NBA Win Shares
By Sean Smith Email: Rallymonkey5@comcast.net
Skip to the good stuff 2002 Stats Career Wins (1951-52 to 2001-02)
The career totals may be off if I missed a season for somebody. If I did, the career games will be wrong.
Why?
To create a system that can compare basketball players across eras. I don't attempt to determine if professional basketball was better in the 60's, the 80's or now. I don't think that can be done conclusively. If Shooting percentages are up, does that mean shooters are better? Or are defenders worse? I don't know, for this exercise a win is a win, no matter what competition a player is facing, I'm trying to measure how many of his team's wins he's responsible for.
How?
Here is the basic formula: (Points – (missed FG) – (missed FT)/2 + Reb + Ast + St + Blocks/2 – turnovers)
This is a modified Tendex rating, invented by Dave Heeren (I think) and copied or modified by just about everyone. For most of the recent history of the NBA, teams have averaged about 1 point per ball possession. For earlier years (50’s, 60’s) this was not the case, and the ball possession stats (rebounds, missed shots) are lowered accordingly, while assists are weighted higher. Free throw misses are weighted half of a field goal miss, which should be obvious. Player A takes a jumper and misses, player B bricks 2 free throws. In both cases the result is the same, their team doesn’t score, and the other team gets the ball.
Blocks are given half credit because you don’t always get possession of the ball. Many will argue that the block has intimidation value, but if this is the case, it will show up in that your opponents will miss more shots. That way, Mutombo gets his credit, and Shawn Bradley (who blocks shots but I’ve never really seen him stop anybody) doesn’t.
Forcing your opponents to miss and keeping them from scoring are important to the win share system, and will be explained soon.
I suppose I should have a name for the above formula, and I tried to find something unique to call it. Being originally a baseball fan and a Bill James reader, I thought about points created, but I think somebody has already done that. To keep things simple, I'm calling it Bob. Bob's a good name. Easy to type, won't change if you spell it backwards.
BOB = (Points – (missed FG) – (missed FT)/2 + Reb + Ast + St + Blocks/2 – turnovers)
BOB is calculated for a team, and is also calculated for the league. This is necessary step to determine each team’s “marginal points”. Subtract (League (Bob/min) * 60% * team minutes) from Team BOB, and you get each team’s marginal points. The 60% figure is an estimate for the “zero level”, a team that has a rate at 60 % of the league average would not be expected to win even one game over an 82 game schedule. Of course, a team that does nothing, puts up a rate of 0 % of league average will also win zero games. A team at 60% would be expected to win just under 0.5 games out of 82, or 1 every 2 years as 0.5 isn’t quite possible.
Once you have marginal points, divide this number by team wins. Marginal points per win are needed for each team to determine a player's win shares. For most teams this number will be between 70 and 120, although it will be very high (200 or more) for extremely bad teams, some teams that win fewer than 20 games. In most cases, the variation is more a product of a team’s game pace and defensive performance than a high win level. For example, in 1997 this number was 71 for the Bulls (69 wins) and 66 for the walk it up Cavaliers (42 wins). This tells me a good player will have as many win shares on a great team as he will on an average team. He may not have as many on a horrible team, but in the NBA, one player can have a huge impact, so if the team is horrible, they don’t have a great player. Shaq could join any team in the game right now and make them an instant playoff team. Jordan at age 39 made the Wizards respectable.
The teams with the lowest marginal points per win are not the 72 Lakers, 86 Celtics, 67 Sixers, or 96 Bulls. Instead, the teams with the lowest MP/W are the teams with the nastiest defenses, like the Hawks, Knicks, and Heat or the late 90's / early 2000's. These teams have numbers in the 50-59 range. Other teams: 72 Lakers: 86, 86 Celtics: 77, 67 Sixers: 92, 96 Bulls: 66. This means that a player for a team like the 1997 Miami Heat (56) does not need to put up huge numbers to have a good win share total, as he is doing more than enough to stop his opponents from putting up big numbers. Teams that play slowdown defense, like the Cavaliers of a few years back, also have low MP/W.
