Archive for the 'Analysis' Category

Nate Silver is primarily a baseball guy. (Or is that a politics guy?) But he weighed in on basketball last weekend -- specifically, the prospect of Carmelo Anthony joining the Knicks.

Some advanced stats underrate Anthony because they assume a quality shot can be created at will, every time down the floor. The logic is that if Anthony (an inefficient scorer) doesn't shoot, the team will just find someone else who can convert at a similar rate. And since Anthony isn't the most complete player in the world when you look beyond his scoring, it stands to reason that formulas which undervalue shot creation will see little reason to pay him top dollar.

But as Nate argues, Anthony is making his teammates better by taking the pressure to create off of them. His skills allow a team to surround him with defense-minded, low-usage players that compliment him, setting up something of a division of labor on the court. Silver lends credibility to this notion by showing that when players play alongside Carmelo, their offensive efficiencies increase.

I tend to agree with Silver's premise. This is why I constantly harp on "skill curves" and usage-efficiency tradeoffs, and why offensive statistical plus-minus contains a squared term for true shooting attempts per minute -- because there's a great deal of evidence that the marginal cost of possession usage declines as a player's offensive role increases. Unlike baseball, where "usage" is evenly spread out across all players and the only concern is an efficiency metric like OPS, the ability to create "at bats" is an important consideration.

In that way, Carmelo Anthony is just the latest in a long line of players who have been confounding statistical analysts for decades (before him, it was Allen Iverson). But as Silver, Kevin Pelton, and Henry Abbott are noting this week, one measuring stick for the evolution of basketball analysis is precisely how it deals with players like Anthony. I can't say he'd be the best fit for the Knicks specifically (New York -- 7th in offense, 23rd in defense, & featuring a player who already commands 31% of possessions -- seems a curious destination for an offense-only gunner), but in general it's useful to recognize his offensive value beyond pure efficiency metrics.

BBR reader Prashant wrote in with a good question yesterday:

"I just read John Hollinger’s article about the sustained success of the Spurs and Mavs and was wondering if there was any way to calculate the average deviation of a given team’s record over time? Basically, which teams are the most consistently good/bad/average over a set timeframe, say a decade? I would imagine the Spurs/Mavs/Clippers are atop that list, while the Celtics and Heat probably have a pretty wild deviation (from lottery team to title contender)."

Sure, the easiest way to look at this is to calculate the standard deviation of each franchise's year-to-year winning percentages over the given timeframe.

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I was reading Brian Burke's excellent Advanced NFL Stats site when I came across this post about predicting future team rushing efficiency (expected points per rushing play). Because a handful of big, somewhat unpredictable rushing plays can have such an outsized impact on overall efficiency, Burke found that past success rate -- simply the percent of plays that had positive expected point values, regardless of their magnitude -- was actually a better predictor of out-of-sample rushing efficiency than past efficiency was.

In basketball, we have two similar (though not totally analogous) metrics: Offensive Rating (average points scored per possession) and Floor% (the probability of scoring at least one point on a given possession). Offensive Rating gets all the publicity, and as well it should -- the entire goal of an offense is to maximize points per possession. However, ORtg can also be heavily impacted by 3-point shooting, so boom-and-bust offenses that over-rely on threes might be like those teams whose running backs bust off a handful of long runs but otherwise get stuffed at the line too often. Their overall efficiency might be good, but their success rate isn't, and in the end success rate is what you can count on going forward.

With that thought in mind, I'm going to replicate Burke's study, hoops-style. The NBA's rapidly-increasing obsession with 3-point shooting finally leveled off from 2008-10, so my sample will include every game from those seasons. For those games, I calculated each team's offensive/defensive rating and floor%; I then broke their seasons up into even- and odd-numbered halves based on the order of games in the year, as well as 1st & 2nd halves of the schedule. Finally, I ran the correlation between ORtg/DRtg or offensive/defensive Floor% in a given half and ORtg/DRtg in the opposite half. Here were the results:

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Among the players in their most common lineup, which teams divvy up possession usage most efficiently?

To answer that question, let's use a method I introduced here. Just like that old post, this one is going to lean heavily on the concept of "skill curves", which says that a player's offensive efficiency drops as he shoulders more and more of a team's possessions. I realize this isn't always the case for all players -- but as a very general rule it holds, so let's pretend for a moment that this simple model does in fact explain the fundamental usage-efficiency tradeoff in basketball. Under those rules, a player using 18% (or fewer) of team possessions while on the court would see his efficiency change by 1.65 points of offensive rating for every 1% change in usage, a player using 18-23% would see a change of 1.24 pts of ORtg for every 1% of usage change, and a player using 23% or more would see a change of 0.82 pts per 1% change in usage.

