Do Stats Lie?

Lately I’ve been thinking about the greatest offensive team of the last 20 years. Led by Michael Adams and Orlando Woolridge the mighty 1991 Denver Nuggets punished opponents by scoring 119.9 points a night. That Nuggets offense just beats out the the 1992 Mullin-Hardaway Warriors (118.7 pts/g) and the 1989 Chambers-K.J. Suns (118.6 pts/g). Certainly since the 1991 Denver Nuggets scored more points per game than any team since 1987, they were the NBA’s best offense in that timespan.

Or are they? This seems to be a dubious claim. Looking at the 1991 Nuggets, none of the players were voted to the All Star team that year. There aren’t any Hall of Famers on that team. Denver went a rancid 20-62 that year. Of the three teams above, there are no champions. No Michael Jordan. No Magic Johnson. No Larry Bird. No Shaq. No Steve Nash.

How can a 20-win team be one of the great offensive teams of all time? You might say that the stats are “lying” because they’re misrepresenting what we believe to be true. But that’s not the case. The numbers are 100% accurate. If you watched every game of the last 20 years, you would not have found a team that scored more points in a season than the 1991 Nuggets. Saying the 1991 Nuggets scored the most points per game in the last 20 years is true. Saying the 1991 Nuggets are the best offensive team in the last 20 years is false. The deception is in the interpretation of the statistics, not in the stats themselves. The problem is in equating “most points per game” with “best offensive team”. The correct interpretation for “most points per game” is “most bountiful offense”, which is quite different from “best offensive team”.

Take this example: Going into the 2007 season, the Chicago Bears have a good chance to win the Super Bowl. One vegas line has their odds at 8-1 to win it all. One of their best players is Rex Grossman who has a fantastic 17-5 record as a starting QB.

Once you pick yourself off the floor laughing, it’s easy to see where the fallacy is. The Bears do have a good chance to win the Super Bowl this year. Their odds to win, at least from one vegas site, is 8-1. Rex Grossman has a 17-5 record as a starter. All these things are true. However they’re not one of the best teams in the NFL due to their QB. Rex Grossman is by all accounts a bad quarterback. Carson Palmer, an All Pro, has a winning percentage of only 55.6%. The deception is in saying that QB win percentage indicates the quality of the QB. There are better ways to judge the ability of a QB like completion percentage, TD-INT ratio, yards per attempt, etc.

Getting back to our original example, those 1991 Nuggets scored so many points per game because they ran a very fast offense (and also a very fast defense). Denver led the league in pace averaging 113.7 possessions per game. To show how much an aberration this was, the league average was only 97.8 and the second fastest team was the Golden State Warriors at 103.6 possessions per game. A team can increase its points per game by simply increasing its pace. This reveals a flaw in the relationship between “points per game” and “best offense.” It’s obvious that points per game isn’t the best measure of a team’s offensive capability.

To more accurately judge which team had the best offense, you need to account for this disparity in possessions per game. Offensive efficiency, sometimes known as offensive rating, calculates how many points a team scores per possession (or more accurately 100 possessions). The importance of offensive efficiency is that it evens the playing field between the fast and slow paced teams. The 1991 Nuggets had an offensive efficiency of 105.2, which placed them 21st out of 27 teams that year. The best offensive team in 1991? The Chicago Bulls, who scored 114.9 points per 100 possessions. This was Jordan’s first championship team, and clearly they were better than the Nuggets on offense that year.

In the end, stats don’t lie. They are numerical records of history. The 1991 Denver Nuggets did score 119.9 points per game. Rex Grossman had a record of 17-5 as a starter going into 2007. The problem is not in the numbers, but rather the people that use these statistics to make claims that they don’t support.


  • For more information on points per possession, check out Dean Oliver’s excellent book: Basketball On Paper. Or read this and that.
  • During the season I keep track of offensive efficiency on the stats page. Historical offensive efficiency can be found at
  • The team with the highest offensive efficiency over the last 20 years? The 1996 Bulls at 115.8. Does this make them the best offensive team of the last 20 years? Well you might want to account for league average, but that’s a discussion for another day.
  • For more information on the 1991 Nuggets, see this link.
  • For a really good way to rate QBs, I would use DVOA.

One More Nail In the Anti-Per Minute Argument’s Coffin?

One of the core tenets of basketball statistical analysis is the usage of per minute stats. When compared to per game stats, per minute stats are highly valuable in the evaluation of individuals. This is because per minute stats puts players of varying playing time on the same level. Using per game stats, starters will always dwarf bench players due to the extended time they get to accumulate various stats. Meanwhile per-minute stats allows to compare players independent of minutes, allowing for a more even approach in player evaluation.

Recently a debate has come up on the validity and usefulness of per minute stats. I’ve quoted the main parts below, but even abbreviated it’s a long read. If you have the time, I suggest reading it now so the rest of this article will make more sense. For those on a limited time constraint, a quicker summary is here:

Hollinger & Kubatko: “Hey per minute stats are a great way to evaluate players! In fact we’ve done a few studies and it seems that a player’s per minute stats increase slightly when they get more minutes. At the worst we can conclude that they should stay relatively the same.”

FreeDarko: “Per minute stats won’t stay the same if a player gets more minutes, because there is a division between greater and lesser players. A player that only gets 10-25 minutes per game is playing against lesser caliber players. Hence when that player sees an increase in playing time, he’s playing against steeper competition, so his stats should decrease.”

