What’s the best measure of a player’s performance? While some are content with conventional stats like points, rebounds, and field goal percentage, I believe the best gauge of a player’s worth to a specific team comes from looking at the difference in how the team plays with the player on court versus performance with the player off court.
More than a dozen years ago, Roland Beech posted the above statement on his site, 82games.com, and in doing so introduced many fans (like me!) to the world of basketball plus-minus stats.
From the basic on-off comparison described above, initially termed a player’s Roland Rating, came the concept of adjusted plus-minus. In April 2004, the Washington Times chronicled Wayne Winston and Jeff Sagarin’s work to develop an adjusted plus-minus model of player performance and 82games featured Dan Rosenbaum’s very similar study and resulting stats. As Rosenbaum explained, the fundamental objective of such a model is to “adjust” each player’s plus-minus “to account for the quality of players that a given player plays with and against” and thereby isolate each player’s individual contribution to the team.
Since then, numerous statisticians and fans have developed their own plus-minus variants. Perhaps in a later post I’ll discuss some of these efforts [particularly Andrew Johnson’s Player Tracking Plus-Minus and Justin Willard’s Dredge, both of which use newly-available player statistics to try to create a more predictive model], but for now let’s focus on the big picture.
Traditional box score stats fail to capture much of what occurs on the court. For example, each of the following contributes to winning but doesn’t really show up in the box score: setting good screens, making proper rotations, cutting off dribble penetration, drawing defensive attention, spacing the floor, boxing out, getting back in transition, and communicating well with teammates.
By looking at aggregate team performance rather than recorded individual performance, plus-minus fills these gaps.
What the box score misses mostly falls into the categories of awareness and fundamentals, and thus it should be no surprise that one of the players who fares best by plus-minus measures is the Big Fundamental himself, Tim Duncan. While Duncan never finished higher than 5th in scoring and never led the league in rebounding, PER, or Win Shares per 48, he was the league’s top player by Regularized Adjusted Plus-Minus (RAPM) in 2003, 2005, and 2007 as he led the Spurs to the title each year.
Those RAPM figures are widely considered the adjusted plus-minus gold standard. They were developed by Jeremias Engelmann and posted on his now-defunct site, stats-for-the-nba.appspot.com, from early 2011 through mid-2015. [These links are courtesy of the indispensable Wayback Machine, a.k.a. Internet Archive.] Before then 82games remained the best source for adjusted plus-minus stats, featuring the work of Steve Ilardi after Rosenbaum began working for the Cavs. Two years ago Engelmann and Ilardi notably teamed up to produce ESPN’s Real Plus-Minus.
Below is an article that I wrote back in 2008 based on Ilardi’s work posted at 82games. As is often the case, I analyzed the issue through the prism of a Bulls fan. If you’re more interested in the Duncan jersey than in a meticulous review of adjusted plus-minus trends and their implications for the Bulls back when Derrick Rose was a rookie, feel free to scroll to the bottom.
November 15, 2008 [posted on Blog-A-Bull]
Anatomy of a Contender: A Look at Adjusted Plus-Minus Stats
Adjusted plus-minus ratings are listed on 82games.com for 2007-08 and 2006-07. Basically, these ratings are estimates of what each player individually contributed to his team’s points scored and points allowed per 100 possessions over the course of the season. The ratings are derived from statistical modeling to adjust for the effects of teammates and isolate each individual’s performance. Though the method provides only estimates and should not be considered to provide any sort of definitive ranking of players, in my opinion it provides the most useful player evaluation tool that I have seen.
I am going to attempt to analyze these ratings to draw conclusions about the distribution of talent in the NBA, the characteristics of a contending team, and the current and future prospects of the Bulls. This is much more theory than fact, so feel free to be critical.
