If Michael Jordan didn't play for the Bulls last season, how many games would Chicago have won?
It's a fairly common question, asked about all the great players and many of the not-so-great players in basketball. It's also a loaded question because it doesn't propose who would be replacing Mr. Jordan. If Michael Jordan didn't play for the Bulls, but Magic Johnson was taking his place, the Bulls still might have won 61 games and the Eastern Conference. On the other hand, if Dennis Hopson, the player actually brought in by the Bulls to give Jordan some relief, took Jordan's minutes, the Bulls obviously would have won substantially fewer games.
"Substantially fewer" - How many is that? Is that 10 games, 20 games, 30 games. Would the Bulls have gone from a 61-win team to a 30-win team? Before seeing the fine play of the other Bulls in the playoffs, some might have said that the Bulls would have been down with Denver and Miami for the worst record in the league. How can we estimate the number of games Mr. Jordan contributed to the Bulls 61 wins?
In the playoffs, there were many comparisons of Jordan's output in '91 to his output in previous years, showing how he has to do less this year, while the Bulls have won more. In '87, Jordan scored 35.4% of the Bulls' points and the team won 40 games, losing 42. In '88, Jordan scored 33.3% of the Bulls' points and the team went 50-32. In '89, Jordan scored 30.2% of the Bulls' points and the team went 52-30. In '90, Jordan scored 30.7% of the Bulls' points and the team went 55-27. And last year, Jordan scored only 28.6% of the Bulls' points and team went 61-21.
Making the false assumption that points scored are the only important things in winning, how do we determine what percentage of the Bulls' wins each year can be attributed the Magnificent One? Can we say that 35.4% of the Bulls' 40 wins (_14) in '87 were due to Jordan? Does that necessarily imply that 35.4% of the Bulls' 42 losses (_15) were also due to Jordan? Michael Jordan contributed a 14-15 record?!? Not many people would ever call Air Jordan your ordinary-everyday-average-0.500 ballplayer. Jordan was obviously much better than his teammates that season. It would make much more sense to find a method that showed Jordan with a winning record and his teammates with a losing record.
[Note: Some basketball analysts have their pet production rating formulae which sum a player's positive contributions - points, rebounds, assists, blocks, and steals - and subtract his negative contributions - missed shots and turnovers - to produce some number. This number, as in the example above with points, does not help to estimate a player's individual win-loss record. If a player is shown to produce 30% of his team's total production (whatever "production" really means), that still doesn't give us any idea how to split up his wins and losses.]
The Method
This method of determining wins and losses for an individual employs many of the techniques I've developed over the past 6 years. None of these techniques have received much public exposure and I will take some time to explain them as they are introduced.
The Pythagorean Formula
The first technique is known as the PYTHAGOREAN METHOD, derived from work done by baseball analysts. This method simply estimates a team's winning percentage from the number of points it scores and allows:
Estimated Winning % = (Points Scored)^16.5/[(Points Scored)^16.5 + (Points Allowed)^16.5]
For instance, the Houston Rockets went 52-30 last season, for a winning percentage of 0.634. The Rockets scored 8753 points and allowed 8466 points on their way to that record. Plugging these values into the formula gives
Esimated Winning % = (8753)^16.5/[(8753)^16.5 + (8466)^16.5]
= 1.11*10^65/(1.11*10^65 + 6.41*10^64)
= 0.634
which is exactly identical to the Rockets' true winning percentage.
If we could then estimate the number of points produced and allowed by individual players, we could use this Pythagorean Method to estimate their winning percentage and be one step away from an actual individual win-loss record. This, however, is the most difficult step in the process.
Possessions & Ratings
Here, it is necessary to define POSSESSIONS. A possession is defined as the period of play between when one team gains control of the ball and when the other team gains control of the ball. If a team misses a shot and gets the offensive rebound, this is still the same single possession. By defining possessions this way, which is now fairly common, teams are seen to alternate possession throughout a game, meaning that at the end of the game, both teams will have had the same number of possessions with which to score.
This also means that at the end of a season, a team will have the same number of possessions as its opponents. The number of possessions a team has reflects its pace. Using the Houston Rockets as an example again, it can be calculated that they had 8309 possessions over the course of the season. The Rockets were known as a running team and this number of possessions was above the league average of 8234, confirming that they indeed ran a lot.
