Friday, March 28, 2008

More March Madness Math

There seems to be a fair amount of interest in the statistical analysis of basketball these days, although the sport is still way behind baseball in terms of the issues being analyzed. The guys at basketball prospectus are doing some good things, but currently, in my opinion, a lot of their work is simplistic and repetitive and caters to the casual bracket-playing public, but not to those of us who really want to understand basketball.

In truth, we probably also must admit that basketball is less susceptible to sweeping statistical generalizations than is baseball. Does anybody doubt anymore the lack of importance of the RBI stat? But ultimately, baseball is a team sport that sums up for the most part the individual actions of separate players.

Basketball, on the other hand, is a team sport played collectively. That is why dogmatic characterizations about who is better or best are rarely appropriate. Recently, one commentator opined that Kevin Love was better than Tyler Hansbrough, no doubt whatsoever in that commentator's mind. Now aside from the insufficient data upon which this commentator, John Gasaway based his conclusion, he also forgot something key. Basketball is a team game, not an individual sport.

Last night, the North Carolina Tar Heels defeated the Washington State University Cougars by a score of 68-47. At half time, Carolina led the game 35-21, and their star player Hansbrough had two points. But how could this be? If Carolina's POY candidate had been completely stiffled, how could the Tar Heels possibly be leading at halftime by such an onerous margin?

Well, its a team game. Gasaway might have you believe that Hansbrough had a horrible half. A more sophisticated view of what happened might be, however, that Hansbrough had a sensational first half, after all, his team had a lead that was equal to 67% percent of the Cougars's first half total. Washington State put so much focus on stopping Hansbrough, that they couldn't stop any of the other players for UNC. This is a team game and Gasaway ignores this reality with his brash and unwarranted, sweeping conclusions about which player is best.

Kevin Love and Tyler Hansbrough are both sensational players and UNC deeply wanted to see Love in Carolina Blue and I doubt UCLA would have turned Hansbrough away, had he shown up on their front door.

Second point: Points per possession analysis is a fundamental analytical tool used by basketball coaches to evaluate their team's play. Coaches in the know have been utilizing PPP analysis for over fifty years, as a means of evaluating a team's play independently of how quickly the ball is changing hands from team to team during a game.

It can help provide insight into the relative strengths of teams that play at different tempos or paces. It is not a secret, but like OBP in baseball, some people think it is such a cool way of looking at the sport, that they overwork the concept.

Or, to start with a joke, only a statistician could make us believe that leading a game by ten points is just as good as leading it by twenty points.

PPP differential is important, but it is not as important as absolute point differential, regardless of what anyone tries to tell you. Why not? Let's look at a simple arithmetic example involving two college teams, the Cheetahs and the Terrapins.

The Cheetahs play fast and have lot's of possessions on average in their games and they average a lot of points as well. By the end of the year, statistics show the Cheetahs score an average of 80 points per game, while giving up only 70 to their opponents in the first 38 minutes of their schedule in the fast and tough, African Coast Conference.

The Terrapins play slow. They have a coach who loves the movie, Hoosiers and believes every bit of that movie is true. Their team averages 40 points per game in the first 38 minutes of their games in the slow and rough, Equatorial Coast Conference, while rendering 35 to their opponents and they only utilize half the possessions per game that the Cheetahs use.

Now which team is better? Advocates of strict PPP analysis will tell you that these teams are equal, because their point differential per possession is exactly the same.

They are wrong.


Let's see what can happen to both teams in a game where they are especially unlucky down the stretch in the last two minutes. In the first game, the Cheetahs's opponent, the Salukis, hit three three-pointers in the last two minutes, after having only made three in the entire game that far. For the Cheetahs, there seems to be a lid on the rim and they don't score a single point down the stretch, laboring to hold on, 80-79.

In the second, game, the Terrapin's opponents, the Sloths hit three three-pointers down the stretch, after having only made three in the entire game that far. For the Terrapins, there seems to be a lid on the rim and they don't score a single point down the stretch, and they lose a heartbreaker, 44-40.