Tom Ziller: “That’s not true. Here is every 10-25 minute player in the last 10 years that saw an increase in minutes. Most of them (70%) saw an increase in per-minute production. To discount any of this data being from young players getting better as they age, I looked at 8+ year vets, and saw that about the same ratio of players increased (69%).

Brian M.: “Tom, the problem with all this data is a causality vs. correlation issue. It’s possible that these players saw more minutes first then improved. But it’s also possible that these players improved first which allowed their coach to play them more minutes.”

Brian’s case is a good one. To use an analogy, imagine I come across a person who calls himself Merlin Appleseed. He claims that just by touching apples he can magically make them taste better. He opens up a box of apples saying that he never touched any of them. He picks out 10, and imbues them with his magic. He asks me to taste each of them. I find all of them to be delicious. He says “here’s the same box I got my apples from. Now I want you to take 10 at random while blindfolded. You can compare them to my magic apples. I bet mine taste better.” I do just as he asks, and indeed my random set of apples are less tasty than his. So does Merlin Appleseed have magical power?

Maybe. Unfortunately this test wouldn’t be able to confirm or deny his magical power. Since Merlin gets to choose his apples, he might be selecting the best ones! To test Merlin’s abilities I would need something to gauge how good his apples are expected to taste. One way to do this would be to find comparable apples that have the same color, size, blemishes, etc. Then I can compare the taste of his apples to my apples. If Merlin’s has the magical powers he claims, then his apples will taste better than my apples.

Similarly with Tom’s study, Brian is saying that by selecting players who have seen an increase in minutes we might be choosing the best apples. This is because players who improve on a per minute basis could be given more playing time by their coaches. Therefore to show whether or not these players have improved, I need to find how good they’re expected to be. Then I can compare their actual performance to their expected performance. If FreeDarko’s theory is true, that role players should decrease their per minute production with more minutes, then they should perform worse than their expected values.

To separate the control group from the test group, I’ll only use players with an even numbered age for the control, and odd numbered ages for the test group. Since this study is intended for role players, which was defined by Ziller, I limited my control group to player seasons where:
* The player age was an even number.
* The player appeared in 41 games or more.
* The season was 1981 or greater.
* The player averaged 10-25 mpg.

Now I can calculate the expected production of the players in my group, by looking at per minute production (PER) over playing time (mpg).

Control Group

Just as expected, the graph tends to go from the bottom left (low production = low minutes) to the top right (high production = high minutes). That is players who receive more minutes are more productive. From the 1840 player-seasons in my data, I’m able to calculate the expected PER based on mpg (PER = .2158*mpg + 8.2941). So if a player averaged 10 mpg, you would expect his PER to be 10.45. This equation is represented by the red line on the graph.

Now that our control group is defined, I need to create the test group. Again this group was defined by Ziller as role players who saw an increase in minutes. I selected player seasons where:
* The player’s age was an odd number.
* The player appeared in 41 games or more.
* The season was 1981 or greater.
* The player averaged 10-25 mpg the year before.
* The player increased his mpg by 5+ from the year before.

Since I have the expected values based on mpg, all that is left is to compare their actual production to the control group. In our test group 185 players did better than their expected PER, while 177 did worse. On average each player gained 0.17 PER. This is a tiny gain, not enough to show that players increase production with more minutes. However it clearly shows that they didn’t decline and at least matched the predicted PER.

Another way to see how our prediction did is to calculate the regression (trendline) of this group, and compare it to the expected equation. The red line in the graph below shows the regression of PER/MPG for our control group.

Test Group

* Control: PER = .2158*mpg + 8.2941
* Test: PER = .2185*mpg + 8.3917

The test group, which has both the higher slope and y-intercept, will slightly outperform the control group. But not by much. The average player who saw 40 mpg, will see a .20 increase in PER, which is negligible. In other words, the test group has neither exceeded nor fallen short of our expectations, but rather has met them.

In the end what does this prove? Specifically this study removes the correlation between the role player group and players that saw extra minutes due to improvement. It debunks the thought that there is some kind of division between per minute stats, where the per minute stats of high minute players are more a representation of actual talent than those who play few minutes per game. But combined with the past works of Hollinger, Kubakto, and Ziller, among others, it makes an overall stronger statement. Players who receive 10 or more minutes per game are likely to keep the same per minute stats no matter what the increase in playing time is. Therefore per minute stats remains far superior to per game stats in terms of comparing and evaluating players.


  • “It’s a pretty simple concept, but one that has largely escaped most NBA front offices: The idea that what a player does on a per-minute basis is far more important than his per-game stats. The latter tend to be influenced more by playing time than by quality of play, yet remain the most common metric of player performance.” — John Hollinger
  • The great thing about this study is that I can perform it again, this time using the “odd” aged players as the control and the “even” aged players as the test group. This time the prediction equation was PER = .2039*mpg + 8.4439. And again our test players slightly outperformed the average. This time 192 did better than their expected PER, while only 161 did worse. On average each player gained 0.23 PER.
  • This article doesn’t mean that every player that has good per minute stats should see more playing time. It’s very clear that basketball stats don’t capture a player’s total ability. A player that does well on a per minute basis may have other flaws, such as poor defense, which prevent him from contributing more. This also isn’t an endorsement for any single per minute ranking system, like PER, WOW, etc. There are flaws in each of these in addition to being unable to account for attributes not captured in box scores.
  • Summary of the events that led to this article.

