It's easy to tell how many possessions a team has in a given game or given season (just ask Basketball Value). A more interesting question is how many possessions each individual player on the floor is responsible for and what percentage of team possessions is taken up by each player (in other words, who hogs the ball).
The way I see it, a possession ends in one of four ways: (1) a made FG, (2) a missed FG that is rebounded by the opponent, (3) some made FTs, (4) some missed FTs that are rebounded by the opponent, and (5) a turnover. A player gets individual credit for taking a possession when he causes any of these events. I came up with a formula that approximates possessions based on this (the formula also splits credit for a possession when an assist is involved).
The Nuggets had 8279 possessions on offense over the course of this past season. Based on my formula, here is how they were allocated individually:
Allen Iverson...........1977
Carmelo Anthony.........1687
Marcus Camby.............787
J.R. Smith...............734
Kenyon Martin............726
Linas Kleiza.............698
Anthony Carter...........697
Eduardo Najera...........408
Yakouba Diawara..........144
Chucky Atkins............126
Nene Hilario..............99
Bobby Jones...............77
Von Wafer.................44
Steven Hunter.............35
Taureen Green.............12
This only tells part of the story. One can also calculate a usage rate, which is the percentage of possessions a player uses while he is on the court. Obviously, a "normal" usage rate is 20% (if the team split its possessions exactly equally among all five players on the court). No team works this way in the real world, especially if the team has two superstars who use a large percentage of possessions.
Here are the usage rates for the Nuggets last season:
Carmelo Anthony...........28.9
Allen Iverson.............27.7
J.R. Smith................24.5
Nene Hilario..............18.3
Linas Kleiza..............17.7
Anthony Carter............17.0
Chucky Atkins.............17.0
Kenyon Martin.............16.2
Steven Hunter.............14.4
Marcus Camby..............13.6
Yakouba Diawara...........12.7
Eduardo Najera............11.8
Again, these numbers represent the percentage of possessions a player uses while he is on the court. That is why Steven Hunter can have a higher number than Marcus Camby, who obviously plays significantly more.
It is amazing that only three Nuggets have usage rate higher than 20. This is because such a large percentage of plays are used by 'Melo and AI. When both of them are on the court, they use a combined 56.5 percent of the available possessions. This does not leave much for everyone else.
Now that we know how many possessions each player accounts for individually, we can calculate how efficiently each player uses his allocated possessions. I do that by calculating how many points a player accounts for and divide it by how many possessions he uses.
Here are the individual offensive efficiencies for the Nuggets players last season (points produced per 100 possessions):
Linas Kleiza.............116.87
J.R. Smith...............115.93
Allen Iverson............114.19
Carmelo Anthony..........111.23
Eduardo Najera...........110.93
Kenyon Martin............110.62
NUGGETS AVERAGE..........109.60
LEAGUE AVERAGE...........106.96
Yakouba Diawara..........106.34
Bobby Jones..............104.43
Anthony Carter............99.92
Marcus Camby..............98.89
Chucky Atkins.............97.70
Steven Hunter.............96.61
Taureen Green.............91.58
Nene Hilario..............84.94
Von Wafer.................59.81
It is mildly surprising that Linas Kleiza is the most efficient Nuggets player on offense. Three point shooters often look really good under this system because they have many possessions where they generate three points (a 300.00 rating). Also, he uses a relatively low percentage of possessions (17.7). It is not necessarily the case that Kleiza would maintain this efficiency if he used a higher percentage of possessions, because in that case, it would be likely that the defense would focus on him.
AI's numbers are remarkable. Defenses prepare for him, he uses a large percentage of possessions, and he averages over 7 points per 100 possessions better than the average NBA player. Needless to say, he is very valuable for this exact reason.
It is interesting to note that two of the Nuggets starters are well below average on offense (Camby and Carter). This probably helps explain why it is easier to defend the AI-Melo duo. Defenses can basically ignore two players and focus on the superstars. This is why the Nuggets lineups with shooters (Smith, Najera, and Kleiza) are significantly better on offense.
5.28.2008
5.27.2008
Lakers-Spurs preview/review
Three games into the Western Conference Finals, we have a decent idea of how the Spurs and the Lakers match up. Here are how the season numbers play out for the teams in this series.
OFFENSIVE QUOTIENT:
Los Angeles Lakers.....5.47
San Antonio Spurs.....-0.20
DEFENSIVE QUOTIENT:
Los Angeles Lakers.....1.71
San Antonio Spurs......5.69
The Spurs are significantly better on defense and the Lakers are significantly better on offense. This is not a surprise. However, I had no idea that the Spurs were below average on offense. With Duncan, Parker and Ginobili, this is a serious indictment of the Spurs' supporting cast. Also, while the Lakers' offensive numbers are impressive, they are even more impressive after Gasol joined the team (+7.44), while still remaining above average on defense (+0.28).