Why the divergence in outcomes? Simple mathematics. The Cheetahs were able to overcome a somewhat unlikely series of outcomes in the final two minutes, because their absolute lead was much greater. The Terrapins could not, even though up to then, their PPP differential had been exactly the same as the Cheetahs.

Thus, the mathematics are basically simple. The better (more talented?) a team is, the faster the tempo they should employ, ceteris paribus, because it gives them an extra cushion against unlikely events occurring to take the game's outcome away from the expected mean. Ceteris paribus is Latin for all other things being equal.

Let's look at some real world examples. In the current basketball ratings, Wisconsin is ranked number 3 and North Carolina is ranked number four. These teams make for good examples because Wisconsin plays much like the Terrapins above, while UNC is more of a Cheetahs-type squad. North Carolina has the better record at 35-2, while Wisconsin has the stronger power index, in spite of having lost twice more and having been blown out in one game.

Basically, this is because Pomeroy has not found a way (or has chosen not to) to incorporate the mathematical notion of standard deviation from the expected outcome into his ratings. I will use his words here:

"Consistency is basically the standard deviation of scoring difference by game for a team. Again, it’s not included in the ratings calculation. It can be an aid in determining which teams are overrated by my system. Highly rated teams that are inconsistent tend to look beatable more often. As of this writing, Georgia is ranked 329 in consistency and Oklahoma is at 334. They’ve played their best games against poor teams, and their worst against good ones.

Ideally, I’d synthesize the consistency and rating into one number, but I haven’t found a way I’m comfortable with. So right now, I’m throwing this system out there with all its warts for everyone to see. The warts tend to decrease as more games are played, but at least I’ve made you aware of them and where they can pop up."

First, I would like to point out, consistent with the above, the fact that WSU was one of the least consistent teams in all of college basketball this year, which may account for a lot of the head scratching by people who could not figure out what was wrong with Pomeroy's rankings here. I would argue that the rankings were wrong with respect to WSU and I think he admits why here, although you have to go trolling into the dark recesses of his fantastic site to find this. I am not sure, however, why he continues with the pretense of multiplying out the logs, given this fundamental defect.

So, getting back to Wisconsin, whom Pomeroy rates above UNC, while the USA Today computer rankings have Wisconsin fifth, with UNC, first, what is the truth of the matter?

Well, there may not be any ultimate truth. If a team is incredibly good but very inconsistent, they might be very likely to be ranked number one all year but then get upset in the tournament, which is a simple one and out format, not best of seven as in the NBA.

And just so I don't get a lot of I-told-you-so emails from either UNC or Wisconsin fans, when one or the other loses, one loss, without more is not enough to defeat the analysis. Unlikely events happen all the time and if they didn't, life would be quite strange and boring!

Nevertheless, here, I believe that Wisconsin being rated more highly is due to a flaw in Pomeroy's system. Not only does UNC have, in fact, fewer losses, their style of play seems to insulate them more from upsets. And if we look at his other catgories, we see it. Carolina is the 56th most consistent team in the country, 2nd only to Memphis among teams still playing, while Wisconsin is the 205th most consistent team. Wisconsin's slow style of playing provides them with less of a cushion against upsets. On the other hand, their style is probably fairly efficiently tailored for their talent composition, and for them to change it, would violate the ceteris paribus part of our mathematical example.

So, what does it all mean? A team like Wisconsin is far less likely to be able to go through an entire season unbeaten, compared to a Memphis or UNC, which have high consistency ratings. Thus, when people say UNC is clearly "better," what this should mean is that UNC is likely to pass through the year with fewer losses. But this does not mean that UNC is necessarily likely to beat Wisconsin in a head to head match-up.

And to take the analysis one step further, let's ask ourselves, who is better between the real Terrapins of Maryland and the inappropriately named Cougars of WSU. Which of those two teams is better? Well, surely you say, it has to be WSU, since they made the NCAA tourney and had a fairly high ranking, while Maryland went out in the second round of the NIT. And yet, Maryland beat UNC and most Carolina fans would probably tell you that they would rather face WSU any day, over Maryland.

