By Kevin Pelton
In my opinion, one of the best uses for statistics in sports is the evaluation of normative claims proffered on the basis of anecdotal evidence. In a sense, I guess you could say that's the purpose of all statistics, to determine if what we think we're seeing is correct. Keith Jackson once claimed that Jerry West averaged 10 steals per game. Since they've kept the stat officially, no player has recorded more steals per game than Alvin Robertson's 3.67 in 1985-86. Somehow I doubt then that West averaged nearly three times the record.
Usually the use of statistics is a little more subtle; the issue a little more clouded. It's one of those cases I'm going to write about today.
Having operated over the past summer a website devoted to the idea of keeping Gary Payton from being traded, I've heard all the reasons why he should be traded. One of the ones I took the greatest umbrage with was the suggestion that a team with a point guard as its leading scorer could never be really successful. While ignoring the fact that Payton was the Sonics' leading scorer in 1996 (by a 13 point margin) as they went to the NBA Finals, I also think this statement simply does not reflect NBA reality.
The critics will back up their argument by pointing out the struggles of point guard-led teams last year. Houston and Seattle, while not bad, did not make the playoffs. New Jersey was awful. Off the top of my head, those were the only teams led in scoring by their point guard, and not one was playing in May.
My anecdotal retort would come in the fact that if we look back over the last fifteen years or so, we see teams with all types of stars winning the championship. There was Magic Johnson as a point guard, Larry Bird as a small forward, Isiah Thomas as another point, Michael Jordan as a shooting guard, Hakeem Olajuwon as a center, Tim Duncan as a power forward, and Shaquille O'Neal as a center. That's every position. Besides, positions are just arbitrary distinctions made to categorize and compare players. It's not like any coach determines his offense based on standard expectations for a position. Instead, they base it around the talents of the individuals.
But if further anecdotal evidence like this were good enough for me, I wouldn't be writing a column named "The Statistical Side of the NBA". No, I want cold, hard fact. But first off, does it even make sense to be talking about this, given what I note about position being arbitrary? To answer this, I turn to someone far more intelligent than myself, Dean Oliver, who did a quick and dirty one-season study of winning percentage by position of leading scorer in his Basketball Hoopla 1988-89:
"Does it make any sense to relate a team's record to its leading scorer? Yes, it does. . . . [What] position the leading scorer plays gives some indication of how the offense is set up and there may be some relation between certain offensive sets and winning. Additionally, a leading scorer may get tired from scoring, which may affect his defense and, thus, his team's record."
Going back to the argument regarding Payton, I first did a quick study of winning percentage by position of leading scorer in November. I went back five years, and found an interesting trend. Center-led teams were far more successful than teams with leading scorers at any other position, but the other four positions were fairly even. That, along with the fact that I read the different conclusions of Oliver's study, which concluded that teams with forwards as their leading scorers were most successful, motivated me to undertake a larger and more in-depth study.
This time, I went back 15 years in an attempt to see whether there has been a change in how the game is played that is evident in the value of having your leading scorer play a certain position. For example, the three pointer has become increasingly more prevalent over that span. In my estimation, that would lead to greater value for centers like Hakeem Olajuwon, whose double teams usually lead to three point attempts for others, as well as guards. The positions that would seem to be adversely affected by increased three-point shooting are the forward positions. While many small forwards shoot threes and many power forwards are scoring as much in the post as centers, my expectation was that they would not see the same benefit from threes.
A note on my method: I generally chose the team's leading scorer as the player with the most total points; however, I tried to use common sense. If player A was 20 points ahead of player B, who had played 10 less games, then I chose player B as the leading scorer.
Here is what I found, starting with the number of players from each position who were their team's leading scorer and followed by the winning percentage of those player's teams:
For those of you who are visual learners, I've also made charts of each of these with the frequency of leading scorer by position turned into percentage to make it easier to see what's happening despite expansion. Here is the chart of frequency and here the chart of winning percentage. Note on this chart that I've drawn in the average for each position in the same color.
So what kinds of things are evident from the tables and charts?
The one thing that is clear is that there is a great deal of variability in both the winning percentage and frequency of leading scorers by position in terms of winning percentage, that doesn't come as much of a surprise to me. Various outside factors would make it that there isn't very much consistency in winning percentage of one team. Over a group as small as these are, a lot of inconsistency is to be expected. The frequency's instability seems a little strange, however. Why would the number of shooting guards who are their team's leading scorers go from 10 to four between 1993 and 1994? I'm afraid I don't have an answer given they weren't all that unsuccessful the first year.