Since the home/road splits have been more accurate this year, here are those full season numbers for each team:
OFFENSE
Lakers Home
Los Angeles Lakers........6.29
San Antonio Spurs........-2.67
Spurs Home
Los Angeles Lakers........4.63
San Antonio Spurs.........2.25
DEFENSE
Lakers Home
Los Angeles Lakers........3.24
San Antonio Spurs.........2.82
Spurs Home
Los Angeles Lakers........0.15
San Antonio Spurs.........8.53
These numbers lead to another series with a wide disparity between home and road performances for each team. So it is not a surprise that the road team has won each game.
A look backwards...
Each team has had approximately 282 possessions in this series. Based on the home raod splits from the numbers above, we would expect the Lakers to have outscored the Spurs by approximately 12.36 points over the course of the series. The actual difference between the two teams is 16 points. This shows that the numbers are fairly accurate and the fact that there has been a significant amount of garbage time in the last two games easily explains the difference between the two figures (although the difference amounts to an error of approximately one percent).
A look forward...
A safe bet would be to assume that each team will win their remaining home games. However, the Lakers have approximately a 48.8% chance of taking one of the remaining two games in San Antonio and the Spurs have a 32.9% chance of taking one of the two final games in LA. Because both of these percentages are below fifty, I would expect this to be a seven game series.
OFFENSIVE QUOTIENT:
Los Angeles Lakers.....5.47
San Antonio Spurs.....-0.20
DEFENSIVE QUOTIENT:
Los Angeles Lakers.....1.71
San Antonio Spurs......5.69
The Spurs are significantly better on defense and the Lakers are significantly better on offense. This is not a surprise. However, I had no idea that the Spurs were below average on offense. With Duncan, Parker and Ginobili, this is a serious indictment of the Spurs' supporting cast. Also, while the Lakers' offensive numbers are impressive, they are even more impressive after Gasol joined the team (+7.44), while still remaining above average on defense (+0.28).
Since the home/road splits have been more accurate this year, here are those full season numbers for each team:
OFFENSE
Lakers Home
Los Angeles Lakers........6.29
San Antonio Spurs........-2.67
Spurs Home
Los Angeles Lakers........4.63
San Antonio Spurs.........2.25
DEFENSE
Lakers Home
Los Angeles Lakers........3.24
San Antonio Spurs.........2.82
Spurs Home
Los Angeles Lakers........0.15
San Antonio Spurs.........8.53
These numbers lead to another series with a wide disparity between home and road performances for each team. So it is not a surprise that the road team has won each game.
A look backwards...
Each team has had approximately 282 possessions in this series. Based on the home raod splits from the numbers above, we would expect the Lakers to have outscored the Spurs by approximately 12.36 points over the course of the series. The actual difference between the two teams is 16 points. This shows that the numbers are fairly accurate and the fact that there has been a significant amount of garbage time in the last two games easily explains the difference between the two figures (although the difference amounts to an error of approximately one percent).
A look forward...
A safe bet would be to assume that each team will win their remaining home games. However, the Lakers have approximately a 48.8% chance of taking one of the remaining two games in San Antonio and the Spurs have a 32.9% chance of taking one of the two final games in LA. Because both of these percentages are below fifty, I would expect this to be a seven game series.
5.20.2008
Eastern Conference Finals Preview
It is probably wrong to do an analysis of a series after the first game, but the numbers I use are not affected by me watching a game, so here are the numbers for the Detroit-Boston matchup.
Again, I have calculated the offensive and defensive quotients for each teams and predicted the results accordingly.
Offensive Numbers:
Boston Celtics......2.45
Detroit Pistons.....3.01
The numbers demonstrate that both teams are above-average offenses and that Detroit is approximately a half a point better per 100 possessions than Boston.
Defensive Numbers:
Boston Celtics......7.96
Detroit Pistons.....4.23
Both teams have superior defenses, however, Boston's defense (as we knew) was unbelievable this year. Boston's defense was almost 8 points per 100 possessions better than the average NBA team. To put this in perspective, their defense was worth about 24-25 wins more than the average team. Although the Pistons are a good defensive team, the Celtics have a clear advantage in this series.
Based on these overall numbers, we can expect the Celtics to prevail in 63.16% of the games played between the teams. This means that the Celtics should win the series 76.87% of the time.
However, we have learned throughout the playoffs that the home-road split numbers are more accurate in determining an outcome than the overall numbers.
BOSTON HOME
Offense:
Boston Celtics.......2.84
Detroit Pistons......0.41
Defense:
Boston Celtics.......10.40
Detroit Pistons......1.74
DETROIT HOME
Offense:
Boston Celtics.......2.06
Detroit Pistons......5.62
Defense:
Boston Celtics.......5.53
Detroit Pistons......6.70
Obviously both teams have the advantage at home, however, Boston's advantage is striking. They are over 10 points better than the average NBA defense at home. Based on these numbers, Boston would be expected to win 86.65% of its home games in this series and Detroit would be expected to win 68.11% of its games at home.