Back in 2005, I wrote an article outlining some of the pioneers in per minute research.

In the 2002 Pro Basketball Prospectus John Hollinger asked and answered the question ?Do players do better with more minutes?? For every Washington player, Hollinger looked at each game and separated the stats on whether or not he played more than 15 minutes. He found that when players played more than 15 minutes, they performed significantly better than when they played less. To check his work, he used a control group of 10 random players, and each one of those improved significantly as well.

The knock on Hollinger?s study is the small sample size, containing less than 25 guys from only one season. Enter Justin Kubatko, the site administrator of the NBA?s best historical stat page Earlier this week Justin decided to re-examine the theory using a bigger sample size. Taking players from 1978-2004, he identified 465 that played at least a half season and saw a 50% increase in minutes the year after. Three out of four players saw an increase in their numbers as they gained more minutes, although the average increase was small (+1.5 PER).

Two independent studies have shown that NBA players get better when they get more minutes. A conservative interpretation is that per-minute numbers are universal regardless of playing time. So if a player averages 18 points per 40 minutes, he?ll do about that regardless of how many minutes he plays. A more liberal summary would say that underused players will see an improvement in their per-minute numbers if given more court time. A player that only averages 20 minutes a game is likely to be a little bit better if given 35. So the straight dope is per minute stats are a fantastic way to evaluate NBA players.

Recently, this research was questioned by the writers of freedarko.

The problem with this line of reasoning is that it assumes the homogeneity of court time. It assumes that if a player scored 20 points in 20 minutes, he would also score 40 points in 40 minutes. That there will by systematic differences between these two situations is almost too obvious to point out. It’s the difference between sharing the ball with Jordan Farmar while being guarded by Kenny Thomas, and sharing the ball with Kobe Bryant while being guarded by Ron Artest.

Insofar as the problem here is one of rotation, small-scale adjustments in minutes played shouldn’t create major distortions (it isn’t unrealistic to think that if Tim Duncan played 5 extra minutes per game, his per-minute production, as influenced by the level defense he’d face, would basically be the same). But when PER catapults bench players into the starting five (or vice-versa), be on the look-out for inflation. Call this the Silverbird-Shoals Hypothesis, or the THEOREM OF INTERTEMPORAL HETEROGENEITY (TOIH).

Enter Sactown Royalty’s Tom Ziller, to refute Free Darko’s theory.

Shoals and Silverbird are arguing that because low-minutes high-PER guys typically play against fellow bench players, their PER is higher than it would be if they played starter minutes. They aren’t arguing (as some surmised) that PER is useless, just that it is prone to inflation. The argument, from seemingly everyone on the ‘anti per-minute statistics’ side, is that if you increase a player’s minutes, his efficiency will suffer.

There’s a problem with this oft-repeated claim: It’s not true.

Thanks to the data-collection efforts of Ballhype’s own Jason Gurney, I’m going to try to ensure this claim never gets stated as fact ever again. Using seasons from 1997-98 to the present, we identified all players whom played at least 45 games in two consecutive seasons and whom saw their minutes per game increase by at least five minutes from the first season to the second. The players must have played between 10 and 25 minutes per game in the first season, to ensure we were not dealing with either folks who went from none-to-some playing time or superstar candidates who took over an offense and thus got a minutes boost. This is aimed at roleplayers whose role becomes more prominent — exactly the candidate FD’s Theorem of Intertemporal Heterogeneity implies will suffer from increased minutes.

Since I seem to express myself more clearly via Photoshop, here is the result of our mini-study.

No, increased minutes do not seem to lead to decreased efficiency. In fact, the data indicates increased minutes lead to… increased efficiency. More than 70% of the players in the study (there were 251 in total) saw their PER (which is, by definition, a per-minute summary statistic) increase with the increase in minutes. Players whose minutes per game increased by five saw an average change of +1.38 in their PER. The correlation between increased minutes and change in PER in this data set was +0.20.

One step further: Players who had at least five years of experience including their first-season in this study and got the requisite 5-minute increase (106 such players) saw an average change of +1.26 in their PER. It’s not just young kids who happen to improving and getting more minutes all at the same time — vets who get more minutes typically see their per-minute production rise. A full 67% of these players so positive changes in PER with the increased minutes. (And this answers one of Carter’s concerns with existing studies.) Let’s bump this up to players who had at least eight years of experience going into their minutes increase; we had 52 such cases. The average change in PER: +1.31. Of these players, 69% saw their PER increase with more minutes.

Case closed right? Well not if Brian M. has something to say about it.

Imagine we wanted to test the relationship between duration of exercise and reports of fatigue. We have two experimental conditions, one group jogs for 10 minutes and the other for 30 minutes. We predict that the group that jogs 30 minutes will report more fatigue.

But we must assign people to the two groups randomly in order for the data to have any bearing on the hypothesis. If we systematically assign people who are in better shape to the 30 minute jogging condition, we may find that in fact, if anything, people report less fatigue with longer durations of exercise. But the study is flawed in a fundamental way and so the data don?t tell us much of anything. At most what the results of this poor experiment tell us is that the effect of exercise duration on reported fatigue is not so strong that it overrides the differences in health between the two groups. But that is a really limited conclusion, especially if we don?t even have means to quantify how much the two groups differed in health to begin with.

A New Standard?