In the first two years of the study, there was only one point guard who showed up as his team's leading scorer, Magic Johnson. Along with Detroit's Isiah Thomas, Johnson helped revolutionize the point guard position and make scoring points acceptable. Thus, we see a general trend upward in number of point guards as leading scorers which reaches a peak in 1997, when seven of the league's 29 leading scorers were points. Since, this number has leveled off at about four. However, this may be changing, thanks largely to the 1999 draft, which produced Steve Francis, Baron Davis, and Andre Miller as quality young point guards. Miller and Davis are leading their teams in scoring this year, as are Gary Payton, Nick Van Exel, Stephon Marbury, and Sam Cassell. Francis only misses this list because he missed so much time with a foot injury earlier this year.
What has happened to the high-scoring center? As recently as 1994, better than a quarter of the league's teams were led in scoring by their big men in the middle. However, with the aging of Hall of Famers David Robinson, Hakeem Olajuwon, and Patrick Ewing and the decline due to illness of Alonzo Mourning, Shaquille O'Neal was left as the only center to lead his team in scoring in the 2000-01 season. Things are worse yet this season; with O'Neal missing nine games to injury, he has been passed by teammate Kobe Bryant and we may well see no player at a given position lead his team in scoring for the first time in at least 15 years.
What makes this fact really curious is just how successful centers have been over the last decade. While other positions have seen success come and go, centers have been the most successful position of leading scorers in the NBA ever since 1992. Looking at the totals for the 15-year period underscores this fact. Teams with their center as their leading scorer have averaged a 58.7% winning percentage, as opposed to 52.6% for the second most successful position, power forward. To make that more tangible, it's a difference of five wins per season.
There are a couple of identifiable trends in the success of teams with leading scorers at various positions over the 15-year span. Centers appear to continually be more successful relative to other positions, starting out near the .500 mark but climbing to the point where only twice in the last ten years their teams have won less than 60% of the time. Most of those wins seem to be coming from small forward-led teams, who were highly successful in the first two years of the study but have bettered .500 only twice since. Because Oliver's study was conducted in one of these first two years, he concluded that it was best to run an offense through a wing player, often a small forward. If that was the case then, it doesn't appear to be so now. Shooting guard and power forward, while showing variability, have generally stayed constant over the course of the study.
Shareef Abdur-Rahim owns the dubious distinction of having been the leading scorer on two of the 10 worst teams in the 15-year study, the 1996-97 and 1999 incarnations of the Vancouver Grizzlies. Does this make Abdur-Rahim an awful player or indicate that the Grizzlies would have been better off feeding the ball in each year to Bryant Reeves at center? Of course not. Correlation does not necessarily imply causation, as statistics professors are fond of saying. And for another thing, who's to say the correlation isn't the other way around, that bad teams create leading scorers at certain positions?
Personally, I tend to think that this is the case to a significant extent. I think we can all agree that interior players, especially centers, are much more difficult to acquire than guards. I'm sure I'm not the only one who's ever used the phrase, "Guards are a dime a dozen." It's very unlikely that, for example, an expansion team will be able to acquire a good center. On the other hand, the odds of them acquiring a good swingman -- at least a high-scoring swingman -- are pretty good. If we look at the recent expansion teams, we have the following leading scorers:
Miami, 1988-89 - Kevin Edwards, SG
Charlotte, 1988-89 - Kelly Tripucka, SF
Orlando, 1989-90 - Reggie Theus, SG
Minnesota, 1989-90 - Tony Campbell, SF
Toronto, 1995-96 - Damon Stoudamire, PG
Vancouver, 1995-96 - Theodore 'Blue' Edwards, SG
Nary a big man in the bunch.
There's another reason it makes sense for bad teams to quote unquote 'cause' guards to be their leading scorers. Guards are less dependent on the quality of the rest of their team than are post players. Double teams are far less effective against a guard than they are against a big man in the post. As well, it is difficult, if not impossible, to 'deny' the ball to a guard, who often will bring the ball up. Add up the facts -- quantity of quality guards and difficulty of getting a scorer attempts -- and it's clear that some trend like this should be seen in the data.
But how to control for this factor?
My answer was to separate groups of teams who were really good -- 50 wins or better -- or really bad -- 50 losses or worse. My expectation was that we'd see fairly even winning percentages by position with this control.
