The Best Basketball Players: "Pound Per Pound"

In an article somewhere I've read on line - I'd give it credit, but I honestly can't remember what it was - a WNBA defender spoke about the foolish dismissals of the WNBA where some fool makes the argument because "my favorite NBA team/college team/local high school team could be a WNBA team". The approach to this defense was one I formulated before, but the article beat me to putting it in print.

Namely, that this argument is never made in boxing. Could Vladimir Klitschko beat up Manny Pacquiao? Probably, since Klitschko is physically stronger than Pacquiao and none of Pacquiao's opponents have hit Pacquiao as hard as Klitschko could. In boxing fandom, there is much discussion as to who is the best "pound per pound" fighter - who is the best fighter taking into account the differing weight classes.

As it turns out, we have a nice "one value" metric to assign worth to a ball player - John Hollinger's Player Efficiency Rating, or PER. PER can be calculated for both NBA players and WNBA players. I therefore decided to count NBA PER as essentially equal to WNBA PER. This equalizes male and female basketball players.

For WNBA players, only players who have played more than 5000 career minutes are included. Sorry, Cynthia Cooper. You probably would have been on this list, but the WNBA started too late.

Top PER Values for NBA and WNBA Players
(min 5000 minutes WNBA, min 15000 minutes NBA)

1. Lauren Jackson (28.55)
2. Michael Jordan (27.91)
3. LeBron James (26.86)
4. Tamika Catchings (26.67)
5. David Robinson (26.18)
6. Wilt Chamberlain (26.13)
7. Dwyane Wade (25.67)
8. Yolanda Griffith (25.49)
9. Bob Pettit (25.37)
10. Tim Duncan (25.02)
11. Neil Johnston (24.72)
12. Diana Taurasi (24.67)
13. Charles Barkley (24.63)
14. Kareem Abdul-Jabbar (24.58)
15. Lisa Leslie (24.24)
(T) Sheryl Swoopes (24.24)
17. Magic Johnson (24.11)
18. Karl Malone (23.90)
19. Dirk Nowitzki (23.76)
20. Kevin Garnett (23.59)

So is Lauren Jackson better than Michael Jordan? That's up for you to decide. (As for me, go Lauren.)

PER and the Triple Trade

The biggest thing in WNBA news is a three-team trade centered around the Phoenix Mercury's Cappie Pondexter. With Phoenix struggling with cap space, they send Pondexter and Kelly Mazzante to the New York Liberty. The Libs send Shameka Christon and Cathrine Kraayeveld to the Chicago Sky, and the Sky's Candice Dupree finds herself in a Mercury uniform.

I decided to look at the weighted Player Efficiency Ratings (PER) of all parties involved in the trade. The parenthesis indicate the minutes played by the given player - the resulting career PER is weighted by minutes.

Weighted Career PER

Dupree: 19.85
Pondexter/Mazzante: 21.63 (4110)/12.24(2852) : 17.78
Christon/Kraayeveld: 15.19 (5382)/13.24(3915) : 14.37

It look like at least in the short term, the winners are going to be the New York Liberty. If they can figure out a way to not play Kelly Mazzante - the weakest player involved in the trade - it's an even bigger win, but I suspect that the Libs need all the players they can get. Pondexter is entering the peak years of her career and as they say, "Pondexter can move product" - she's popular and fun. New York seems to have an affinity for players that have names that others find hard to spell, but I think that Pondexter is less likely to be misspelled than Cathrine Kraayeveld.

In the long term, the winner might be the Phoenix Mercury. Dupree isn't as good as Pondexter, but she's two years younger and there's more upside. Dupree is already a three-time All-Star and playing for a WNBA champion can't hurt her pedigree.

I suspect the losers are going to be the Chicago Sky. They lose their franchise player and Christon is two years away from the red light going off in her palm. However, Christon's last two years have been better than the previous years. Kraayeveld will just be glad to play.

New Fanpost at Swish Appeal

This time, it's about Career Player Efficiency Ratings (PER) for the WNBA. Give them a visit.

PER Ratings: Atlanta Dream

On Swish Appeal, I've gone ahead and posted the WNBA's player efficiency ratings for 2009.

