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Archive for January, 2011

“Get good looks” is a common phrase in basketball Coach Speak. It means: try and break down the defense to create good, open shots. Generally speaking, open shots are higher percentage. Covered shots are lower percentage. But can we measure what “higher percentage” actually means? Let’s try.

The Method

As long as zones aren’t involved, a typical defensive set begins with picking up an offensive player. That player is now being “guarded.” As long as his defender follows him within reasonable distance for the rest of the possession, he will still be guarding him. Occasionally, “reasonable distance” creates some ambiguity, but the majority of the time a defensive assignment is quite clear.

When a player takes a shot while still being guarded, whether it’s in the post or off the dribble, it’s a “guarded” attempt. So, how do players lose their defender and become “unguarded?” Typically this occurs in one of the following ways:

  • Due to defensive errors
  • In transition
  • From screens
  • Off of double teams

Rotations and help defense allow a defensive player to switch onto someone else during a possession. This happens a lot on penetration or double teams. Using this methodology, closeouts on open shots are not guarding situations (unless the defender literally blocks the shot). Which means screens, double teams and transition opportunities provide the majority of “unguarded” shots in a game.

Some examples of “guarded” attempts:

Some examples of “unguarded” attempts:

  • John Paxson’s game-winner in the 1993 NBA Finals
  • John Stockton’s shot to send Utah to the 1997 NBA Finals
  • Michael Jordan’sflu” game-winner in the 1997 NBA Finals
  • Robert Horry’s game-winner in the 2005 NBA Finals

The Results

I tracked all 164 playoff games from 2010 and 28 games from 2011 thus far. I get the following results:

The Discussion

1. Human error does exist. There are ambiguous possessions with pseudo-screens or quick-hitting action that create the potential for mistakes. Heck, despite best efforts, notational mistakes occasionally occur as well. Although that’s not necessarily too different from a standard box score, since I’ve seen FGA’s not counted, phantom assists and fouls called on bench players. Still, the data are not perfect.

2. The varying difficulty of 2-point shots. 2-point shots include wide open layups and 23-foot jumpers with Dwight Howard running at a shooter. These numbers are a starting point, not a definitive conclusion, so for the sake of simplicity these events are both “unguarded” shots. However, the 23-foot shot is clearly harder than a layup when a player is wide open. It’s becomes an even lower percentage attempt with a giant leaper running out at the shooter.

3. Perhaps because of point No. 2, 2-point% has a much higher variance than 3-point%. The difference in 3-point% and the accuracy of “unguarded” 3-point shots has been fairly consistent since I began tracking this stuff, right around an 11-13% difference. However in smaller samples, 2-point% has varied from a 10-20% difference, depending on environments, teams, and offensive players involved.

4. Dividing two-point shots by location would obviously provide a better idea of percentage difference going forward. Layups, we can safely assume, are converted at an incredibly high rate when they are open. But after that, it’s likely that there is a dropoff in percentage the farther away from the hoop we go, whether a player is guarded or not. It might be interesting to note these differences by floor location.

Nonetheless, these results at least give us a good ballpark as to what happens when players are able to lose a defender, for a myriad of reasons, and take higher percentage shots.

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Unfortunately, Basketball-Reference doesn’t have a pace-adjusted scoring metric. I normalize most of my stats to an estimated 75 possessions played, which for points produces a “scoring rate,” per se. For instance, Wilt Chamberlain averaged over 50 points per game in 1962. But he played more than 130 possessions a game using the simple method of pace estimation. That comes out to about 28.1 pts/75, not enough to make the cut here.

Up to that point in NBA history, Chamberlain’s number was the highest scoring rate. Individual players just didn’t score as much — teams were more balanced before expansion and the advent of the 3-point line. So Wilt’s season did stand out in its time. For comparison, some other notable pre-1980 players and their highest career mark:

  • Bob McAdoo 26.7 in 1975.
  • Kareem Abdul-Jabbar 25.4 in 1972.
  • Rick Barry 25.3 in 1975.
  • Tiny Archibald 25.0 in 1973.
  • Elgin Baylor, 24.7 in 1962.
  • Jerry West 23.4 in 1965.
  • Oscar Robertson 21.5 in 1968.

Listed below are the top scoring rate seasons in NBA history, measured in points scored per 75 possessions. “Rel TS%” is True Shooting% (TS%) relative to the league average. For example, if league average is 50% TS, and a player boasted a TS% of 53%, he would have a Rel TS% of 3%.