I will let the reader puzzle over that one, but will finish by stating that it seems that teams that play slow will generally be more at risk at the ends of games when playing inferior opponents. While this might not be a huge problem over the course of an 18 game regular season schedule, it can be huge when the rule is one and done. That may help explain how Georgetown got upset by Davidson and why Wisconsin could be at risk today, as well as UCLA against Xavier.

Ultimately, it's because, no matter how you slice it, leading 50-40 is not as good as leading 100-80 and don't let anybody lie to you with statistics and imply that it is.

Wednesday, March 26, 2008

Washington State versus UNC

Washington State travels to Charlotte as a number four seed to face UNC, the number one seed in a Sweet 16 match-up that pits virtually the fastest playing squad in college basketball against the Cougars, who are near the bottom in tempo among college teams.

Thus far in the tournament, both teams have won their games easily, leading some to pick WSU as an upset possiblity, while a few others (very few), such as Ken Pomeroy, see the game as a virtual pick 'em match-up.

Let's look a few things about this game to get an idea of some of the factors. First, of all, neither team has defeated many top twenty-five teams. Carolina has four or five such wins, if you count the Tar Heels win at Davidson, while Washington State beat USC twice and won at Gonzaga, and now Notre Dame, three teams sort of on the fringe of the top twenty of the various polls and rating organizations.

In terms of elite wins, say among the top 15, Carolina won at Duke, while WSU doesn't have any elite wins, having lost 3 times to Stanford, and twice to UCLA. Of these games, only their loss to Stanford at home was close, coming in over-time. They also lost to Cal and barely beat rival UW at home. They also have beaten Baylor, Oregon, Winthrop and ASU.

Surprisingly, Pomeroy believes that Washington State is better than Stanford. I know that styles make match-ups and all that, but Stanford has beaten them 3 times, the last 2 convincingly, and finished two games ahead of them in conference and also went farther in the Pac Ten tournament, so once again this year, Pomeroy's ratings have some rankings that make very little sense. One wonders exactly what Stanford would have to do to be ranked ahead of WSU by Pomeroy if beating them 3 times and finishing two games ahead of them in a conference where everyone plays each other twice, is not enough!

Sagarin's ratings are much more likely to be in line with reality this year than Pomeroy's. Why this is so, I do not know, but something has gone badly askew this year with the Pomeroy ratings. While no one knows his exact ranking formula, there appears to be some system bias in favor of teams that play in conferences in which the play is slower, in that he has the two fastest-paced teams in the tournament rated far more lowly than other ratings services, while UMass, another team that plays at lightning pace is also rated less highly. On the other hand, plodding teams, such as WSU, Wisconsin and Illinois, all of whom play at a snail's pace, are rated more highly by Pomeroy than by fans and the experts in the field.

While his data collection is still top-notch, Pomeroy probably needs to tinker a bit more with his ratings. He truly may be the only single person in the entire United States who believes that Washington State is better than Stanford and essentially as good as UNC.

In terms of defense, Pomeroy has WSU slated as a far better defensive squad. In terms of offense, he has UNC as the better squad. However, there may be some other clues as to why UNC is more likely to win.

First of all, UNC has much better talent. Almost everyone agrees that for WSU to have any chance, it probably needs to be a game in the 50's or 60's, to keep Carolina from having extra possession and a fast game in which it can exploit its depth. This is a fancy way of saying that Washington State doesn't have all that many good players so they have to try to take the air out of the ball to have any chance to win.

I have to admit that I am a bit more biased against this team than perhaps against other foes, because they pride themselves on their plodding way of playing. They are pretty much the slowest-playing team in the entire NCAA Division I, brandishing a style of basketball that, if further adopted, could be a new non-narcotic form of sleep aid. Their coach is already trying to turn this into some sort of grudge match against Roy Williams, who he claims, was disrespectful to his father back in the 1990's, and apparently, said father also taught players to play as though they had on muddy workboots.

Well, as pathetic and boring as WSU's style of play might be, it is still within the rules, so let's look at some other factors.

Looking at something Pomeroy calls consistency rating, we see that UNC is the 59th most consistent team, which is pretty good--only Memphis and Western Kentucky are ranked ahead of them among teams still in the tourney. WSU is 311th, which is very poor--only West Virginia is less consistent among tourney teams.