Last night I had a nice column written about baseball, basketball, and statistics. Unfortunately when I hit the save button, my browser notified me that was down for scheduled repairs. Hitting the back button, revealed to me what I had dreaded, that my entire blog was gone. In another parallel universe I imagine my readers enjoyed an entertaining column. Barring a Stan Lee spectacular bending of the laws of physics sending me to that universe to save my blog, I’m just going to have to rewrite the darn thing.

In baseball there is a simple notation to represent hitters. I don’t know when it became common to represent players this way, but I remember as a kid that when a batter came up to the plate you saw three numbers that were suppose to represent their hitting skills. For example it might say “Jackson .286 – 32 – 110” (BA – HR – RBI) for Reggie’s first season as a Yankee. Just three numbers would tell you that Reggie was a better hitter than fellow teammate Roy White .268 – 14 – 52.

A lot has changed in the world of sports since Mr. October roamed the Bronx’s greens. Today there is a large group of fans that understand that those three stats aren’t best representative of a hitter’s worth. However the three number notation lives on for cutting edge sports columnists. Today the three numbers are BA/OBP/SLG. It’s because these three numbers are very representative of a player’s worth. Let’s look at two of Reggie’s back to back seasons:

Old Notation:
1978 .274/27/97
1979 .297/29/89

By the old notation, these two seasons look about the same. If you had to choose one, you might flip a coin.

New Notation:
1978 274/356/477
1979 297/382/544

By the new notation it’s clear that Reggie’s second season is the far superior one. This is a huge advantage when talking about baseball players. With a small amount of data, you have a good idea of a player’s worth.

The question is can we apply this to basketball? The first thought that came to my mind was to use shooting percentages: FG%, 3P%, and FT%. So Allan Houston’s career numbers look like 444/402/863. It tells us that when Houston does shoot he’s very accurate from downtown & the free throw line. The problem is it doesn’t tell us how good of a player Houston is. Put Houston’s line next to Kobe’s, and it would seem that H20 is the superior shooter:

H20 444/402/863
Kobe 454/331/833

We could use more accurate measures of skill, PTS/G, PTS/MIN, eFG%, or TS%, but shooting is only one aspect of a basketball player’s game. For baseball hitters, their hitting is a large part of their game. Sure there are differences between positional players (SS & C hit worse than OF & 1B), and some players are better defensively than others (Irod & Piazza). Defense in baseball is primarily handled by pitchers, so it isn’t as important an aspect as it is in basketball.

Actually in basketball there is more than just shooting and playing defense. Rebounding and passing are also integral roles. Right now due to two recent events, I think we have a way to approximate a player’s skill. Due to the hard work of Jon Hollinger we have a stat that incorporates a player’s total value, called PER. PER is a good approximation of a player’s total offensive value, but is a bit lacking on the defensive side. In comes the guys at Not only do they calculate a player’s PER, but the PER of his opponent at the same position.

You would think we’d have a pretty good idea of a player’s ranking, but defensive PER isn’t a precise measurement. Let’s assume Stephon Marbury has blown by his PG defender & is heading for the hoop. Marbury’s chances of scoring are less if Tim Duncan or Ben Wallace is that person’s teammate than a lesser defender (let’s say uhhhh… how about Wang Zhi-Zhi). So players that have good defenders on their team will do better than those that have poor defensive teammates. Same thing for guys like Bowen and Artest who routinely will take on the better offensive player, leaving guys like Ginobili and Miller to handle the easier assignment.

So a third number is needed. I prefer Roland Rating, which is a +/- number that shows how the team performs relative to the player being on or off the court. It’s certainly flawed as well. For example if a player has a weak substitute or strong teammates, his +/- might seem higher. Not one of the three stats are all encompassing, but I prefer having some kind of cross between tabulating individual effort with a +/- system that may catch some things that aren’t calculated by traditional means.

Let’s just take a look at a system like this. Reggie Miller has a very good Roland Rating (+11.7), about as good as Shaq & Kidd (+12.1). Our intuition tells us that Miller isn’t that good, so we look at his PER numbers: 16.8 on offense and 10.5 on defense. An average PER is about 15, so Reggie is pretty good if the defense is actually his doing and not Artest’s. However we know that Reggie isn’t in the same league offensively as Shaq (25.3) or Kidd (20.4). Reggie’s numbers by my notation would look like 16.8/10.5/+12.1. We can probably round off to the nearest PER so 17/11/+12.1. Here are a few NBA stars in no particular order:

Name	PER(O)	PER(D)	RR+/-
Shaq	25	11	+12.1	
Kobe	24	14	+6.8
KG	31	14	+20.2
Duncan	29	12	+9.3
T-Mac	26	17	+4.4
Dirk	24	18	+8.6
Yao	23	11	+5.9
Kidd	20	14	+12.1
AI	20	16	+0.7
Stoja	22	16	+6.6
Carter	21	13	+10.4
Marbury	21	15	+1.6

A few things to ponder about this system. Duncan has a lower Roland Rating than some other players, but his PER numbers are excellent on both ends of the court. Kidd is thought of as a great defender, so his defensive PER is puzzling. However his Roland Rating is an excellent 12.1. Just looking at the PER numbers you’d think Marbury is on Kidd’s par, but Marbury’s low Roland Rating shows the difference.