Regular Season

Yes, Michael Jordan owns seven of the eight best normalized scoring seasons ever. Not too shabby. Two other names that might surprise people are LeBron James and Karl Malone. Malone has three top-30 seasons, all at ridiculous shooting efficiency. James was a scoring machine before winning his first MVP, and holds four top-30 seasons.

What about playoff rates? Let’s only consider players who have played in at least two postseason series in a given playoff. If we do that, we get the following select club over 30 pts/75:

Playoffs (minimum 2 series played)

Again, MJ occupies more than half of the list, with LeBron’s 2009 epic playoff run topping the list. Some notable single-series performances that did not qualify: Jordan vs. Boston in 1986 (35.7 pts/75), Hakeem Olajuwon vs. Dallas in 1988 (34.9) and Dwyane Wade in 2009 (vs. Atlanta) and 2010 (vs. Boston) posted 31.2 pts/75 in both series.

The big Chicken and Egg question here: Are top-end scorers better than they were in the past, or have changes in the game simply facilitated more individual dominance?

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People have been conflating team success with individual success in sports forever –81% in this decidedly unscientific poll. And it’s most frequently seen in basketball because one player can have such a large impact on a game. But even if it were once a decent correlative measure of a player back in the 50s and 60s, in a larger league with a larger talent pool, there are problems with it:

  • There are fewer and fewer opportunities for individuals to even play on a legitimate championship contender.
  • If they do, a dynasty can completely muck up the situation because the 2nd, 3rd, 4th…nth best player basically never wins. (See: Barkley, Malone, Ewing, Chamberlain, West, Robertson and so on.)
  • Even elite teams vary in strength

At the heart of individual player analysis is how much a player impacts the game and raises the probability his team will win. Again, that’s probabalistic, not dichotomous. Good players increase the chance of winning, just like good shooters increase the chance the shot goes in. It’s not black and white. No one shoots 100%.

Figuring out who is the best is a “bottom-up” process. We examine all the factors involved and conclude a result. But using championships is top-down. It starts with an individual winning and assigns credit from that result, all the while ignoring the massive confounds of teammates, competition, coaching and injuries.

There shouldn’t be some magical rankings boost given to a player because he was traded to a team with Ray Allen and Paul Pierce. You had to be living under a rock if you couldn’t see that pairing Kevin Garnett with good players wouldn’t instantly create a championship-level team. Yet KG was labeled as a choker and loser during his best years in Minnesota, despite strong evidence to the contrary.

In our minds, which are constantly subject to cognitive biases, winning maximizes strengths and losing exposes weaknesses. And we shine a light on both.

When a player develops a reputation, we remember it and actually look to affirm it in the future. Kobe misses more late-game shots than anyone, but he’s made a boatload too by virtue of taking so many, so people remember the ones he made. And they just ignore the ones he misses. Skip Bayless still seems to be under the impression that LeBron James isn’t good at the end of the games. Probably because of one or two readily accessible memories from the past. Similarly, most people were shocked by these results.

The media sells stories. Winners and loser. Good and bad. Make a key play at the end of the game, and you’re the hero — nothing else matters. Mess up at the end of the game, you’re the goat, nothing else matters. (That’s goat, the animal not the acronym.)

In the big picture, I have no problem saying Player A might “add 15-20 wins” to his team, or even any team on average. That’s kind of the Rosetta Stone of player value estimations. But to look at the extremely small sample size of the playoffs, ignore matchups, injuries and other circumstance and use the single championship every year in player analysis is just so far removed from the relationship to how good a player is, it seems, quite literally, useless.

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Thanks to the recent statistical movement in major sports, basketball now has its share of “advanced” metrics to dazzle the eye and confuse the mind. All the new acronyms can be a little overwhelming at times: PER. WS. APM. TNT. OK, so the last one’s a TV network, but there are enough formulae that we need genius George Costanza to explain things:

Player Efficiency Rating (PER)

PER is a decent all-encompassing stat for summarizing basic box score data. But it has issues. The major failures of PER can be read about here, with the big flaw explained nicely:

Given these values, with a bit of math we can show that a player will break even on his two point field goal attempts if he hits on 30.4% of these shots. On three pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA played does so with respect to two-point shots, the more he shoots the higher his value in PERs. So a player can be an inefficient scorer and simply inflate his value by taking a large number of shots.

