Numbers never lie (except when they do)


Bill Simmons has a new piece up at Grantland about the just-retired Tracy McGrady and what might have been. It’s a characteristically long and in-depth article, but I wanted to focus on one claim in it: that Tracy McGrady should have been a legitimate candidate for league MVP for the 2006-07 season (Rockets’ GM Darryl Morey, whom Simmons called while preparing the article, said that McGrady could have been league MVP; Simmons had him fourth). Simmons case is this: “he dragged a mediocre Rockets team to 52 wins, even though Yao missed 34 games with a fractured kneecap. The Rockets were 50-21 when T-Mac played that year. To put that record in perspective, Rafer Alston was their third-leading scorer, Luther Head averaged 27.6 minutes a game and a fairly washed-up Juwan Howard played 26.5 minutes a night.”

Whether they acknowledge it or not, most commentators tend to overvalue, some times greatly, players who score lots of points. And Simmons is fairly typical in this regard. This is sometimes referred to as the “Yay Points!” method of evaluation and it’s similar in lots of ways to the mindset that evaluates MVP candidates in baseball primarily based on their RBI totals (while simultaneously insisting that the geeky statheads rely too much on statistics to determine who is a great player).

There has been an effort in recent years to bring something like a sabermetric approach to basketball. Dean Oliver’s Win Shares (WS), Dave Berri’s Wins Produced (WP) and Player Efficiency Rating (PER), created by former ESPN writer and current Memphis Grizzlies exec John Hollinger all try to take account of all of a player’s statistical contributions in evaluating player performance. Hollinger’s PER is notable because it embodies the Yay Points! approach to player eval, and is the advanced stat most likely to be cited by basketball commentators, including Simmons. Simmons has been especially critical of Berri’s Wins Produced (WP) which, it happens, is the advanced stat that values contributions other than scoring the most. This sometimes puts WP at odds with the conventional wisdom.

This brings us to McGrady’s 2006-07 season. Now keep in mind that almost the entire point of Simmons’ piece on McGrady is that while T-Mac was an incredibly talented player – and a great one earlier in his career – he was never a leader. That unlike other superstars, he shied away from taking the reins of his teams and that this personality trait is a crucial reason why his clubs never made it past the first round of the playoffs (until the 2013 Spurs made the NBA finals, and McGrady was a benchwarmer by then). McGrady was a nice, laid back guy with an almost “sleepy” look when he played. He wasn’t a ball-buster and wouldn’t play that role even when his coaches asked him to.

It would be hard, therefore, to argue that McGrady possessed some great intangibles or off-the-court influence to explain why a seemingly mediocre team like the 2006-07 Rockets managed to win 52 games. Which leaves us to evaluate McGrady’s 2006-07 season on the court. In 71 games, McGrady averaged 24.6 points, 6.5 assists and 5.3 rebounds per game. He finished with a PER of 23.2 (15 is considered average, 20 is all-star caliber, 30 is historically good). On the other hand, according to WP, McGrady was a merely good player (.100 is average; .200 is all-star caliber. McGrady was .111 if you consider him a small forward, and .139 as a 2 guard). McGrady was a wing, playing both shooting guard and small forward, so we’ll try to split the difference when we compare him to the average player.

What did McGrady do well in 2006-07? He was an outstanding passer, especially compared to other small forwards and still excellent compared to shooting guards. In fact, 2006-07 was the best year of McGrady’s career in terms of passing (though otherwise his best seasons were already behind him). Compared to small forwards, he’s about an average rebounder. But relative to other shooting guards, he was a very good rebounder in 2006-07. If we split the difference, he was above average, but not great as a rebounder in 2006-07. He turned the ball over a lot that season, well above the average for either of his normal positions. He was pretty much exactly average in terms of steals and blocks.

What about scoring, presumably one of McGrady’s primary strengths?  On a per minute basis, McGrady scored a lot more points than the average wing player – 33 per 48 minutes in 2006-07, compared to 20-21 points for the typical player at his position. How did he accomplish that? McGrady shot 43% overall from the field in 2006-07. This is slightly below average for a wing player. He was almost exactly average in terms of shooting percentage from 2-point range. He shot 33% from 3-point range, below average for either a 2 player or a 3 player (Simmons notes that one of McGrady’s worst habits was shooting many more threes than his proficiency from downtown warranted).  He also shot 71% from the line, a very subpar figure. Overall, his true shooting percentage (TS%) was below average. He scored a lot of points, because he took a lot of shots – 28 per 48 minutes, whereas the average wing puts up about 17-18.

Could a player really be a legitimate league MVP candidate if he’s not only not a great shooter, but actually below average, unless there are other things that player excels at? In McGrady’s case, there’s really only one thing he did exceptionally well in 2006-07 – pass the basketball. That’s great, an important part of winning basketball. But please don’t tell me that that is enough to make an MVP. McGrady’s in the conversation because he scored a lot of points. And he scored a lot of points because he took a lot of shots, even though he shot quite inefficiently when he did hoist up the basketball.