For teams, one more number is needed, defensive rebounds per minute.
For players, calculate their formula points as for teams, with the following modifications:
Instead of rebounds, add Offensive rebounds + Defensive rebounds *.5 + Estimated defensive stops *.5. A player's defensive stops are estimated by multiplying his minutes by the team's defensive rebounds per minute. A defensive rebound occurs when you make your opponent miss and get the ball back. This formula gives credit to the rebounder, but also to the defenders who are necessary to cause a miss. We have the number at a team level, but not for individuals, so we credit the individuals on a team for defensive stops equally, based on minutes played. ( Minutes * Team DR/Min).
Stopping the other team from scoring consists of A) stealing the ball, B) Blocking the shot, C) drawing an offensive foul D) guarding your opponent, forcing a bad shot, and getting the rebound. For D), I am trying to give credit to all players involved in the defense, not just the player who gets the rebound. This still doesn't credit great defenders who do more than their teammates but don't steal or block shots. Offensive fouls drawn are not available, so I can't use those either.
The whole effect of calculating defensive stops, using steal and blocks, and team dependent marginal points per win rewards players who, by their own effort and by their team's effectiveness, stop their opponents from scoring.
Now that BOB is calculated for each player, figure marginal points by subtracting (Minutes * League rate * 60%). Divide player marginal points by team marginal points per win, and you get win shares.
Until 1974, steals, blocks, turnovers, and def/off rebound breakdowns were not calculated, so they are dropped from the formula. This doesn’t change the number of win shares, as that by definition equals the number of team wins, but it could change the distribution. For most players, the difference is minimal, since win shares are rounded to the nearest whole number. For all players, points, rebounds, and assists are the numbers that do most to determine win shares. Bill Russell and Wilt Chamberlain are probably hurt most. They dominated defensively in their time, and faced many more shots than today’s teams faced, due to the high pace of the games. Did Wilt block 500 shots a year? 700? 1000? We’ll never know, but my guess is that not knowing may have cost him 2-3 win shares per year.
Players who play great defense in some cases will be underrated. The defensive stop estimation assumes all defenders are equal for a team. Joe Dumars, a great defender on a great defensive team, will get his credit. A defensive specialist on a bad team may not, if he doesn't get a good amount of steals and/or blocks. Bruce Bowen is an interesting case. He doesn't get many win shares (some years he has zero). He doesn't score, rebound or pass. He doesn't get a lot of blocks or steals the way Bo Outlaw does. What he does do is stop the player he's defending. I have seen studies based on box scores showing him as a top defender because he holds his opponents well below their season averages. I haven't included anything like this in win shares for two reasons. First, I'm not sure what this tells us. Is Bowen stopping his opponent or is the other small forward not able to drive to the basket because Robinson and Duncan waiting for them? We can't tell from a box score who he was actually guarding and how many points they score with Bowen, and how many with other players in the lineup. Second, it takes an incredibly long time to figure. There's no way I could do it for every player. If I put full faith in the estimates made of his defense, Bowen may take a point off his opponent every 10 minutes. Playing 1700 minutes like last year, that would add 2-3 win shares.
Sometimes players putting up the same numbers on bad teams will have fewer win shares than players on good teams, but that may be a case that the players are not equal, only the numbers are. Case in point, Ron Harper scored 20 ppg his last year with the Clippers. He got 4 win shares. With the Bulls next year he had only half as much playing time, and his scoring dropped to 6.9. He got 2 win shares, the next year he was up to 4. He was creating wins at the same rate (he is, after all, the same player), its just that the Bulls had better options than the Clippers, so his raw numbers looked worse. Some players put up impressive numbers because they are on a bad team which has no other options, win shares will not overrate them the way a tendex type system might.