To find every team's most common lineup, I gathered data from 82games.com, and scaled the sum of those players' season-long possession usages to equal 100%. I found their predicted lineup efficiency based on actual ORtgs and usage patterns, and also found the optimal distribution of possessions that would maximize offensive efficiency according to the rules above. The teams with the smallest difference between their actual usage pattern and the optimal pattern can be considered to be efficiently allocating their possessions.

Here are the teams, sorted by the squared difference between their actual and optimal usage patterns:

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I was browsing the stats this morning when I noticed that Ron Artest is currently using 14.7% of the Lakers' possessions when he's on the court, the 19th-lowest possession-usage rate of any qualified player in the NBA. Before joining L.A., Artest was accustomed to usage rates well over the league average of 20%, which had me wondering how Artest's decline in usage compares to other players who changed roles at varying times in the their careers.

It turns out that Artest is currently on pace to be one of only 5 players in NBA history (since 1952, at least) to have one qualified season with a possession rate of at least 25% and another with a rate of 15% of less:

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These days, the NBA always schedules its Christmas Day games to be marquee matchups, with announcers copiously throwing around phrases like "playoff preview" during the broadcast. But historically, how often have holiday combatants actually gone on to meet again in the postseason? And when they did meet, how often did the Christmas winner repeat their victory?

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In honor of the Christmas Day games tomorrow, here are some great Christmas performances from the past. First, the best individual games (from 1986-2009) according to "APMVAL", the adjusted plus/minus-based game score metric I introduced here:

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You'd better read this post from August if you haven't yet.

In it, I looked at the year-to-year correlation coefficients for various offensive rate stats (TS%, AST Rate, TOV Rate, FTA/FGA, & OReb%) when a player changed his role in the offense. Essentially, I concluded that offensive rebounding and assists are relatively immune to changes in a player's possession usage, foul-drawing & turnover avoidance are less immune, and scoring efficiency is the most prone to fluctuate with a role change.

Today I wanted to expand on that post by adding another variable into the mix: changing teams. Other than the new variable, though, this study's format is basically the same as in the first post -- except I used touches per minute rather than possession % to define a player's role, and I added Dean Oliver's Offensive Rating (ORtg) into the mix.

Here's the setup: Once again, I found every player from 1974-2010 who was between 24 and 34 years old and played at least 1,000 minutes in back-to-back seasons. I then sorted those players by the absolute change in their touches/min, and took the top quartile as my sample of players who changed roles. I also isolated players who played for a different team than they had the previous season, forming four groups: players who changed team & role; players who changed role only; players who changed team only; and players who changed neither team nor role. Finally, I ran correlation coefficients on the year-to-year offensive rate stat performances for each group:

The results:

• Shooting/offensive efficiency is actually far more impacted when a player changes teams than when he changes roles. This suggests that a team's system, coaching effects, and teammate interactions play a much bigger role in determining shooting percentages than "skill curve" effects.
• Assists are more dependent on role than team -- for obvious reasons, how much you have the ball in your hands is a major factor when it comes to how often you set up your teammates.
• Turnovers, fouls drawn, and offensive rebounds are all more team-dependent than role-dependent, but the differences are nowhere near as drastic as those observed in shooting efficiency or assists.
• For players with no major contextual changes, assists and offensive rebounds are relatively stable; foul-drawing and turnover avoidance are less consistent; and scoring efficiency is the least consistent of all. This mirrors the findings of the original study.
• Finally, it bears mentioning that even at its least consistent (TS% for players who changed teams), NBA player performance is way more predictable than that of the NFL quarterbacks Jason Lisk looked at in the football study that inspired these posts.

In early November, we had a reader point out that James Posey & James Jones were having historic seasons -- namely, the two Jameses were 1-2 all-time in terms of the highest single-season percentage of shot attempts coming from beyond the 3-point arc. A month and a half later, I thought we'd check in once again on that pair, to see if they're still on a collision course with history.

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So, I was thinking now would be a good time to talk about Gilbert Arenas.

First of all, I'm an unabashed Gilbert fan; I've always found him to be one of the NBA's most interesting people, in addition to one of its most gifted players. And after everything that's happened over the past few years, I'm glad he finally has an opportunity to make a fresh start in Orlando.

That said, I'm not sure he can help the Magic very much at this stage of his career.

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