Now, I suppose consistency can cut both ways when looking at a one game match-up, as opposed to winning the entire tournament, where it is essential to be consistent. We can expect North Carolina to be pretty good, just like they have been all season. But WSU, will it be the team that beat Notre Dame badly, or the team that lost badly to a mediocre Arizona team twice.

Pomeroy also has a figure called luck rating in which he rates UNC as being one of the luckier teams left in the tournament, which is most likely due to a slew of close games they had while Ty Lawson was hurt. He also has WSU as being relatively unlucky this year, which is truly puzzling. A glance at their results indicates that they split two overtime games this year and that most of their losses have been by more than three points. Their schedules appear to be relatively even, with UNC playing tougher defensive teams and WSU playing tougher offensive teams.

There have recently been some articles published that state that Vegas uses the Pomeroy ratings to set its lines. Vegas is currently predicting a 142.5 over/under, which is 2.5 points higher than the Pomeroy prediction, so that could possibly be the case here.

However, if Vegas used the Pomeroy predictions to set its points plus or minus, then the public immediately moved the line far away from the Pomeroy setting.

Pomeroy predicts that UNC will only win 71-69, which seems frankly amazing. His system predicts that WSU will be playing in a site three time zones away, on a highly partisan "neutral" court, against a team that everyone agrees has far more talent and that UNC, with all those advantages, is only a 2-point favorite.

This is ludicrous and indicates something deeply wrong with the manner in which he is currently rating teams. WSU has an excellent shot at winning. In a one game and out tournament, unlikely events occur somewhat frequently. Davidson beat Georgetown, albeit while playing in Davidson's home state. Nevertheless, there is a huge difference between a team winning an upset and being deemed essentially an equally good team, which is what Pomeroy would have you believe is the case in the WSU-UNC match-up.

It is difficult to perceive how Pomeroy's system could predict such a thing, about as difficult as figuring out why he ranks them above Stanford. The current Vegas odds are Carolina by 8 points, which seems about right given that WSU will try to hold down the score as much as they possibly can.

Everyone seems to agree that Washington State is a very unselfish team that maximizes their chances to win, given the talent at their disposal. But is that likely to be enough? Pomeroy says almost, and he means this in general, seeing them beating Carolina 43 times out of 100.

While I am definitely not neutral in terms of my rooting interests, I am not sure any other neutral observer can agree with Ken Pomeroy.

Washington State has not beaten any of the supremely talented teams that they have faced this year, losing all 7 games against UCLA, Stanford and Arizona, a disappointing team with injuries, but top-notch talent. They may finally achieve that break-through win Thursday night in Charlotte, but if they do, it will be a huge, overachieving upset, not a battle between two even teams.

I have to believe that WSU has not shown much ability to beat teams that exceed them in talent. They have beaten decent squads like Arizona State, Baylor, Winthrop, Oregon and now Notre Dame. They have not, however, beaten anyone that would surprise you while reading your morning newspaper. With virtually all the intangibles leaning UNC's way, it's hard to see them doing that now.

Monday, March 24, 2008

More Math and March Madness

One of the interesting things in life is when a person becomes a leader in a field and develops devoted accolytes and then changes beliefs, or "sins", if you will in the eyes of his or her accolyes.

Robert Nozick, was a noted libertarian philosopher, famous for his debates with John Rawls concerning the proper reach of government. Nozick is noted furthermore by hoops fans for using the unmatched talent of Wilt Chamberlain as one of his main analogies against government, in his opus, Anarchy, State and Utopia. Unfortunately, Nozick later had the temerity to sue his landlord for violating a rent-control statute, and his libertarian followers were not happy.

In the field of sports statistical analysis, Bill James is king. Dean Oliver wrote an excellent, aforementioned book, extending statistical analysis to basketball, called Basketball On Paper, which caught the eye of Ken Pomeroy, someone who is well known to virtually all college basketball fans who are interested in the statistical analysis of college basketball. His site,, is a smorgasborg of interesting data, with link data, which leads to predictions of upcoming games, although for most, it seems not used for gambling, but simply to buttress arguments about which team is truly superior in the world of college basketball.