Which means that volume shooting is rewarded by that metric as opposed to volume scoring. 11-30 shooting (37%) scores better than 5-12 shooting (42%). Yet at low percentages, the more attempts there are the worse the outcome is for overall offensive efficiency. Sorry, but I don’t find too much “advanced” information in a stat like that.

Wins Produced (WP)

The other advanced stat that I rarely ever use. There is a good detailed discussion of Wins Produced here.

The biggest issue with the stat is how it treats scoring and rebounding, which is how it was possible to predict 57-wins for the Warriors this year after summer transactions, while simultaneously identifying shooting guard as their weakest position. Monta Ellis, the team’s leading scorer and ostensibly its best player, happens to play SG.

With WP, a player who shoots under 50% from 2-point range hurts his score, regardless of how much he scores. Rebounding is given tremendous importance and there is no way to generate a negative rebounding score. Compare the following results based on the marginal values:

  • Player A: 17-30, 5 rebounds
  • Player B: 3-3, 15 rebounds

Player A earns 0.288 WP’s. Player B 0.576. Which means Ben Wallace is way better than Kobe Bryant. In other words, Wins Produced just assumes that scoring at a reasonably high baseline-rate will happen automatically. So the flaw with both WP and PER is the way they treat scoring, which happens to be the most important element of the game. Kind of a major flaw in a metric.

Plus-Minus Statistics

There is an entire family of +/- numbers that have been tracked this decade stemming from raw plus-minus.

  • Raw +/- is borrowed from hockey, and measures the team’s net result with a player on the court. When player A is in the game, if his team is 10 points better than the opponent, Player A’s +/- is +10.
  • On/Off looks at what happens when Player A leaves the game as well. If Player is +10 for the half of the game he plays, and in the other half his team is +10 without him, his on/off is 0. In theory, he didn’t affect team play much.
  • Adjusted Plus-Minus (APM) attempts to correct for teammate and opponent quality when a player is on the court.

Raw +/- has its obvious issues, some fleshed out in this New York Times article. Namely, team quality is the primary force behind the stat. Derek Fisher has an enormous +/- figure, but that probably has something to do with being on the floor with Kobe Bryant and Pau Gasol. It’s hard to find too much value in raw PM, particularly over short periods.

On/Off corrects much of that issue by looking at how a player performs relative to his own team. It’s an incredibly good stat for measuring situational value, assuming adequate sample sizes APM models also have some theoretical value, although not without issues.

There are three important things to be mindful of when comparing on/off and APM:

  1. The worse a team is, the easier it is to have a large number
  2. Noise
  3. The problem of Multicollinearity

First, when Kevin Garnett used to leave the game for the Minnesota Timberwolves, they’d fall apart. In a nutshell, Garnett’s impact measured in on/off and APM was enormous in Minnesota because it’s a lot easier to improve a 20-win team than a 60-win team. When Michael Jordan subbed off the court for the Dream Team, they probably didn’t miss a beat.

Second, there is an incredible amount of noise in plus-minus figures. A 10-0 run here, an injury there, some garbage time, whatever. In a small sample — something that plagues the plus-minus family — these make a big difference. Ken Pomeroy ran an interesting simulation to show how profound this effect can be in small samples.

Third, multicollinearity is a statistical phenomenon that, in this context, means the same players are constantly playing together. For example, Odom and Bryant in LA or Varejao and LeBron in Cleveland. It becomes difficult for any plus-minus model to differentiate between two players if they always play together.

For further issues facing APM models, I suggest Joe Sill’s paper on Regularized APM (RAPM). I will not delve into RAPM models because even Genius Costanza would be bored by machine learning techniques.

Win Shares

The good news about Win Shares (WS) is that they require no Ph.D. and yet they aren’t bland (the full explanation is here). WS are the resident stat over at Basketball-Reference and based largely on Dean Oliver’s great work with the box score. Win Shares are an extension of the individual ORtg and DRtg stats based on Oliver’s work.

Win Shares use box scores values, compares them to league averages (like points per possession) and finally adjusts for possessions played. The number of win shares is not based on actual team win-loss record, but the formula is designed to estimate contributions to a win based on these numbers, and the resulting shares approximates win-loss record quite well.

So, how in the world do we interpret Win Shares? First, similar to PER, they are limited by using only traditional box score metrics. However, unlike PER, I’ve yet to find a glaring flaw in WS. PER will break down if there aren’t enough shots to go around, which happens on a balanced team like the 2008 Celtics. Which result passes the sniff test?