This certainly not the greatest way to measure a player. Everyone from Dean Oliver to Kevin Pelton to Bob Chaikin to Dan Rosenbaum all have ways that may better represent how good a player is. However I don’t have the tools (or the brains) to do the type of calculations that they do. With only a few clicks I (or my readers) can look up any current player. It’s relatively easy to do and you can compare players in different positions on different teams. Looking at the above chart, it seems that with a few numbers, I have gauged the overall worth of those players.

NOTE: Edited by me Thursday Morning 9am, after a night of sleep. Only small changes were made to better illustrate my ideas.

Quick Recap Of My Finals Thoughts

Early in the series, I wrote what the Lakers and the Pistons each needed to do to win. I think since we’re half way through the series I should revisit what I wrote:

For Detroit to win, they should:
1. They can’t fall too far behind, which breaks up into:
1a. Score. They need efficient scoring from Hamilton, Billups, and Rasheed. If they can get an outburst from someone else (Prince), then all the better.
1b. Shut down the non-Shaq Lakers.
2. Stay close in turnovers.

For all you chart fans, here’s one breaking down exactly what I wrote.

Name	G1	G2	G3	G4
1a. -- Efficient Scoring --
Hamltn	N	Y	Y	Y
'Sheed	Y	N*	N	Y
Billps	Y	Y	Y	Y
Others	Y	N**	Y	N
1b. -- Shut Down non-Shaq Lakers --
Kobe	N	N	Y	Y
Others	Y	Y	Y	Y
2. -- Stay Close In Turnovers --
*Game 2 Sheed 11PTS 5-14 - scoring but inefficient.
** Ben Wallace was 2nd best with 12 points in an OT game.

As for the Lakers:

1. Score, and not just Shaq. Kobe, Malone, and one random Laker per game. It’d be nice if Gary Payton would actually do something to earn that ring. If not anyone will do: George, Fisher, Rush, or anyone. By scoring they’ll put the pressure on the Pistons to score as well. The Pistons weren’t a great offensive team, so shutting them down shouldn’t be all that hard.
2. Turn the heat on with turnovers. The Lakers were 7th in the league in net turnovers (per 100 possessions), so they should be able to get some extra points from the Pistons.
3. Get to the foul line, and not just Shaq. Shaq will make Detroit foul more often. Normally Detroit is very good at not putting opponents at the line. The Lakers need to use Shaq to gain an advantage here. The rest of the gang have to drive to the hoop & try to make things happen.

Name	G1	G2	G3	G4
1. -- LA Scoring --
Shaq	Y	Y	N	Y
Kobe	Y	Y	N	N**
Malone	N	N	N	N
Others	N	N	N	N
2. -- Create Turnovers --
3. -- Get To the Foul Line --

*L.A. had 25 FTA, but Detroit had 31
** Kobe had 20PTS but shot 8-25 (2 3PTM)

Look at all the Y’s in the Pistons’ table and the N’s in the Lakers table. It seems clear that Detroit is doing almost everything they can to win. It seemed that the Pistons’ biggest weakness would be scoring, since they don’t have the great scorers that the Lakers have in Shaq and Kobe. However, they’ve been able to get production from 4 guys: Hamilton, Billups, Rasheed, and Prince. They’ve won every game where they’ve gotten offensive production from at least 3 of these players.

On the other hand, the Lakers haven’t done anything they’ve needed to win. Their offense has been horrible. The Pistons have “let” Shaq score, but have tried to shut down everyone else. Kobe has been ineffective since game 2. I can’t blame Karl Malone, because he’s been hurt, but where are the rest of the Lakers?

During the regular season, Detroit turned the ball over often enough (20th in TO/Poss), and the Lakers were 7th in net turnovers. I expected the Lakers to have an advantage in Turnovers, but it has been a non-factor. The other place where I thought L.A. could make a difference would be to use Shaq to get the Pistons in foul trouble. My prediction was way off base here, since everyone knows by now that the Pistons are getting to the line while the Lakers are begging for calls.

This series hasn’t been close. What’s really amazing is if it weren’t for Kobe’s three point shot at the end of regulation in game 2, the Pistons would have swept the Lakers. In fact since that game, the non-Kobe & non-Shaq Lakers are 25-79 (7 3PTM – eFG% 36%). Detroit’s defense is just that good.

Does Phil Have A Legitimate Gripe?

In my recap of game 1, I wrote:

The Pistons only sent three Lakers to the foul line: Shaq, Kobe, and Medvedenko. That was expected by the stat-heads, but I’m sure that Phil Jackson will point this out to the media sometime in this series try to get some calls go his way. I wonder how effective this is, since he seems to do it every year.

Everyone can set their watches to “NBA Finals”, since Phil is at it again. Yes he’s appeared on just about every sports news channel noting the disparity of fouls called in the series. In another one of my posts, I noted how good Detroit was in not fouling their opponents:

Factor 4. Free Throws (FTM/FGA)
LA	.244	107%	7th
DET	.247	108%	4th
LA	.222	103%	16th
DET	.202	113%	3rd

The numbers clearly show Detroit as one of the best teams in the league in this respect. They are 8% better than the league in getting to the line, and 13% better in sending their opponents to the foul line. So it comes at no shock to me that Detroit is getting to the line more often in the Finals.

The question becomes does Jackson have a leg to stand on, or is he crying wolf as always? We should be able to figure out how many fouls to expect in this series, but it isn’t as simple as you would think. I hate to switch sports, but baseball makes this analogy easier. Let’s say Ken Harvey, currently hitting .360, is facing Mark Redman, who batters have hit an even .300 against. What would you think Harvey’s odds are of getting a hit.