This is all well and good enough, except lately some of Pomeroy's accolyes, if you will, are beginning to question some of his methods and some of the conclusions reached by him and other commentators at

Recently, John Gasaway, another writer and commentator at this web site, known to many college hoops fans formerly as the entertaining and irreverent, Big Ten Wonk, wrote an article asserting that basketball writers were wrong to award Tyler Hansbrough the 2008 Player of the Year Award.

Based upon Gasaway's analysis of their statistics. Kevin Love of UCLA, and nephew of the Beach Boys, believe it or not, deserved the award, Gasaway tell us, and that is that. Love is best--wasn't that a Beach Boys' song or was it the Monkees?--and Hansbrough should be happy being second best. After all, it was good enough for Avis, wasn't it?

Now to be fair, Gasaway has made his name by being hardhitting and writing with a certain verve and flair and this article seemed to get plenty of attention. Somewhat like J.J. Redick or Bobby Hurley, Hansbrough seems to be the kind of person that many people dislike because they feel like he gets too much media attention, although it is hard to believe that a 6' 10", basketball-playing, nephew of the Beach Boys is likely to be underexposed by the media. Happily, there doesn't seem to be any racial issues at play, as both Love and Hanbrough are, well, kind of big, goofy-looking white guys.

I am a big fan of revisionism, myself, so what's the problem you might be asking,

Well, Gasaway tries to make statistics do something that they simply can't do here. First of all, he really didn't have a lot of data upon which to base a conclusive determination. While snarkiness is a trait that I highly admire, the emperor needs to have a bit more clothes on before engaging therein--Gasaway is scarcely wearing a banana hammock with the data he presents.

UCLA and UNC, the teams of the two players that Gasaway compares, haven't played this year and they play in two different conferences whose teams rarely play head to head. Gasaway never tells us how reliable his data are, whether they are significant, or how he can compare two guys conclusively who are not playing in the same league. This differs greatly from baseball, where until recently, all teams in the same league played exactly the same schedule with a number of iterations (162) which produces much nicer and more reliable data sets.

Perhaps even more importantly, Gasaway fails to discuss the defensive sets that UCLA and UNC both employ and how that might affect defensive rebounding, nor does he alert the reader to the facts, as to whether or not Hansbrough's team, is indeed, the better rebounding team overall, perhaps due to Hansbrough place in that scheme.

Secondly, the data Gasaway did have, seemed pretty even. Perhaps he knows so much more than the rest of us about the value of defensive rebounding, which is basically the crux of his argument against Hansbrough and in favor of UCLA post man, Kevin Love, that he doesn't feel the need to explain. Nevertheless, not all that many people seemed convinced by his argument. A quick internet search shows even Duke people deriding Gasaway's arguments.

One sentence particularly stands out for me: "The Player of the Year award rightly belongs to the player who's as good as Hansbrough on offense, but vastly superior to Hansbrough on defense. It rightly belongs to Kevin Love." This stands out because it reminds me of what legal writing teachers and many judges often point out.

When lawyers don't have cases or statutes that are open and shut, they tend to fall back upon words such as "clearly," or "vastly," because in fact, they implicitly recognize that the case they are arguing is far from open and shut. Some judges go as far as telling their law clerks to circle it in red every time a lawyer uses the word "clearly" in his legal briefs, just so the judge can be clear about what the proponent's weakness in fact, are. Recently, another writer at the site has tried to tip-toe away from what Gasaway in fact said, but Gasaway's article makes it clear that he will brook no debate.

I won't go into a full statistical rebuttal, as others have done this, but I will reiterate that while Gasaway makes some good points on behalf of Love, ultimately, his article fails because it doesn't carry its premise.

Surely, I am biased. I am a Carolina and ACC fan, but that doesn’t mean that I am not also a basketball fan first and that I don’t want to know what really makes the game tick. Nevertheless, when things don’t make sense to me, I am not just going to receive the wisdom from on high. The baseball stats guys generally don’t do that. They argue about everything, from the value of base stealing to whether pitchers can cause ground balls or prevent home runs, until people are generally convinced of the truth of their assertions.

