly turning it up a notch?

We're now prepared to address our original question: Have the Heat actually been any better than we might have expected this postseason?

Let's consider their most recently completed series -- the second-round matchup against the Nets.

Coming into the series, Miami had a projected advantage of about 6.9 points (11.73 - 4.85) per 100 possessions, not counting the home-court advantage, itself worth about 4 points per 100 possessions ( 3.75 points per game) in the playoffs. Since Miami ended up with one more home game than Brooklyn in this series, the Heat received an added overall advantage of about +0.8 points per 100 possessions.

Our analysis thus would have predicted an overall Miami advantage of 7.7 points per 100 possessions for the series.

How does the prediction compare with the actual series outcome? It's remarkably spot-on: Miami outscored Brooklyn by 8.2 points per 100 possessions, well within any reasonable margin of error.

In other words, there is little evidence that Miami "turned it up a notch" for the Brooklyn series. Furthermore, Miami actually *underperformed* its RPM-based prediction for the Charlotte series, with an expected efficiency advantage of +13.0 and an actual margin of "only" +10.1.

### What about Indiana?

In comparison with the Heat, Indiana has received a more modest RPM bump due to its shortened playoff rotations. The Pacers' RPM-based efficiency advantage for the regular season works out to +4.6, and it jumps up to only +6.7 in the playoffs (based on minutes played through the first two completed rounds).

#### 2013-14 POSTSEASON*

In fact, the RPM-based analysis suggested, coming into the Eastern Conference finals, a clear advantage for Miami (+11.0) over Indiana (+6.7). Assuming both teams eventually allocate their playing time more or less as they did during the first two rounds, the Heat had an implied edge of about 4.3 points per 100 possessions.

(The Heat's projected efficiency advantage would even be slightly higher, at +4.8, based on the lineups used through the first two games of the series, mostly due to increased playing time thus far for Miami's RPM stud, Chris Andersen.)

Should we thus consider the Heat the decisive favorites to win the series? Not necessarily. There are two important caveats to consider.

First, matchups.

Each player's RPM rating is simply a weighted average of his estimated impact across every role he assumed during the season. But it's always possible -- indeed, it's likely -- that some players will have a far greater impact in some matchups as opposed to others. Indiana's Roy Hibbert, in particular, seems to cause numerous matchup difficulties for Miami, so it may well be the case that his RPM impact versus the Heat far exceeds his season-derived average of +1.78. If so, then our above RPM-derived analysis might be overstating Miami's advantage in the series.

Second, random effects.

Even if every player for both teams were to perform exactly at the level of his expected (season-average) RPM impact, there's something else we need to keep in mind: randomness. Simply put, each team's performance tends to vary randomly from one game to the next, and such fluctuations can be surprisingly large.

How large? When we measure and plot actual NBA game outcomes against the best predicted outcomes (for example, as approximated by sophisticated modeling, or even the Vegas spread), we find the outcomes scattered all over the place. Over thousands of observed games, actual outcomes (scoring margins) form a nice bell curve (a normal distribution), with many of the values much higher or lower than expected.

So even if two teams were perfectly (evenly) matched and played 100 games on a neutral court, each one would end up winning many of the games by a large margin. In fact, because the standard deviation in NBA game outcomes "against the spread" is known to be about 11 points, we can use our knowledge of the normal distribution to calculate that each team will win by at least 11 points about 16 percent of the time. (Likewise, each will win by at least 22 points about 2.5 percent of the time.)

### What about the Heat-Pacers matchup?

If we assume the Heat truly have an overall edge of +4.3, as implied by our RPM analysis, and if we factor in the average +4.0 efficiency advantage to each team when playing at home, we can again use the normal distribution to deduce that Miami has about a 51 percent chance of winning each game in Indiana, and a roughly 78 percent chance of winning each game played in South Beach.

These outcome probabilities can then be used to derive the likelihood of each team winning the entire series. They suggest that Miami entered the series with a 76 percent probability of advancing to the Finals.

Those odds changed, of course, after Indiana's victory in Game 1 and Miami's late rally in Game 2. Now our RPM analysis implies that the Heat -- after reclaiming the home-court advantage -- are now a 6-1 favorite in the series heading into Game 3.

On the other hand, even though Miami earned a split of the first two games on the road, the Heat have still underperformed their RPM-based projection for the series. Remember, they had a slight implied efficiency edge (+0.2 points) even when playing in Indiana, and yet the Pacers have outplayed the Heat through the first two games by an average margin of 5.7 points per 100 possessions.

So much for Miami turning it up a notch.

What do we make of this as it affects the rest of the series? Should we view the Pacers' overall superior play thus far as evidence the team matches up better with Miami than the above RPM analyses would imply, or just as further confirmation that NBA single-game outcomes are highly (and randomly) variable?

Only time -- and a few more games' worth of data -- will tell.