League Distribution of Player Performance
Each year there are only a few players who approach or exceed +10 points per 100 possessions. Among players who get major minutes, there are only a few worse than -5 points per 100 possessions. Given this range, I divided player performance into tiers, with each tier spanning 2 points. Below is a chart of the tiers, the symbols I use to denote them, the number of NBA players that fall within each tier in a typical season, and the corresponding label for players in each tier according to the structure of the league:
| Adj + / – | Symbol | # of Players | Label |
| 9 & Above | + + + + + | 3 | MVP |
| 7 to 9 | + + + + | 7 | All-NBA |
| 5 to 7 | + + + | 15 | All-Star |
| 3 to 5 | + + | 25 | Near All-Star |
| 1 to 3 | + | 40 | Solid Starter |
| -1 to 1 | Even | 75 | Fringe Starter/ Sixth Man |
| -3 to -1 | – | 75 | Bench Play |
| -5 to -3 | – – | 50 | Bench Sit |
| Below -5 | – – – | 70 | Scrub |
Some observations:
In each of the past 2 years, the top 3 players in the league have been Kevin Garnett, LeBron James, and Tim Duncan. They have all averaged better than a +9 over that span, while no other player has reached that level in either season. At lower levels, there is less consistency in terms of which players meet the standard, but you will find roughly the same number of players on a given tier both years and a great deal of overlap. Kobe, Paul Pierce, and Baron Davis were at the All-NBA level both years, and Ginobili, Nowitzki, Nash, and Kidd came close.
The distribution of performance is heavily bunched in the average to slightly below average range, with over 40% of the league’s players qualifying as “Even” or “-”.
Only 90 players are meaningfully above average, or 3 per team. The mean of these players is “+ +”, or in other words, the top 3 players on an average team sum to “+ + + + + +” (equal to approximately +12 points per 100 possessions).
The tier sizes correspond well with the organization of a roster. There are 240 players “-” or better, or 8 per team, so a franchise that hopes to contend should be able to construct an 8-man rotation with no one below that level.
Relationship between Player Performance and Team Success
There are two aspects of team success: regular season and postseason. In terms of the regular season, I find that summing the ratings of a team’s basic 8-man rotation gives a pretty good indication of its standing. This is very inexact, and it assumes that the lesser players will cancel out or not play enough meaningful minutes to make much of a difference (it seems more accurate than factoring them in as equals and much quicker and easier than weighing everyone by playing time). In terms of the “+” and “-” symbols I use above to signify 2 points per 100 possessions, here is the breakdown:
| Team Success | Net “+” total (8-man rotation) |
| Elite (60+ wins) | 9-12 |
| Contender (top-4) | 5-8 |
| Bubble (low seed / out) | 0-4 |
| Failure (clear lottery) | Negative |
Postseason success is a little different. The rotation gets shorter, and a team can’t make up for a lack of stars by having great depth. This relates to why the Bulls of a couple years ago never really had a chance. They may have been nominal contenders, with lots of average and somewhat above average players summing to the 5-8 range, but there’s a second component to winning a title. Teams that are serious threats to win it all tend to have a top 2 summing to at least 7. According to the distribution, this means a top 3 player (MVP) and a top 50 (Near All-Star) or top 10 player (All-NBA) and a top 25 (All-Star). Each of the teams reaching the Finals in the past 2 years has met this standard.
Bulls Roster by Adjusted Plus-Minus
Given these numbers, here’s what I think we can reasonably expect from each player for the rest of the season:
(Note: I tried to base my expectations on approximately 50% 2007-08 figures, 25% 2006-07 figures, and 25% subjective evaluation.)
PG:
Rose (+ +): + + + / –
Hinrich (Even): – / +
I have no stats to go on for Rose, so his portion is nothing more than an educated guess. A typical PG is a couple notches better offensively than defensively (the reverse is true for C), meaning that a standard line for the position would be “(Even): + / -”. I’m projecting Rose to play average PG defense this season and be a few points better than average offensively.
Hinrich won’t play for awhile, but when healthy, he’s one of the few guys at his position to be appreciably above average on defense. That’s roughly cancelled out by his play on the other end of the floor, making him a low-end starter or sixth man type.
SG:
Gordon (Even): + + / – –
Thabo (-): – – – / + +
Hughes (- -): – / –
Gordon is the toughest guy to project. He rated very well two years ago and very poorly last year. I think we can expect him to be quite good offensively and equally bad defensively, but I wouldn’t be at all surprised if he matches or even exceeds the level of a typical starter. However, I don’t think he could realistically ever reach an All-Star level. His upside is somewhat limited by his size at SG, meaning that he is unlikely to be better than a minus defensively no matter how much effort he exerts.
I have always thought that Thabo is terrible, and that his defensive reputation exceeds his performance. Now I think I’ve been wrong. He’s probably subpar overall, but his defense really does seem to be excellent. He should be in the rotation, coming off the bench.
Hughes is very bad. He’s bad offensively, and he’s bad defensively. I hope he doesn’t play meaningful minutes.