One reason, in fact, that Pomeroy has many Carolina fans as readers is because his site has tended to advocate many of the basketball insights utilized by North Carolina coaches such as Frank McGuire, Dean Smith and Roy Williams, and Carolina fans are more than willing to debate these issues, but understandably did not much like it when Gasaway laid down the gauntlet and essentially said, "if you are a stats guy, then you support Kevin Love as player of the year over Tyler Hansbrough.

The other important point is that I don’t believe that Gasway realizes that he has traded in his Big Wonk hat for a different one at Basketball Prospectus, where we expect him to develop detailed arguments with data, not to decide things for us based upon his seeming whims, likes and dislikes. He had that freedom as the Big Ten Wonk, but now he should be applying sounder principles or at least, how about a disclaimer?

I will give him credit for starting a debate about the true worth of players, although let the record reflect that the awards are generally called either Player of the Year or Most Valuable Player, not most efficient, and may indeed, include recognition for attributes such as exceptional hustle or guts.

He starts out by making some interesting arguments that made me want to watch Kevin Love some more and which make me wonder if Love isn’t the top player this year. Thankfully, Gasaway only obliquely makes the often prevalent and irrelevant and unprovable argument ad hominem, that Love will be a better professional player than Hansbrough.

But Gasaway ends up precluding you and me from deciding for ourselves based upon watching the two of them and their teams play, and then taking a look at their stats. Gasaway has determined that Love is better and there simoly is no way around that.

This is silly because first of all, there is not a lot of difference that I can see between the numbers Gasaway presented. Secondly, unlike a full season of baseball where raw data is more persuasive, Gasaway seems to think that we don’t even need to watch the guys to know who is better.

This seems especially specious, given that virtually everyone who watches Hansbrough comes away impressed by the sheer audacious will and tenacity that he shows on the court. Love looks good out there too, but not in the crazed, frenetic, win at all costs manner that Tyler has. Coaches and commentators from Dick Vitale to Billy Packer to Coach K have all expressed the notion that Tyler Hansbrough is sui generis and they derive this belief from having watched him and thousands of other players in person during their lifetimes.

But according to Gasaway, their eyes deceive them. Hansbrough isn't so special at all. Just look at the stat sheet, you dunces, and you will see it.

I guess there was a similar argument years ago regarding East coast and West coast jazz and we all knew who won that one.(East coast). But just imagine if someone told us we should just look at the sheet music without ever actually listening to it, in order to decide which was “best.”

Gasaway’s approach, whether he realizes it or not, is anti-basketball. You don’t even need to watch the games and just based upon a few statistics, he can tell you who is better.

This is not the way that Dean Oliver did it. Take a look at his book. He talks about stats being persuasive but doesn’t tell people that it is his way or the highway. I recently did a short review of one of his chapters where Oliver purports to tell us who was better, Wilt or Bill Russell, and guess what, Oliver goes through all the arguments and then makes a hypothesis but lets us draw our own conclusions. That is how you do it, not by trying to shove it down people’s throats.

Well, that is enough for now--I won't even go into the issue of Ken Pomeroy's allegedly fudging his possession calculations, which makes Carolina look even worse on defense than it actually is, and to those who think that I am making mountains out of unimportant molehills, well that is true, but I can't always be writing every article about the incredibly large U.S. prison population as it gets depressing after a while, no?

Math, March Madness and Michael Jordan

Given that we are in the midst of March Madness and that I am a huge basketball fan, I thought that I might address some of the things going on out there in the college basketball world.

One of the more interesting trends to me, is the continuing adoption of applying statistical methods to basketball, in an attempt to follow in the footsteps of baseball, which has a big headstart over its basketball stats devotees. For those interested, the Bible would be the book, Basketball On Paper, by Dean Oliver, in which the author attempts to combine the methods of Bill James with the coaching philosophy of Dean Smith.

It is a great and instructive book whose only lacking is that it focuses on the NBA instead of the vastly more interesting college game, presumably due to the greater availability of statistical data from the professional league.