It is possible to have a negative win share total, this would mean you are so bad that you negate positive wins that teammates contribute. I was happy to see that with the marginal level set where it is, very few players are in the negatives. Players like this usually don’t get a chance to play very much before they are cut, or see a lot of DNP-CD next to their name in the box score. There are a few every year, but they don’t play much and their win shares usually round to 0. The last player to post a full –1 win share was Gerald Wilkins in 1997-98, who shot 33%, did nothing else to contribute, and played 1200 minutes. No player that I’ve found has ever had –2 win shares.
Point Values
Why is it that just about every event is rated at one? Rebounds, assists, steals, turnovers, missed field goals. It's a convenient number, but how do I know it shouldn't be .97 or 1.12 or something?
The 1.0 is an estimate. For most of the recent history of the NBA, the value of a ball possession has been around one, teams average one point for each possession. Using a figure of .97 or another specific number depending on the season, if it was more accurate, will not change overall ratings much at all. I have only changed this number at certain breakpoints in history where the normal possession value has changed radically. For the 1950's I use .80, for the 60's .90, and 1.0 for every year since then. While shooting percentages have declined in recent years, points per possession has changed only a little, as teams shoot more three pointers than ever before.
The value of a rebound, steal, turnover, and missed field goals will always be equal to each other. I've seen other systems that weight each event differently, but I don't get it. As an example, player A makes a bad pass and turns the ball over. Player B takes a shot and misses, the other team getting the board. Either way, you had a ball possession, you failed to score, and the other guy now has the ball. You could argue that the team that got the steal has a better chance of scoring now than the team that got the rebound, but so what? If they score, those 2 points go in their plus column. No need to give artificial credit based on how they got the ball. I've seen some systems that give extra credit to offensive rebounds, more than the negative value for missed shots. Moses Malone would love this. His offensive strategy, when he was in trouble, was to throw the ball up on the glass with the sole intent of getting his own rebound. At least that's what it seemed like. Under a flawed system like this, Moses would get credits added every time he did this, even if he didn't score.
Assists can differ from the other events, they are figured by (2- value of possession).
Player Rating
(BOB/minutes)
Adjusted player rating = Player Rating * (100/Opponents PPG)
I use this as an intermediate step towards win shares, but it can be useful by itself as well. The 100 is used to put teams on an equal level for comparison. Opponents PPG is used where other systems have used a game pace estimate. In my opinion, Opponents PPG is the only thing that matters. If your opponent scores 100, why should your rating be treated any differently if they do it on 120 ball possessions or 90? Either way you need to score 101.
Greatest Season
This one surprised me, but it was Shaq in his MVP year (99-00), with 27. Kareem Abdul-Jabbar had 26 in 1971-72, in leading the Bucks to 63 wins. Wilt Chamberlain has the next 4 best at 24 (62,64,66,67). 7 Players had 23, with Michael Jordan doing it 3 times.
If Blocks, steals, and turnovers were not counted for Shaq, he would still get 27 win shares. I can’t say the same about Wilt, however. He may have blocked enough shots that he would have equaled or surpassed Shaq’s 27. Or maybe not, but its something to keep in mind.
Bill Russell’s best years were at 16, in 1964 and 1965. If I had the resources for playoff win shares, he’d be closer to the top. Unfortunately, I don't have enough data now for playoff win shares. I'd like to at some point. In baseball we can almost ignore Barry Bonds playoff record because the sample size is so small. In basketball, the playoffs can last up to 25% of the regular season length. The games are much more important, so playoff performance should be kept in mind when considering the greatest players of all time.
Sources:
Stats: Doug's NBA stats page http://home.rmi.net/~doug/ He has a great site for NBA or MLB stats.
The Sporting News Official NBA Guide
Yes my fingers are tired after putting all those numbers in a spreadsheet.
Inspiration for the project: Bill James and his Win Shares book for baseball
Copyright Ó 2002 by Sean Smith