Player PER Rank WS per48 Rank
K. Garnett 25.6 5th .265 2nd
P. Pierce 19.6 30th .207 10th
R. Allen 16.4 81st .177 21st

It’s fairly obvious that Win Shares is doing a pretty decent job ball-parking a player’s value using just the box. As such, I think it’s a really good summary/quick glance stat and much prefer it over PER. Of course, it will sometimes incorrectly assign credit based on certain roles because of failures in the box score. For instance, distributors like Steve Nash are thought to be slightly undervalued by Win Shares. Defensive players who don’t bode well in rebounding, blocks or steals will be undervalued by WS.

The other factor to be wary of when looking at the per 48 minute rate is just how much that player plays. Manu Ginobili is a great example of being able to do more well because he’s logging shorter periods on the court.

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Usage is a term typically associated with offense. It’s an estimate of how often a player “uses” an offensive possession (the standard formula involves true shot attempts and turnovers). But we can think of usage in terms of defense too. That is, how often a player has a shot attempt taken by someone he is in the act of guarding.

According to my tracking, in the 2010 NBA Playoffs, 56.3% of true shot attempts (FGA’s + 0.44 * FT’s) were taken while being guarded. 14.0% of possessions ended in turnovers. The other 29.7% were either:

  • open shots (as a result of a defensive breakdown, defenders being effectively screened out or from transition opportunities)
  • free throws (from non-shooting fouls — the penalty — intentional fouls and technical fouls)

Of the 56.3% of TS attempts that were guarded, the positional breakdown is as follows:

As expected, PG’s foul in the act of shooting less, they face fewer shots when guarding, and as a result fewer TS attempts. It scales up the “bigger” the position, with bigs facing more than half of the shots despite occupying only two of the five positions on the court. This is primarily because they play close to the basket and engage all of the players driving down the lane while protecting the basket.

In America’s favorite visual form, the pie chart, it looks like this:

This means that the range of defensive impacts will be much wider for interior players than perimeter plays. The difference between a good and bad defensive point guard won’t be nearly as pronounced as the difference between a good and bad defensive center. Using a simple mathematical example, imagine the following:

  • A “Bad” Defender allows 50% eFG shooting
  • A “Good” Defender allows 40%e FG shooting

Assume free throw accuracy is a constant (the league average). Based on these shooting percentages, at the center position the difference between our bad defender and good defender is 2.9 pts/100 (a difference in efficiency this year between an average team and the 8th-best team). But at PG, the difference between our good and bad defenders shrinks to 1.2 pts/100.

But that’s just looking at shooting. If we want to create a “Defensive Usage” stat to mirror the offensive one, we need to incorporate turnovers as well. When we do that, we end up with the following positional breakdown:

Practically speaking, individual defenders can have a slightly larger influence than presented above, as this methodology ignores factors like deterring a shot in the first place, defending the 3-point line and disrupting penetration on pick and rolls (incredibly valuable in today’s game). Those tasks fall primarily on the shoulders of little guys, so it’s possible for them to make up some of the difference in “usage” there. Nonetheless, it should seem quite intuitive that the giant men who protect the basket face the most shots — and the most high-efficiency shots — in a position to grab the most rebounds, and thus have the largest impact on the defensive end.

One last point to note is that all of this explains why great individual defensive players can’t have the same impact great individual offensive players can have. This should also be intuitive, as on offense, teams can choose to run the majority of plays through one player. On defense, they can’t choose to have the other team always attack their best defender; Great defenders are essentially saddled by guarding their own man or helping on a slasher down the lane. But as you can see, even that doesn’t involve them on nearly as many possessions as is possible on offense.

We can compare our new Defensive Usage stat with the traditional offensive Usage stat. Here are the leaders from last year’s playoffs:

Offensive Usage (min 300 possessions)

  1. Durant – 34.0%
  2. Wade – 34.0%
  3. Bryant – 33.2%
  4. Anthony – 32.1%
  5. Rose – 31.5%

Defensive Usage (min 300 possesions)

  1. Gortat – 23.7%
  2. Perkins – 21.6%
  3. Frye – 20.9%
  4. T. Allen – 19.4%
  5. McDyess – 19.4%

In reality, the difference is even greater than seen here because of the number of plays in which an offensive player creates for others yet the result isn’t attributed to usage totals. Although that’s the topic of a future post.