A. .360 (Ken Harvey’s BA)
B. .300 (Redman’s oppBA)
C. .330 (the average between A & B)
D. .398 (hmmmmm)

If you said D, you are correct. If it doesn’t make sense, think of it this way. Ken Harvey is a good hitter facing a bad pitcher. He should hit higher than he normally does. Here is the equation I used to come up with .398, basically you are comparing both averages to the league average.

So let’s get down to the numbers:

Free Throws Made / 100 possessions
LAL	17.0	17.9	9.1	14.7	21.7
DET	25.6	23.8	25.0	24.8	24.0

For those of you that are chart-ally challenged, it says the Lakers should hit about 21.7 free throws (per 100 possessions), but in the series so far they’ve only hit 14.7. Detroit looks right on target with what they’re averaging to what is expected. Let’s double check and check out free throw attempts:

Free Throws Attempted / 100 possessions
LAL	21.9	26.3	14.7	21.0	27.6
DET	36.6	35.1	35.7	35.8	27.5

Ouch! The Lakers are nowhere near where they should be, while the Pistons are exceeding their average by a large amount.

There are many reasons why this is occurring. One could be Phil Jackson’s theory that the officials are calling a one sided game. Another is Larry Brown’s theory that the Lakers are taking more three pointers than normal. Is this even true?

Three Pointers Attempted / 100 possessions
TEAM	G1	G2	G3	Fnls	Reg Season
LAL	15.8	17.9	30.6	21.4	14.5

Coach Brown could have a point here. They’re taking a lot more threes than normal. Right now I’ll take the diplomatic approach and say they’re both right. The Lakers should get more calls, and maybe Phil should send some of his players towards the hoop to achieve this.

Predicting the Finals (The Long Way)

Predicting sports events is a losing endeavor. There is a reason that gambling is a such a lucrative business, for the bookmaker that is. Professional gamblers, like “psychics”, want to sell you their “knowledge”. Even wonder why don’t they use their “gifts” to make themselves rich without your money? Nobody can see into the future, and nobody’s system is good enough to beat Vegas’ odds consistently.

However for those that write about sports, predicting teams is a winning proposition (as long as there is no money on the table). If the prediction is correct, I can refer to it later. If it’s wrong, I’m sure no one will care, since it’s foolish to be held to that kind of accountability. Everybody has their own way of picking who will win. Some people decide which team is more hungry. Some people use which team has more heart. Other will look at which team has more playoff experience. I’m sure these people have varying degrees of success with these methods. I don’t know how anyone could quantify which team has more heart without getting a cardiologist involved.

I prefer something more tangible. As I’m typing this right now, I don’t know who I will predict to win. I’m going to look over all the data I have & make an educated guess at the end. I’m going to use Dean Oliver’s four factors of winning. Despite digging around, I haven’t found how he came to these results. This bothers me a little, but since his work in Basketball on Paper is so thorough and logical, I can let it slide for now. There are actually 2 sides to each factor, an offensive and defensive component.

Factor 1. Shooting (eFG%)


L.A.	48.1%	102%	7th
DET	46.1%	98%	20th

[NOTE: The first number is eFG%, the second is their percentage of the league average, the last is their rank.]

Los Angeles has the advantage here, and it should be no surprise. Shaq led the league in eFG% with his massive FG% (58%). Payton, Malone, and Kobe all had better eFG% than the Pistons’ team average.

On the other hand Detroit is a poor shooting team. Adding Rasheed (47%) slightly improves their percentage, but their big scorers Hamilton and Billups have an eFG% of 46%. Meanwhile Larry Brown’s Ben Wallace experiment has me scratching my head. Wallace’s offensive contributions used to be limited to put backs and easy shots, which gave him a near 50% FG%. This year Brown has asked Wallace to take a more active role, and he’s been horrible (42%). Brown’s logic is to keep teams honest by using a defender on Big Ben, which should give the other Detroit shooters a small edge. Either it hasn’t worked as Detroit is 20th in eFG%, or the Pistons are a worse shooting team than I expected.


L.A.	47.1%	100%	15th
DET	44.1%	107%	2nd

This is where the Pistons shine. Although L.A. is simply average, Detroit is awesome, only behind the Spurs. Which brings an interesting comparison, since Los Angeles beat the Spurs earlier this year. Here’s a little chart of L.A.’s big 4 scoring in that series.

Name	1	2	3	4	5	6	1-2avg	3-6avg
Shaq	19	32	28	28	11	17	25.5	21
Kobe	31	15	22	42	22	26	23	28
Payton	4	7	15	8	5	15	5.5	10.8
Malone	10	13	13	9	7	8	11.5	9.3
?????	32	33	28	23	28	25	32.5	26

Los Angeles lost the first two games, but won the next 4. The difference seemed to be Kobe Bryant, who averaged 5 more points in the Laker’s wins. The last row is Bruce Bowen’s minutes, Kobe’s main defender. Granted Kobe torched him in game 1, but it’s apparent the less Bowen played, the more points Bryant scored. The reason Bowen played less is the Spurs’ offense fizzled and they needed more scorers on the court. San Antonio’s offense was ranked 14th, slightly better than the Pistons. Detroit should learn a lesson from the Spurs. They have to stay close in the game, so Brown won’t be tempted to take his defenders out for more firepower.