If you're interested, here's how the various players of the Atlanta Dream did in PER:

Angel McCoughtry (23.2)
Sancho Lyttle (21.3)
Erika de Souza (20,0)
Chamique Holdsclaw (14.8)
Michelle Snow (14.6)
Ivory Latta (13.5)
Tamera Young (12.1)
Coco Miller (10.4)
Iziane Castro Marques (9.8)
Shalee Lehning (8.7)
Jennifer Lacy (5.8)
Armintie Price (4.2)

If the numbers aren't pleasing, you might want to beat up on John Hollinger, the guy who created the formula.

A Bevy of Stats

Player Efficiency Rating (PER) can be found in here....

A commenter asked me to break down John Hollinger's Player Efficiency Rating, or PER. To whom I say with a grin, "Sure."

Now, according to Mr. Hollinger himself, "The PER sums up all a player's positive accomplishments, subtracts the negative accomplishments, and returns a per-minute rating of a player's performance."

Sounds nice, doesn't it? Now, let's go to the definition of PER from Basketball-Reference.com:


uPER = (1 / MP) *
[ 3P
+ (2/3) * AST
+ (2 - factor * (team_AST / team_FG)) * FG
+ (FT *0.5 * (1 + (1 - (team_AST / team_FG)) + (2/3) * (team_AST / team_FG)))
- VOP * TOV
- VOP * DRB% * (FGA - FG)
- VOP * 0.44 * (0.44 + (0.56 * DRB%)) * (FTA - FT)
+ VOP * (1 - DRB%) * (TRB - ORB)
+ VOP * DRB% * ORB
+ VOP * STL
+ VOP * DRB% * BLK
- PF * ((lg_FT / lg_PF) - 0.44 * (lg_FTA / lg_PF) * VOP) ]

Most of the terms in the formula above should be clear, but let me define the less obvious ones:

factor = (2 / 3) - (0.5 * (lg_AST / lg_FG)) / (2 * (lg_FG / lg_FT))
VOP = lg_PTS / (lg_FGA - lg_ORB + lg_TOV + 0.44 * lg_FTA)
DRB% = (lg_TRB - lg_ORB) / lg_TRB


Did any of that make a damn bit of sense to you? I have a degree in mathematics, and the first time I looked at that formula, I said, "huh"? It's certainly clear that field goals, assists, turnovers, rebounds both offensive and defensive, steals, blocks, and some league averages and team averages go in there somewhere.

However, there is nothing intuitive about any of this. If you read Hollinger's book (which I don't have), he'll be glad to go over each component with you in an explanation probably requiring several pages. And all of the above is just the first part of PER!

So our anonymous Jennifer Lacy fan might ask the question, "Pet, if not even you can explain PER, why the hell do you use it?" My answer:

a) I trust John Hollinger,
b) the results pass the "smell test": by that I mean that you'd expect the people you'd think are the best players in the league to have high PER and the worst to have low PER - which they do - and
c) the final number can be translated to something meaningful.

If you've got a PER of 30 or more, you're having one of the WNBA's great seasons. If you've got a PER of 15, you are an average WNBA player. The arithmetic mean (average) of a bunch of unadjusted PER numbers is taken, more adjustments are made, and the number "15" is thrown in there so that the mean PER for the WNBA comes out to be exactly 15.00. We have defined "average mean unadjusted PER" to be precisely equal to 15.00.

Once you get into a PER of 9.00, we're pretty much at what Hollinger called "replacement level", meaning that you could probably find some overlooked college player who just missed being drafted or got cut at training camp, get her up to speed, throw her out on the court and she could probably rack up a PER of 9.00 under good conditions. I don't really agree with that, because Hollinger's analysis was done with NBA players and not WNBA players. I will agree that a PER of 9.00 is nothing to be proud of.

PER has its weaknesses, and its detractors. For one thing, PER undervalues defensive contribution, so a player who is a defensive specialist won't have that value reflected in PER. Those players will have lower PER than a more just and fair allotment of PER should give them.

I keep all of this crap in a spreadsheet which I'll be glad to send anyone. Unfortunately, if you didn't understand any of that above formula (and I'm with you), you might not feel any better. PER suffers from the "black box problem" - you dump a bunch of stats in one end of the black box and out comes one number from the other end, but you don't really know what takes place inside the box.