The number of points a team scores with its possessions reflects its offensive ability. The number of points a team allows with those possessions reflects its defensive ability. The Rockets' OFFENSIVE RATING is thus defined as the number of points they scored per 100 possessions:
Rockets' Offensive Rating = (Points Scored/Possessions) * 100
= (8753/8309) * 100
= 105.3
Similarly, the Rockets' DEFENSIVE RATING is defined as the number of points they allowed per 100 possessions:
Rockets' Defensive Rating = (Points Allowed/Possessions) ¥ 100
= (8466/8309) * 100
= 101.9
Putting Ratings and the Pythagorean Formula Together
What do ratings have to do with determining individual win-loss records? Ratings can be put into the Pythagorean formula in place of Points Scored and Points Allowed:
Estimated Winning % = (Points Scored)^16.5/[(Points Scored)^16.5 + (Points Allowed)^16.5]
= (Offensive Rating)^16.5/[(Offensive Rating)^16.5 + (Defensive Rating)^16.5]
Though I've only presented team offensive and defensive ratings so far, ratings can also be determined for individual players and inserted into this equation to get an individual winning percentage.
Individual Ratings
Now, we have to determine ratings for individual players. This is not a simple procedure and I will admit right now that there is no good way to estimate defensive ratings for players. In this method, the team defensive rating is used as a surrogate for individual defensive rating until something better comes along.
Offensive ratings can be determined, however, and they are the major thrust of this entire individual win-loss method. The details of the heavily mathematical method will not be spelled out, but the essence of its theory can be described easily enough:
A player creates points by either scoring a field goal or free throw or by assisting on a teammate's field goal. A player uses a certain number of possessions in order to create those points. Those possessions are determined from field goals attempted, free throws attempted, assists made, turnovers, and offensive rebounds. I should emphasize that offensive rebounds do not "create" points; rather, they preserve possessions. After summing an individual's points created and his total possessions, his offensive rating is simply
Offensive Rating = (Points Created/Possessions) * 100
The average offensive rating in the league last year was 105.9, meaning that 105.9 points were scored per 100 possessions. An offensive player of average efficiency then would have an offensive rating of 105.9. The Houston Rockets' sixth man, Sleepy Floyd, happens to have that rating, meaning he is an average offensive player by league standards. But, because Houston had a better than average defense, Floyd's offense helped to make Houston a better than average team. This can be seen by inserting Floyd's offensive rating of 105.9 and the team's defensive rating of 101.9 into the equation in the previous section:
Floyd's Winning % = (105.9)^16.5/[(105.9)^16.5 + (101.9)^16.5]
= 2.58*10^33/(2.58*10^33 + 1.36*10^33)
= 0.654
Voila! This is our first individual winning percentage. It shows that Sleepy Floyd's offense, in the context of the good Houston defense, should win 65.4% of the time.
From Individual Winning Percentage to Individual Wins and Losses
All that is needed to now convert a winning percentage to wins and losses is the number of games played. For individual players, this means we need to know how many games their offense represents. If a player averages 40 minutes per 48 minute game, we could say that the number of games he is responsible is equal to
Games = (40/48) * (1/5) * 82 = 13.7
where the factor of 1/5 comes about because each player shares the court with four other teammates. But this is not what is done. Players who stand around and have little part in the offense do not contribute as much per minute as those who try to score. Because of this, the number of games played by an individual is estimated by
Games = Individual Possessions/[Sum(Individual Possessions on the Team)] * 82
where (_Individual Possessions on the Team) is the sum of all individual possessions on the team. [This should be approximately equal to Team Possessions minus Team Turnovers.] Sleepy Floyd's rating of 105.9 came by creating 1099 points on 1037 possessions. Summing the individual possessions for all the Rockets gives 8264. This means that Floyd's winning percentage of 0.654 can be applied to 10.3 games:
Floyd's games = (1037/8264) * 82
= 10.3
This shows Sleepy Floyd's win-loss record for 1990-91 was 6.7-3.6.
A Disclaimer
These calculated win-loss records are best used for a player's offensive contributions. Players like Dennis Rodman and Akeem Olajuwon, whose primary contributions are defensive, may not be accurately represented by these records. Their defensive efforts are taken into account in team defensive ratings, but they are not as heavily weighted as their offensive play.
The determination of individual defensive ratings is a difficult task that needs to be solved for this method to be accurate for all players. Unfortunately, defense is much less individual and more teamwork, making the concept of a defensive rating somewhat difficult to define. For example, turnovers are often created when two players double-team the player with the ball, forcing him to throw it away. Another teammate may get credit for a steal on the play, but the players who double-teamed were an important part of the turnover. Also, some players who don't pick up a lot of defensive stats - blocks, steals, and defensive rebounds - may still be very good defensive players. Two that come to mind are Joe Dumars and Michael Cooper. Neither blocks many shots, has many steals, or gets many defensive rebounds, but they both force the players they guard into poor shots or into no shot at all. They are classic conservative defenders who deny scorers their comfort zones - their favorite places on the court, their favorite moves, their rhythm off picks. This is hard to measure, but it is not a trivial part of playing defense. Picks are an important part of an offense, but they are not as important (mainly because they are easier) as having someone, like Dumars or Cooper, who can shut down a top scorer.