I found 127 'good' teams and 103 'bad' teams. What's extremely interesting is how these groups are distributed amongst the positions, relative to the overall distribution. Another quick table:
|Pct. of 'good' teams||.087||.230||.157||.276||.197|
|Relative to overall||.665||.963||.695||1.260||1.512|
|Pct. of 'bad' teams||.146||.408||.252||.175||.019|
|Relative to overall||1.118||1.386||1.114||.799||.149|
In case anyone doesn't understand how I've set up the table, centers are . . . uh . . . a little under represented. Just two of the 103 bad teams were led in scoring by their centers. As the flip side of that coin, obviously, centers are very over represented on the good teams, with about a fifth of them led in scoring by their center. Point guards, on the other hand, almost rarely lead good teams in scoring. Oddly, they are not as over represented amongst poor teams as shooting guards. Bad teams are more often led in scoring by guards than good teams . . . not a big surprise to anyone, I don't think.
But what of the winning percentages by position once we control for this fact? Another table:
|'Good' win %||.717||.686||.662||.682||.679|
|'Bad' win %||.286||.275||.267||.267||.269|
Looking at this table, there doesn't appear to be a big difference between win percentage by position. Point guard actually comes up ahead on both charts, but I don't think that really means anything. The differences seen in the total winning percentage seem to be explained rather well by certain positions being over represented amongst bad teams and others amongst good teams.
So what conclusion can we draw from this? On the one hand, there doesn't appear to really be a difference of winning percentage based on position of leading scorer when looking at a given win percentage, but on the other hand there are varying numbers of teams in those groups. Here's my interpretation. In my opinion, this whole study could be said to be looking at two different things -- through what position an offense should be run and also what position one should target to have a star player at. Using this perspective, I think that the fact that within a given range there isn't much variability of winning percentage based on position indicates that no single type of offense is necessarily more effective. A post-based offense isn't necessarily better than a perimeter-based one or vice versa. On the second point, I think the fact that post players are over represented amongst the good teams indicates that a star power forward or especially center is far more valuable than a star perimeter player.
This leaves a natural follow-up question -- why are star post players more valuable than star perimeter players? I've been e-mailing Oliver about various issues, including my study, and here's the theory he offered to explain this:
"Before you tell me results, I really want to come up with a theory for what should happen. I can definitely see why teams with good centers are winners. This is because centers are so important defensively -- they can definitely help a defense more than any other position -- that if they are good offensively, that builds in more time for them to be on the court to improve the defense. This would then imply that the teams with highest scorers as centers are not the most efficient offensive teams, but are good defensively and pretty good offensively and, hence, winners. Since forwards (esp small forwards) and guards aren't as critical to a defense, their time on the court may not be helping the team defense as much and there is no guarantee that the team wins."
In order to test this theory, I decided to look at a pair of years (this few because it is far more time-consuming) by finding the offensive and defensive efficiencies (as calculated by pts/(fga+(.4*fta)+to-or) of each team and matching these with the position of the leading scorer. I ended up choosing 1991 and 1997 because I wanted to have one fairly recent year and a bit older year, and because in both of these years there was no position that only had a couple of players who were their team's leading scorer. Here's what I found:
|1997||Off. Eff.||Def. Eff.|
|1991||Off. Eff.||Def. Eff.|
The caveat here is that these numbers represent only two seasons, and they might not provide a complete picture, which could only emerge from an even larger study than this one. Looking at this data, however, Oliver's theory looks pretty good. In 1997, all the different positions of leading scorers had teams with essentially similar offenses. There's not much difference between the best and worst efficiency. The difference, as theorized, comes from the defense. Centers are the leading scorers on very good defensive teams, indicating perhaps that there is a significant effect from their defense.
More on the All-Star game
Thanks to the injuries that struck leading vote getters Shaquille O'Neal and Vince Carter, the NBA had a chance to rectify both of the mistakes made in the selection of reserves. Unfortunately, as the league is apt to do, they blew the chance, going only one for two.
In the West, Elton Brand makes his first All-Star appearance courtesy of O'Neal's absence. Chris Webber moves into the starting lineup, as the West now has no player listed at center on the All-Star roster. In the East, Carter's absence should have allowed the NBA to select Andre Miller. Indeed, the league chose a third-year point guard from the Eastern Conference, but it was the wrong one, Charlotte's Baron Davis. Davis is an excellent young point guard, but he's simply not in Miller's class. I'm afraid for Miller's sake that he's going to have to get out of Cleveland before anyone is really going to recognize what a fabulous player he is. What a shame.