How did the Rockets win 52 games that year? It turns out that, in addition to McGrady, who was a good, not great player, they had other guys who played really well (in spite of Simmons’ claim to the contrary). The aforementioned Luther Head was actually very good that year. On a team in which offense wasn’t a particular strength, Head connected on 44% of his threes and had an excellent TS%. Dikembe Mutombo was long in the tooth by that season, and only averaged about 20 minutes a game. But he was actually great when he did step on the court – a terrific shot blocker and rebounder who converted his field goals at a very high percentage. Dikembe was vastly better than the average center in all of those areas. Chuck Hayes, unmentioned by Simmons, also had a terrific year – an excellent rebounder who converted a very high percentage of his shots. Shane Battier was also a very high percentage shooter, connecting on better than 42% of his attempts from distance. Yao was excellent in the 50 or so games he did play. Overall, the 2006-07 Rockets were primarily good at rebounding, shooting threes and defending. McGrady was a good rebounder, but not especially notable in those other areas. In sum, it’s hard to find in the numbers, taken as a whole,  a case for McGrady as team MVP, let alone candidate for league MVP.

But, see, guys like Chuck Hayes, or an aging Mutombo or an efficient but not high volume shooter like Luther Head – they don’t fit our image of a good basketball player. You can talk about nonsense like the “eye test,” but when it comes to evaluating value on the hardwood, usually the formula is pretty straightforward – if you score a lot of points, people think you’re great, even when you clearly aren’t. (cough, Carmelo Anthony, cough)

In the end, like it or not, pretty much everyone relies predominantly on the numbers. Bill Simmons just wrote a long article that essentially says – as great a talent as Tracy McGrady was – he lacked the drive, the intangibles and so on necessary for a superstar to spur his teams to championships. And in the same article, he told us that McGrady, in a season in which he did one thing exceptionally well – pass the basketball – was a serious MVP candidate. Why? Not because he was a leader or somehow inspired the guys around him to play beyond their natural talents. Bill Simmons thinks McGrady ought to have been in the conversation for league MVP because he scored a lot of points, even if he had to shoot quite poorly to do so (PER,  John Hollinger’s stat, overweights shot-taking, which results in guys who score lots of points because they take lots of shots getting lots of love they don’t deserve).

If you want to give T-Mac some credit for opening up shooting lanes for his teammates, that’s fine. But there’s no magical alchemy that converts lots of misses into winning basketball. Nor is there deep insight about how the game is “really” played leading to the belief that Tracy McGrady was a great player in 2006-07. Just an over-reliance on one statistic above all others to tell us how basketball games are won.



  1. I think that Houston team is a pretty classic example of a team whose high percentage scorers had very low marginal fg%s.

    Take Dikembe as an example, though the same is true to a lesser extent of both Head and Battier: Do you honestly think you could have transferred a significant portion of the possessions that ended in a shot from McGrady and got attempts from Mutumbo at his average fg%? If so, you’ve just solved basketball: give most or all of your team’s shots to the big guy who shoots around 60% on low single figure attempts – Mutumbo, Biedrins, it doesn’t matter – and then watch the championships roll in.

    The alternative hypothesis is that there was something that restricted the number of possessions Mutumbo could use at that high fg% – that there was something special about them and that they were a finite resource – because the arose from a defensive breakdown or followed an offensive rebound for instance. That’s why the coach didn’t just call for more of them, despite being perfectly aware that Mutumbo was scoring a higher percentage than McGrady.

    So, your model assumes than possessions are systematically being allocated inefficiently, so that every team could win the championship just by making a small change obvious to anyone who reads the box score. I think you probably need to affirmatively prove a hypothesis like that, and I also think you haven’t and can’t.

    I think possessions are being allocated efficiently based on equalising marginal field goal percentages, and that McGrady performed a valuable service for that rockets team by using so many possessions in what must have been (ex hypothesi) the most efficient manner possible.

    Now, I can’t prove my theory either – because I hypothesise that shot allocation is endogenous we won’t be able to find a correlation between shots and fg%. But my thesis probably deserves to be treated as the default, but refutable, presumption because it doesn’t rely on professional coaches, players and team ignoring the obvious and acting like complete idiots.

    1. No, I definitely haven’t solved basketball. There are things we do know, however. We know that missing shots is a bad thing. We know that “usage” doesn’t hold up very well under scrutiny. We know that it is, in fact, a repeatable skill to be able to convert a high percentage of your attempts, and that many players can’t do it, even when they have a limited number of attempts and even when they’re big men. As I said in the piece, if you want to give McGrady some extra credit for making the players around him better, go ahead. His excellent assist totals already make him an above-average player. But it’s a very large leap from a guy who was a below average shooter to MVP candidate because, well, other guys on his team played well, so he must be responsible. By that logic, every high usage player on a winning team in the league should have been an MVP candidate.

  2. I point out right in my post, and not for the first time, that if shots are allocated optimally usage will be endogenously related to shooting %. So you guys need, need, need to stop linking to graphs which attempt to prove no relationship by assuming that shot allocation is uncorrelated with shot making ability. Seriously, stop doing it, because it makes it crystal clear that you don’t get the argument.

    But, let me repeat, if you are right that Dikembe Mutumbo could have scored some significant number of extra points at his existing average fg% then you are claiming to have solved basketball, because that is a recipe for repeated championships with just about any roster you can imagine.

    So if you don’t believe that to be the case you need a model of how shots are allocated at present and how marginal fg% would respond to reallocating them. Your current one, assuming essentially random allocation and constant marginal fg%, doesn’t work.

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