Back to Michael Jordan
So how many wins did Michael Jordan create for the Bulls? In 1986-87, when he scored more than 3000 points and people were complaining that he was shooting too much, Jordan had an offensive rating of 115.3, which, along with a team defensive rating of 105.7, gave him a record of 20.1 wins and 4.8 losses, for a winning percentage of 0.807. The Bulls won only 40 games that year, meaning that Jordan accounted for half of them. When people were saying that the Bulls would be as bad as the Clippers (who went 12-70), they were getting pretty close to the truth.
In '87-88, Jordan tempered his scoring a bit, improving his shooting percentage with a better jump shot and hiking his assist total 20% as new additions Horace Grant and Scottie Pippen showed promise. Jordan's offensive rating went up to 122.6 and his win-loss record improved to his new best of 21.6-1.4, for a 0.941 winning percentage. The team improved to 50-32, with the improvement due primarily to better support for Jordan. Air Jordan also won his first MVP award, which was certainly well deserved.
The '88-89 season saw the addition of Bill Cartwright to the Bulls from the Knicks, in exchange for rebounding monster Charles Oakley. This was a trade that Jordan did not like, but he has since admitted that it worked out well. This season required Cartwright, as well as Pippen and Grant, to step up and help Jordan make the team a winner. The core of the present team was established this year and the team improved to 52-30, with Jordan steady at 20.2-2.0, for a 0.911 winning percentage. Strangely enough, Jordan has called this season his best, though the numbers don't really say so. If you're as good as Jordan, though, it must be hard to tell your best from your very best.
In '89-90, Jordan's offensive rating was 122.4, but because of a strange drop in defensive quality, his winning percentage dropped to 0.898, for a win-loss record of 17.8-2.3. This was the fewest number of games that Jordan was accountable for during his career (except when he missed most of the '86 season). Though Scottie Pippen was named to the All-Star Game, he was still inconsistent, especially with his jump shot. His improvement over the previous year was small compared to the improvements in Grant and John Paxson. Though neither scored very frequently, both learned to score efficiently, making them solid starters. The team's improvement to 55 wins reflected their increasing confidence.
Finally, when the '90-91 season began, the biggest weakness with the Bulls - Scottie Pippen's jump shot - was gone. Pippen deserved a spot on the All-Star team this year, but didn't get it. Grant and Paxson also continued to score well. This allowed Jordan to watch and enjoy the work of his teammates. Fewer minutes and fewer possessions allowed Jordan to be the best he has ever been. His offensive rating soared to a career best 125.5. The Bulls' defense improved dramatically, allowing only 103.2 points per 100 possessions. Jordan's winning percentage was an incredible 0.962, winning 19.6 games and losing only 0.8.
Not many players have won 20 games in a season for their teams. Not Magic. Not Bird. They didn't have to, unlike Jordan. I'm sure Wilt Chamberlain won 20 in a season, but the numbers don't exist to check it. There is no need to harp on how great Mr. Jordan is. At least now we have a numerical estimate of that greatness.
The Rest of the League
There is more to the NBA than Michael Jordan. In fact, there are a few players who have numbers comparable to his. Jordan's winning percentage of 0.962 wasn't even the best in the league. It wasn't even second best. It was third, behind Terry Porter's at 0.985 and Magic Johnson's at 0.975. In reality, the errors in the method are large enough to say that all three of these players are essentially equal. But, then again, Jordan was on the All-Defense Team, and defense isn't completely taken into account by this method. I wouldn't argue if anyone said that Jordan had the highest winning percentage in the league.
How did everyone else do? Attached is a list of the NBA players who accumulated 10 or more wins last season.