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The Patriots 28-21 bouncing last week at the hands of the Jets wasn’t quite as surprising as many made it out to be. No, this has nothing to do with Tom Brady’s broken foot. (Or feet of any kind, Rex.) Sure, Football Outsiders pegged the Pats as an all-time juggernaut and the Jets as merely this year’s 6th-best team. But this loss is a lesson in two of the simplest elements in football: stopping the run and winning the turnover battle.

Turnovers are often cited as a good in-game predictor of victory. Win the turnover margin and more often that not you will win the game. Which was the first potential red-flag for the Patriots, since so much of their success and efficiency was predicated on turnovers. In its last eight games, New England was +23 in turnover margin. They set the NFL record for fewest turnovers in a season with ten.

The only problem with relying too heavily on turnovers is that it doesn’t take much for even the best teams to eventually fumble or have a tipped pass intercepted. The Patriots had three games this year in which they turned it over more than their opponents:

  1. @ Cleveland (35-14 loss)
  2. vs. Baltimore (23-20 win)
  3. @ New York Jets (28-14 loss)

And in each case, they were at least -2 in turnover differential. That’s 19% of their games in one of the best turnover seasons of all-time. In a single-elimination tournament, it’s not the best predictor of victory. Instead, that seems to be rush defense. According to Burke, from 1998 to 2008 (121 playoff games) 66% of the time the team with the better run defense wins. Note the relatively small correlation between the turnover-based factors.

This year, the Jets defense ranked third in rushing yards per attempt. The Patriots 16th. Ironically, just as the Jets won the turnover battle — the Patriots botched punt was effectively a second turnover — the Patriots actually averaged more yards per carry in the game than New York. But much of that was allowed by the Jets in time-consuming drives during the second half. The Patriots averaged just 3.8 yards per carry in the first half.

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At the unofficial halfway poll of the 2011 NBA season, the MVP picture is the murkiest it has been since  the legendary non-race of 1978. One popular candidate is Amar’e Stoudemire, who was signed by the Knicks over the Summer of LeBron and has been credited with reinvigorating basketball in the Big Apple. He’s averaging a career-best 26.4 points per game. But his offensive advantage comes at a cost.

Stoudemire is a natural power forward. And one with a face-up game to boot. By playing at center, Stoudemire creates an automatic mismatch every night on the offensive end; there simply aren’t many centers in the league who can guard a quick, jump-shooting forward. And New York makes it impossible to switch a forward on to Amar’e by pairing him with Danilo Gallinari, himself a perimeter player masquerading as a four. Teams can’t switch their center off of Stoudemire and guard him with a small player, unless they expose the likes of Shaq and Andrew Bynum to chasing Gallinari around the 3-point line.

According to the 82games lineups, New York is +98 with lineups lacking a big next to Stoudemire (in 673.3 minutes). When natural bigs Ronny Turiaf or Timofey Mozgov are in the game with Amar’e, New York’s -28 (315.4 minutes). Almost all of that differential is at the offensive end; When Amar’e’s on the court with a center, New York’s offensive rating is ~107. Without another big man, ~116. It’s no wonder Turiaf and Mozgov are 7th and 10th on the team in minutes played, respectively.

Stoudemire isn’t the first example of an athletic center playing like a wing and overwhelming slower defenders. In 1975, coach Jack Ramsay rode Bob McAdoo at center all the way to the MVP award. McAdoo, like Amar’e, possessed a solid outside jumper and could drive the ball off the dribble by a slower man. Like New York, Buffalo paired smaller players with McAdoo like Gar Heard and Jim McMillan making switches impossible.

In theory, these teams are giving up something on the defensive end to create matchup problems on offense. Note the jarring drop-off in New York’s defensive rating with Amar’e in the game:

Amar'e Stoudemire ON/OFF

That can’t be ignored when evaluating the performance of players like Stoudmire and McAdoo in these situations. Both should be given ample credit for having the ability to create these matchups and hold their own on defense — the resulting gain on offense still yields a net positive from anything lost on defense — but since the classical box score is so offense-centric, we should keep this in mind when evaluating players in similar circumstances.

In a comparable vein, we should pay attention to the offense-defense tradeoffs seen in fastbreak teams — a sacrifice of defensive rebounding to leak out on offense — and in great defensive teams, who crash the defensive boards in lieu of fastbreaking. There might not be as many individual situations as glaring as Amar’e and McAdoo, but we should keep offense-defense tradeoffs in mind when judging performance in mismatched situations like these.

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