There were 193 people who took part in the WNBA season last year: here are the top PER performers.

Leaders in Player Efficiency Rating, 2008

1. Diana Taurasi 29.83
2. Candace Parker 27.28
3. Sancho Lyttle 27.17
4. Lauren Jackson 26.63
5. Lindsay Whalen 24.68
6. Janel McCarville 24.57
7. Sophia Young 23.39
8. Tamika Catchings 23.14
9. Candice Wiggins 23.13
10. Jia Perkins 22.94

These numbers seem to make sense, although the computer would have given Taurasi the MVP and not Candace Parker. This might be why computers don't award MVPs, although I think Phoenix Mercury fans would jump up and say, "PER was right! PER was right!"

Who is the WNBA's "Most Average Player"?

61. Ivory Latta 15.03

Now there's a surprise!

Out of the 193 players, where does Jennifer Lacy show up? In the #135 slot.

134. Quianna Chaney 8.33
135. Jennifer Lacy 8.31
136. Sandora Irvin 8.31

"Okay," you might say, "this is just a bunch of numbers. It doesn't prove anything."

I agree. But here's the question: "do the results pass the smell test?" Suppose were were talking to say, Bill Laimbeer or Bill Dolan or whoever. And suppose we were to say, "given all things being equal - that is, we're not looking at salary or team need - who would you rather have on your team, Diana Taurasi or Ivory Latta?"

Is Diana Taurasi better than Ivory Latta? I would say "yes" - and I LIKE Ivory Latta! Likewise, who is better, Ivory Latta or Jennifer Lacy?

I think Ivory Latta is better than Jennifer Lacy. I'm not knocking Jennifer Lacy, I'm just saying that Ivory Latta brings more value on the floor than Jennifer does. In terms of leadership or the locker room or coaching or gameplan, it might be a different story. However, I think that Latta is more productive than Lacy, in which case, I agree with PER.

PER might not be right every time - was Sancho Lyttle worth more to the Comets than Lauren Jackson was to the Storm last year? - but it's right often enough for me to like it.

Of course, the next question would be "why don't you just use traditional stats?" More on that later. I'm just getting warmed up. :D

2008 Dream Player Efficiency Ratings

At last, I've finally managed to enter the results of every season played by every player in my WNBA Player Biofile database. This includes a calculation of John Hollinger's Player Efficiency Rating (PER) for every player. My ratings are different than the ones on Basketball-Reference. There are some irregularities at the B-R.com site - I won't name all the examples but I cast a sort of jaundiced eye at my results. (GIGO)

Here are the final PER ratings for the Atlanta Dream in 2008. They have been split into three groups:

Erika de Souza: 21.84
Betty Lennox: 18.72
Katie Mattera: 16.25
Stacey Lovelace: 15.28
Ivory Latta: 15.03

Alison Bales: 13.66
Iziane Castro Marques: 11.32
Camille Little: 10.40
Kristin Haynie: 10.00
Kasha Terry: 9.64
Ann Strother: 9.54
Tamera Young: 9.31

Jennifer Lacy: 8.31
Kristen Mann: 7.35
Chioma Nnamaka: 3.08

Players in italics departed the Dream in mid-season.

The first group is the group of players with better than average PER ratings. PER is equalized so that 15.00 is the automatic average rating for whole league in any season.

Erika's rating makes her a "Borderline All-Star", and if you saw her play for Ros Casares this year, you'd definitely agree. All you can do is sigh and wish she'd been healthy in 2008 and hitting the boards for the DReam.

Betty Lennox might be the Dream's leading scorer, but PER has her as a "Solid Second Option". Katie Mattera, Stacy Lovelace, and Ivory Latta are given some praise, at least - they're "Pretty Good Players".

The second group are players that are worse than average players, but are better than the bottom of the bench. According to Hollinger, Alison Bales is "In the Rotation". Whereas Iziane Castro Marques and Camille Little, in a just world, would be "Scrounging for Minutes". Kasha Terry, Ann Strother, and Tamera Young should visit a realtor, because they are "Definitely Renting" according to Hollinger's PER rating.