SF:
Deng (+ +): + + / Even
Nocioni (-): + / – –
Deng has had a poor start to the season, but he’s been by far the team’s best player by this metric each of the past two years. I think he’ll eventually figure out how to play best with Rose, and he should be able to meet this estimate going forward.
Unlike Deng, Noc has looked good so far. He’s meshed well with Rose and has certainly given a boost to the offense. He still can’t play defense, though, so I think his ceiling is as a fringe starter or sixth man. I only feel comfortable projecting him as a rotation player off the bench, since that seems to have been his performance level in the recent past.
PF:
Tyrus (Even): – – / + +
Gooden (-): Even / –
Tyrus has looked horrendous on offense most of the time thus far, and in the last game he even looked bad defensively. However, he’s been approximately average in both of his seasons in the league thus far, so that’s how I’ll project him. Hopefully he can get it back into his head only to sell out for the block on help defense and stand his ground while playing on the ball.
I’m amazed at the extent to which many people are praising Gooden based on a few strong games. Yes, he’s a much better shooter than the other big men and he’s gotten off to a hot start, but he doesn’t have a good track record. In fact, by adjusted plus-minus, he’s been downright Hughesian the past two years. Maybe he’ll drastically exceed my expectations all season—it is a contract year—but I’m not yet a believer.
Center:
Noah (Even): – / +
Gray (-): Even / –
These guys only have a year of stats to consider, so the numbers on them probably shouldn’t carry as much weight.
Noah looks like a typical starting C by the numbers, but I’ll downgrade him a bit. He appears to be behind in terms of preparation this year [This was an understatement. Noah’s had a habit of playing himself into shape over the first couple months of the season through much of his career, and that year was no exception. Seriously, check out Noah’s splits in 2008-09, including 40% FG in October/ November], and I want to see another year of data before expecting him to play to that level.
My opinion of Gray mirrors my thoughts on Thabo. He looks clumsy and ineffective, but if the numbers are any indication, he might actually be a suitable backup C. In other words, I’m now open to the idea that he could deserve some non-trivial amount of playing time. That’s not exactly a ringing endorsement, but it’s better than I imagined.
What the Bulls Need to Contend
Right now, the Bulls 8-man rotation looks to be:
Rose (+ +)
Gordon (Even)
Deng (+ +)
Tyrus (Even)
Gooden (-)
Noc (-)
Noah (Even)
Thabo (-) OR Hughes (- -) -> Hinrich (Even) when healthy
That puts the team at 0-1 with Hinrich out, or low bubble status (outside shot at the playoffs). In addition, the Bulls don’t have anyone I’m willing to project to an All-Star level this year, with only 2 above-average players summing to + + + +. If the Bulls are going to seriously contend in the future, they need major improvement at the top. Here are my most likely scenarios for how the Bulls can get there:
- Rose + Deng: Rose develops into a top 10 player and Deng becomes a consistent top 25 guy. Clearly the most obvious way for the Bulls to improve is for Rose to become an elite player. Deng is the only other guy on the current roster that I reasonably see as top 25. He won’t dominate a game, but he could be very effective on both ends of the floor.
- FA + Rose: The Bulls add a top 10 player from the 2010 free agent class. Rose is at least a top 25 player.
- Rose + Trade: Rose becomes a top 10 player and the Bulls trade expiring contracts and/or cheap young players for a top 25 guy on a rebuilding team.
- Rose: Rose develops into a top 3 player. The Bulls should be able to pair him with a top 50 guy at the very least, whether that guy is someone currently on the roster or not.
- FA + Deng: Just like scenario 2 except that Deng is the best player on the existing team. This probably would mean that Rose has injury problems. I hope this isn’t what the Bulls need to bank on.
The Jersey
Spotting the differences in Spurs jerseys over the years is a lot like playing Photo Hunt. The basic design has stayed the same for decades, so you’re left with minor variations like adjustments to the color of the trim, the shape of the collar, or the size of the jersey number. Take a look and see for yourself.
This particular jersey is from the 1999 Finals, when in just his second NBA season Tim Duncan led the Spurs to the title as Finals MVP. Duncan averaged an efficient 27 points and 14 rebounds per game in the series, while holding his counterpart Larry Johnson (“Grandmama”) to 7.6 points, 4.8 rebounds, and a 30.6% effective field goal percentage. Here are some highlights from the series-clinching game 5 in which Duncan scored 31 of San Antonio’s 78 points:
You can find the jersey at Mitchell & Ness.
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