Factor 2. Turnovers (TO/100poss)


LA	14.2	109%	5th
DET	16.2	96%	20th


LA	15.4	99%	16th
DET	16.5	106%	7th

Again, the Lakers are better on offense, while the Pistons are better on defense. However the Lakers have the edge here. How? They turnover the ball 14.2 times per 100 possessions, but force turnovers 15.4 times, which is a net of +1.2. Meanwhile the Pistons give it up 16.2 times, and get it back 16.5 times, which is a small +.3 net.

Factor 3. Offensive Rebounds (oREB%)


LA	28.1%	98%	16th
DET	30.1%	105%	9th


LA	26.7%	108%	5th
DET	28.3%	101%	12th

Getting this far is seems that these two teams have strengths & weaknesses in the opposite areas in just about every aspect. Detroit is better on the offensive glass, while the Lakers are better on the defensive. I can’t tell who has the advantage here. The Lakers’ great offensive rebounding is tempered by their below average offensive rebounding. Detroit is above average in both respects, but nowhere near the Lakers’ efficiency on the defensive end. I would guess that Detroit has a slight edge, but not by much.

Factor 4. Free Throws (FTM/FGA)


LA	.244	107%	7th
DET	.247	108%	4th


LA	.222	103%	16th
DET	.202	113%	3rd

I guess I spoke too soon about their strengths & weaknesses. Detroit is clearly superior here at both getting to the line, and keeping their opponents from the charity stripe. One thing to consider is how will Shaq change this? Surely the Pistons will foul Shaq when it suits them, so will this negate this advantage? For example, maybe the Pistons can get away with a foul here & there, because their big men don’t foul often. Giving a few free fouls to Shaq, will that put them in the penalty sooner? It might, but I don’t think it’ll be as much of a factor, since Detroit is so good in this respect.

Detroit has an edge in the weaker categories, free throws & rebounding, and Detroit’s defense should put them over the top. However Los Angeles is very efficient when it comes to scoring and not turning the ball over, combined with Detroit’s weakness in these same categories gives the edge to the Lakers. In simpler terms, Los Angeles has a good offense, and an average defense, while Detroit has a good defense, but a bad offense. It’s Detroit’s lack of offense that will hurt them.

Does this mean that the Lakers will definitely win? No. I’ll spare you from the all too familiar “anything can happen in a 7 game series.” Instead I’ll say that the statistics don’t tell the entire story. This entire column is based on the regular season stats. However, Kobe only played 65 games, Shaq 67, and Malone 42. On the other side of the ball, Rasheed only played in 21 games for the Pistons. We really don’t know exactly what these teams are like at full strength. I won’t write off Detroit yet, but I do think they’ll have to do a few things to keep themselves in the game.

No one can stop Shaq for a long period of time. The Pistons will likely do what everyone else has done, which is to put a body on him as best they can & foul him when it’s profitable. Detroit needs to stop the rest of the gang, especially Kobe. If L.A. can jump out to a lead, they’ll force Detroit to do something they’re not good at, which is try to score. The Pistons move at a slow pace, and turning out lots of points very quickly isn’t how they got here. The key for Detroit is to keep the games close. They can do that by keeping the non-Shaq Lakers from scoring, and getting good production out of Hamilton, Billups, & Rasheed.

The key for the Lakers is to score and put the pressure on Detroit. They need points out of someone other than Shaq & Kobe. Malone has done well enough (13PPG), despite facing two great defenders in Garnett and Duncan. Gary Payton has all but disappeared from the offense, scoring 8.8PPG in the playoffs. The Lakers need production from the rest of the gang, whether it be Fisher, George, or Rush. They’ll want to score points off of turnovers, while minimizing any damage the Pistons might cause on the offensive boards and at the free throw line.

I said I would make a prediction at the beginning of this column, and I’ll stick with it. If Detroit wins I won’t be surprised (or sad), but I have to go with the evidence I have. I know I said over a month ago that the Lakers wouldn’t be holding the trophy by summertime, but I’m going with the Lakers, in a hard fought 7 game series. The Lakers’ offense and the Pistons’ lack of offense give Los Angeles the edge they need.

Home Is Where the Background Is?

I have various saved incomplete blog entries that will never see the light of day. One of them was about what gives a team the home court advantage. Last week, Raptorblog asked the same question:

In my mind, the greatest mystery about NBA basketball is why homecourt advantage has such a profound effect on game results. I understand that the home team is allowed final substitutions and has the support of their fans (outside of Atlanta and New Orleans) but I can’t figure out why NBA home teams have a higher winning percentage than the other three major sports.

So I decided to revive one of my unfinished posts.

Everyone reading this (I hope) is familiar with the scene from Hoosiers where the team makes the finals & they go to visit the court they will be playing on. Gene Hackman (the coach) has the players measure various parts of the court. The hoop is exactly 10 feet high, just as their home court. This is to prove to his players that this (and all) courts are exactly the same dimensions (unlike baseball stadiums, or even football fields with their different turfs & weather). So in basketball we can eliminate any kind of home field bias due to the playing surface (although some people claim that the floors of some courts have weird bounces, I think everyone can agree that this is highly unlikely of a 61% home field advantage).