The third group are players that are playing below replacement level in Hollinger's eyes. Replacement level is 9.00, which is supposedly the thin line between being the worst of WNBA players and being an emergency replacement - maybe someone who got washed out of a pre-draft camp that you can call and not have to pay too much money.

According to Hollinger, Jennifer Lacy and Kristen Mann are on "The Next Train to Yakima". Unfortunately, the WNBA doesn't have a Continental Basketball Association franchise. What would be the WNBA equivalent? "Next Plane to Albania? Next Plane to Malta?"

Chioma Nnamaka's 3.08 PER isn't even dignified with a cute name by Hollinger.

Oh well. Maybe next year the Dream will please the APBRmetric gods.

Whatever Happened to Dana Wynne?

Dana Wynne in a more familiar uniform .

In looking at a series of players with very high Player Efficiency Ratings (PER) but very low career minutes played, we come to the case of Dana Wynne. Wynne had a PER of 51.70 in 2001, the highest I've seen (so far) for a single season. The highest value of a player that actually played was that of Yolanda Griffith's 28.43. Based on PER alone, you could make the argument that Yo deserved the MVP more than Lisa Leslie, but Leslie wasn't far off with 27.59 and Leslie happened to lead her Los Angeles Sparks to their first of their two straight WNBA championships.

In her one-game, three-minute outing with the Monarchs in 2001, she didn't attempt any field goals, but she went 2-for-2 from the line in free throws. She also had one offensive rebound and one blocked shot. Not bad for three minutes or less of play.

However, Wynne's case is misleading. This wasn't just some rookie-for-a-cup-of-coffee. Wynne graduated from Seton Hall in 1997 and the 6-2, 175 pound guard/forward was a third round pick in the 1997 American Basketball League draft, playing for the Colorado Xplosion in both 1996-97 and 1997-98. From my understanding, she was also a player in 1998-99 until the league suspended operations in December 1998.

The problem is that there is no storehouse of statistics for the ABL from its 1996-97 through (aborted) 1998-1999 seasons. Oh John Sage has a site that will give you an tantalizing glimpse of some abbreviated stats, but there's nothing comprehensive. Trust me, if I had the comprehensive stats, I'd put them in the database. The ABL was the equal of the WNBA in my opinion, and it's sort of unfair that I have to ignore Wynne's previous two seasons. Maybe someday, when I win the lottery, I'll get those stats from somewhere.

So what happened to Dana Wynne? In 2002, she returned to the Monarchs, but was waived in May. I have a tantalizing glimpse of an article from the LA Daily News (hidden behind a paywall) that suggests that from 2003-04, Wynne was playing in Greece along with former UCLA player Michelle Greco. We know that at least from 2004-07 she was an assistant coach at Seton Hall University, her alma mater. After that, Dana Wynne disappears from the internet, or at least any mention of her in context with basketball disappears.

Dana, if you're out there somewhere, we at the Atlanta Dream Blog hope that you're okay. And that you're playing hoops every once in a while.

Whatever Happened to Christy Smith?

If you hang on to John Hollinger's Player Efficiency Rating (PER) the way a drunk hangs on to a lamp post - "for support, not illumination", Christy Smith of the Charlotte Sting in 1999 had the best season in the WNBA that year with a PER rating of 36.08, a good 4.16 points above eventual MVP Yolanda Griffith.

Christy Smith played a grand total of 19 minutes over four games in 1999. She took four field goal attempts - three from 3-point land - and hit three of them. She also went 5-for-6 from the free throw line, and had one assist and one steal. Not bad at all.

So what happened? Hard to say. I found note of an article on Google News that she was put on the injured list by the Sting in 1999. She had had an ACL injury at Arkansas in 1996; maybe it was exacerbated by WNBA play. Apparently, she never recovered from the injury. She went back to Arkansas and earned her master's degree in exercise science in 2001. Somewhere along the line, she became Christy Smith Flowers, the wife of Arkansas Razorback defensive back Jeremy Flowers. She had two children.

I assume she did what a lot of ex-WNBA players do after that - go into coaching. She was an assistant high school coach in 2006-07, a head high school coach in 2007-08, and in August 2008, joined the Valparaiso University women's basketball staff as an assistant coach.

The Crusaders are 5-5 this year. If you see Christy Smith Flowers on the sidelines, be sure to say "Hello" for me.