One thing in the book that I found especially interesting is that Oliver attempts to answer the decades old question as to who was better between Wilt Chamberlain and Bill Russell. He doesn't really answer the question, which may be to his credit, as basketball is a team game after all. We have lately seen other writers who make a pretense of using statistical analysis to give definitive answers as to which of two excellent players is better, which actually ends up being more opinion than statistics based.

For examples of this, see a recent article on Basketball Prospectus, a little brother of Baseball Prospectus, trying to find its feet:, in which the writer makes some jarring leaps to conclusions based upon fairly even and imperfect statistical data, and does this without even deeming it necessary for a person to have seen the two players in question in game action. This is the misuse of statistics and it obscures rather than elucidates in helping the fan understand what makes players and teams successful.

Oliver, by contrast, uses the numbers to try to analyze each player's strengths, recognizing that the numbers are not enough to carry the day either way.

What Oliver concludes about Russell and Chamberlain, is that basically Russell played on teams that always had several Hall of Famers on them during his career, while Chamberlain did so only a couple of times.

When Chamberlain was accompanied by Hall of Fame caliber talent like Billy Cunningham, Chet Walker, Gail Goodrich and Jerry West, he broke through and won two championships, altering his game to focus more on defense and rebounding in the process.

By winning two NBA titles, Chamberlain stands among the few all time greats who have even won more than one, given the Celtics dominance up to about 1975. His two championship are more than this following Hall of Fame contingent, all of whom were his contemporaries, and who either won only one title or none at all: Jerry West, Elgin Baylor, Nate Thurmond, Walt Bellamy, Jerry Lucas, Oscar Robertson, Elvin Hayes, Rick Barry, and Wes Unseld. And yet, none of these great players has ever been deemed a "loser," in the way that Chamberlain has. Also peculiar is the way that Chamberlain was derided for his foul shooting, when he was essentially even with Russell statistically in free throw percentage.

It is also worth noting that Chamberlain bridged the careers of Bill Russell and Kareem Abdul-Jabbar, the two most successful centers in NBA history in terms of winning titles and Wilt's teams dethroned both of them, in 1967, with the 76'ers annihilating the Celtics in five games, and in 1972 with the Lakers defeating the 66-16 defending champs, the Bucks, in 6 games.

But unlike the 7' 4" Tom Burleson with NC State, who along with David Thompson dethroned the smaller Bill Walton and UCLA after years of Bruin dominance, did Wilt ever get his due for ending the Celtics string of 8 titles in a row? Not really.

Ultimately, for Oliver, Russell may have been better for a team like the Celtics, which had many great shooters and scorers, while Wilt was the player who could take a team to respectability overnight all by himself.

But to me, what was even more interesting is that Oliver then ends up more focused on evaluating Wilt, who retired in the early 1970's, as compared to Michael Jordan, the greatest player of more recent times.

Just looking at the raw numbers, one wonders how anyone could compare to Wilt, who scored 100 points in a single game while playing for coach Frank McGuire's Philadelphia Warriors, and who averaged over fifty points that season while carrying his team to an excellent second place finish to the Celtics, of course.

But what Oliver points out, is something completely counter-intuitive. Basketball was played much faster in the 1960's than it is today. There were far more shots taken per game back then, which resulted in higher scoring and higher rebounding averages. It's just those jerky film clips that make them seem so awkward and slow!

After adjusting the numbers garned by Chamberlain during his career and then adjusting for the difference in tempo in the way the game was played, Oliver discovers that Wilt was indeed overrated and nowhere close to the unmatchable titan that we all imagine when looking at his raw stats.

Wilt was human,and after adjusting his statistics downward to account for all the extra shots and rebounds, it turns out that Wilt in actuality was probably only a little bit better than Michael Jordan!

But if anyone out there saw both of them play and wants to make an argument the other way, Oliver gives us the tools to help make more concrete arguments with data about which player we ultimately prefer. But let's not get the horse before the carriage.

Basketball is a beautiful thing to be watched first and enjoyed and then just maybe, the data can help us understand and appreciate the sport even more. But you have to watch and see the players to really know and for those of us too young to have ever seen Chamberlain, we will just have to read the accounts of those who did and watch old game films. The numbers by themselves will never be enough.