Rating Win-Loss Winning%
1 Jordan M. CHI 125.5 19.6-0.8 0.962
2 Johnson M. LAL 128.0 16.6-0.4 0.975
3 Stockton UTA 125.4 16.3-0.7 0.960
4 Malone K. UTA 112.1 15.5-4.1 0.791
5 Johnson K. PHO 123.9 15.3-0.9 0.946
6 Robinson D. SAS 113.3 14.2-2.3 0.861
7 Hardaway GSW 117.4 14.1-3.8 0.789
8 Dumars J. DET 117.2 14.1-1.6 0.899
9 Drexler POR 116.0 13.8-1.7 0.890
10 Mullin C. GSW 120.5 13.7-2.4 0.853
11 Barkley PHI 119.2 13.1-2.0 0.870
12 Miller R. IND 129.8 12.9-0.9 0.937
13 Smith K. HOU 122.1 12.5-0.6 0.952
14 Porter T. POR 131.6 12.0-0.2 0.985
15 Hawkins PHI 115.2 12.0-3.2 0.790
16 Skiles ORL 119.2 11.8-2.2 0.842
17 Wilkins D. ATL 113.6 11.8-5.5 0.683
18 Worthy J. LAL 111.9 11.8-2.8 0.809
19 Pippen S. CHI 113.1 11.7-2.6 0.817
20 Richardson MIN 114.0 11.2-4.7 0.706
21 Harper D. DAL 114.9 11.0-4.4 0.715
22 Humphries MIL 122.6 10.9-0.9 0.926
23 Pierce SEA 117.9 10.8-1.9 0.852
24 Hornacek PHO 123.6 10.5-0.6 0.944
25 Adams M. DEN 118.0 10.5-4.8 0.686
You might notice that some of the league's big names aren't on this list: Bird, McHale, Thomas, Olajuwon, Ewing. Bird, McHale, and Thomas all would have made the list had they not had injuries. Olajuwon, on the other hand, would not have made the list of players with 10+ victories even if his injuries hadn't chopped off about 1000 minutes of playing time. Olajuwon's offense has never been very good and, last year, with a rating of 105.0 and teammates Kenny Smith and Otis Thorpe scoring more, it wasn't good enough to give him ten wins. Again, as mentioned above, if his complete defensive contributions could be measured, it is likely that Olajuwon would approach ten wins, even in his limited playing time. Patrick Ewing didn't make this list mainly because he had a bad season, his worst in three years. Before this year, Ewing's offense was as efficient as David Robinson, but with more double-teams and his efforts to pass more, Ewing had a few more turnovers and shot a few more bricks. With additional help in the lineup, expect Ewing to post offensive numbers like Robinson's; his win-loss record may not be as good as Robinson's, though, because he's not the defensive player that Robinson is.
The second list attached is the win-loss records for NBA rookies. Notice that the All-Rookie First Team don't have great records. This is fairly typical. What this list doesn't show is that Kendall Gill, Derrick Coleman, Dennis Scott, and Lionel Simmons all improved their offensive ratings dramatically in the second half of the season. The other member of the All-Rookie First Team, Dee Brown, scored about the same in both halves, which was very impressive. The members of the Second Team - Chris Jackson, Willie Burton, Felton Spencer, Travis Mays, and Gary Payton - also showed improvement, though only Burton and Payton showed as large an improvement as the four First Teamers.
Player Rtg W - L Win% Robinson R. ATL 96.6 0.4 2.9 0.130 *1 Brown D. BOS 110.0 5.4 2.3 0.696 *1 Gill K. CHA 100.2 2.1 7.7 0.212 Ferry D. CLV 94.2 0.8 6.4 0.112 James H. CLV 98.9 0.6 2.1 0.222 *2 Jackson C. DEN 99.0 0.9 7.5 0.108 Liberty M. DEN 92.5 0.2 4.2 0.038 Hill T. GSW 91.8 0.2 3.2 0.060 Kimble B. LAC 90.2 0.4 4.1 0.080 Vaught L. LAC 98.1 0.9 2.6 0.259 Smith T. LAL 98.2 1.0 2.1 0.330 Campbell E. LAL 96.0 0.3 1.0 0.251 *2 Burton W. MIA 98.0 1.8 6.6 0.216 Kessler A. MIA 82.3 0.1 4.9 0.015 Coles B. MIA 100.9 1.5 3.4 0.308 Henson S. MIL 113.7 2.0 0.5 0.783 *2 Spencer F. MIN 106.1 2.1 2.8 0.421 Glass G. MIN 96.3 0.4 3.0 0.129 *1 Coleman D. NJN 101.1 4.2 8.1 0.343 George T. NJN 103.0 1.0 1.4 0.415 Buechler J. NJN 98.8 0.6 1.7 0.263 Mustaf J. NYK 86.9 0.1 2.7 0.039 *1 Scott D. ORL 103.5 3.8 7.3 0.342 Oliver B. PHI 94.7 0.4 2.8 0.129 Ceballos C. PHO 97.9 1.2 3.2 0.265 Knight N. PHO 100.6 1.5 2.6 0.363 *1 Simmons L. SAC 94.0 1.6 13.9 0.102 *2 Mays T. SAC 102.5 3.1 6.5 0.319 Bonner A. SAC 90.1 0.1 2.6 0.053 Causwell D. SAC 94.7 0.6 4.6 0.113 Higgins S. SAS 90.9 0.3 1.9 0.141 *2 Payton G. SEA 107.4 4.5 3.8 0.541 English A. WAS 95.8 1.1 5.5 0.163
*1 indicates member of First Team All-Rookie *2 indicates member of Second Team All-Rookie