To figure out what gives a team the home court advantage, I decided to take the playoff teams and split them into 2 groups, the top 8 & bottom 8. I choose these groups to isolate a few variables. First the bottom 8 teams all lost & were vastly inferior to their opponents. Second they played less games than the top 8. Using ESPN I was able to get their home & road splits. I also decided to use the regular season statistics as well, getting the home/road splits for every team this year. So what kind of theories do we have?

Theory #1: Home Cooked Refs

Referees with their fragile egos & fearful of being booed give the home team better foul calls. If this is true teams will have less free throw attempts on the road than at home. So what do the numbers say?

[Note: the first set of numbers are the home numbers, the second set road numbers, the third set the difference.]


Top 8 18.9 26.7 70% 19.1 26.5 72% -0.2 0.2 -2%
Bot 8 16.2 22.3 73% 18.1 23.3 78% -1.9 -1.0 -4%

There really isn’t much of a difference in shots attempted. On the road the bottom 8 playoff teams averaged an extra of 1 free throw per game with a higher percentage, so if anything it appears that the bias is the other way. In fact just to be sure I checked with the regular season stats. Teams attempted only 1.2 more free throws at home than on the road. The top 5 teams in getting more FTA at home were: Atlanta, Golden State, New Orleans, Memphis & Milwaukee; meanwhile the bottom 5 teams were a mixed bag as well: Philly, Washington, Boston, Houston, and Toronto.

I really can’t conclude anything from this, but I would certainly lean to the side that refs don’t give the home team special treatment with respect to free throws. Having one extra free throw per game doesn’t seem to be a large advantage.

Theory #2: Better Free Throw Shooting

Maybe the refs don’t give players an advantage, but once the player arrives at the charity stripe do the fans make the difference? When a home player is shooting the fans are calm, but when an opposing player is trying to make a free throw the fans go nuts, trying to distract him from making his shot. What do the numbers say?

Using the same chart as above, oddly enough teams in the playoffs this year have shot better on the road. Again to verify my results I’ll look at the regular season. The league shot a FT% of 75.2% at the comfort of home this year, and 75.3% on the road. That’s right on the road they shot 0.01% better. Certainly not significant.

Theory #3: Able to See the Rim Better

On the comments for his post, Kamahsutra came up with this theory:

It has been noted for basketball, that the home field advantage may be due to the shooting. No doubt all the court dimensions are exactly the same in all NBA arenas, however the rest of the surroundings are not, eg, the look of the backboard relative to the background. Anything that may affect the shooter’s comfort level. This would be tell tale, if you were able to look at the shooting percentages of visiting against home teams during playoffs.

I tend to notice this at my local gym. The guys that have been playing there for years have little adjustment period when the season starts up. However when I bring someone new there, they always seem to struggle to hit their shots. It’s a large size court – something that’s rare to find in New York city parks. The backboard is glass (again rare to find in public parks), and the background is a monotonous beige. At times it’s hard to pickup the rim, but since I’ve been there for 4 years, now I have no problem knowing where it is. Once or twice we’ve had to use another gym for a short period of time, and my first time there I have trouble hitting my shots.

Could this be true in the NBA?

Top 8 35.0 76.7 45.6% 31.7 76.6 41.5% 3.3 0.1 4.2%
Bot 8 34.6 81.8 42.5% 30.6 77.7 39.3% 4.0 4.1 3.2%

The initial numbers look good. The good teams shot 4% better at home, and the bad teams were 3% better. The regular season shows similar yet reduced results: 44.5% at home, 43.2% on the road. The reason for the regular season numbers being smaller is the better teams make the playoffs. For example sorting the regular season by biggest difference in FG% would put most of the playoff teams near the top (Dallas, San Antonio, Milwaukee, New Jersey, Miami, and Sacramento), and weaker teams at the bottom (Chicago, Indiana, Boston, Cleveland, Seattle, and Orlando).

What if this is due to another reason. One could be maybe teams on the road feel more desperate and shoot more 3s (which would lower their fg%). Let’s try to break down FG% & see where the difference is, first with two pointers:

TEAM	2PM	2PA	2P%	2PM	2PA	2P%	2PM	2PA	2P%	
Top 8 29.2 60.7 48.2% 26.7 61.2 43.7% 2.5 -0.5 4.5%
Bot 8 29.3 65.9 44.9% 26.2 63.1 41.3% 3.1 2.8 3.6%

There seems to be a significant difference here, around 4%. The regular season nets a smaller 1.2% difference. There are 10 of the 16 playoff teams which rank in the top half. Now about FG%’s other half, three pointers?

TEAM	3PM	3PA	3P%	3PM	3PA	3P%	3PM	3PA	3P%	

Top 8 5.8 16.0 35.9% 5.0 15.4 32.1% 0.7 0.6 3.8%
Bot 8 5.2 15.9 33.3% 4.4 14.6 29.3% 0.9 1.3 4.0%

Again a big difference here, near 4%. During the regular season, the home team had a 1.3% advantage at home when shooting threes. So to conclude this section teams in the playoffs this year so far have shot about 4% better overall which is about evenly distributed between 2 pointers & 3 pointers.

Right now I have to conclude that this is a possibility. The cause may not be what we think, but the results are clear. There could be a host of reasons why teams shoot better at home, including sleeping in your own bed or eating familiar food. However I don’t think science has come far enough that we can isolate such variables.

Is this enough evidence to come to a certain conclusion that it’s the backdrop that effects shooters? No. But it’s certainly a start.