Based on these numbers, the safest prediction is that Boston wins in 7 (although, Boston has a 68.4% chance to take one of the three games in Detroit -- I say "safest" pick because, in case you haven't heard, Boston hasn't played too well on the road recently).
Now that I have seen Game 1, we can take a look at how the numbers played out. My models predicted that Boston would win the first home game by a score of about 97-87. The actual score was 88-79. My prediction could have been off because of an incorrect calculation of the pace of the game or because each defense played better than the calculations bore out (or offenses played worse, whichever you prefer). I had to look deeper to see why the numbers were off.
My models predicted that the games in Boston would be played at about 91-92 possessions/game. Both teams played incredibly slow in the regular season (for example, about 11 possessions/game slower than the Nuggets) and there was no reason to expect that this would change. However, after looking at the game stat sheet, I realized that the game had about 84 possessions. This seems be due to Detroit's conscious effort to slow down the game to a snail's pace. This is a GREAT strategy when you are an underdog (as Detroit is in the games played in Boston). When I recalculate the outcome of Game 1 based on 84 possessions instead of 91-92, I get a final score of (no joke!) 88.49-79.00.
Although this evidence is admittedly a TINY sample size, it appears that I may be on to something.
Again, I have calculated the offensive and defensive quotients for each teams and predicted the results accordingly.
Offensive Numbers:
Boston Celtics......2.45
Detroit Pistons.....3.01
The numbers demonstrate that both teams are above-average offenses and that Detroit is approximately a half a point better per 100 possessions than Boston.
Defensive Numbers:
Boston Celtics......7.96
Detroit Pistons.....4.23
Both teams have superior defenses, however, Boston's defense (as we knew) was unbelievable this year. Boston's defense was almost 8 points per 100 possessions better than the average NBA team. To put this in perspective, their defense was worth about 24-25 wins more than the average team. Although the Pistons are a good defensive team, the Celtics have a clear advantage in this series.
Based on these overall numbers, we can expect the Celtics to prevail in 63.16% of the games played between the teams. This means that the Celtics should win the series 76.87% of the time.
However, we have learned throughout the playoffs that the home-road split numbers are more accurate in determining an outcome than the overall numbers.
BOSTON HOME
Offense:
Boston Celtics.......2.84
Detroit Pistons......0.41
Defense:
Boston Celtics.......10.40
Detroit Pistons......1.74
DETROIT HOME
Offense:
Boston Celtics.......2.06
Detroit Pistons......5.62
Defense:
Boston Celtics.......5.53
Detroit Pistons......6.70
Obviously both teams have the advantage at home, however, Boston's advantage is striking. They are over 10 points better than the average NBA defense at home. Based on these numbers, Boston would be expected to win 86.65% of its home games in this series and Detroit would be expected to win 68.11% of its games at home.
Based on these numbers, the safest prediction is that Boston wins in 7 (although, Boston has a 68.4% chance to take one of the three games in Detroit -- I say "safest" pick because, in case you haven't heard, Boston hasn't played too well on the road recently).
Now that I have seen Game 1, we can take a look at how the numbers played out. My models predicted that Boston would win the first home game by a score of about 97-87. The actual score was 88-79. My prediction could have been off because of an incorrect calculation of the pace of the game or because each defense played better than the calculations bore out (or offenses played worse, whichever you prefer). I had to look deeper to see why the numbers were off.
My models predicted that the games in Boston would be played at about 91-92 possessions/game. Both teams played incredibly slow in the regular season (for example, about 11 possessions/game slower than the Nuggets) and there was no reason to expect that this would change. However, after looking at the game stat sheet, I realized that the game had about 84 possessions. This seems be due to Detroit's conscious effort to slow down the game to a snail's pace. This is a GREAT strategy when you are an underdog (as Detroit is in the games played in Boston). When I recalculate the outcome of Game 1 based on 84 possessions instead of 91-92, I get a final score of (no joke!) 88.49-79.00.
Although this evidence is admittedly a TINY sample size, it appears that I may be on to something.
5.16.2008
Do the best teams really win the close games?
It seems to be a popular theory that the best teams in the NBA are those who execute down the stretch and win close games. Therefore, it would stand to reason that the best teams would have the best records in close games. However, this is not the case.
Here are the records of teams in games decided by three points or fewer in 2007-2008:
Portland Trailblazers...10-2
Golden State Wariors.....9-2
Houston Rockets..........9-3
New Jersey Nets..........7-3
New Orleans Hornets......8-4
Detroit Pistons..........5-3
San Antonio Spurs........8-6
Charlotte Bobcats........8-6
Utah Jazz................4-3
Indiana Pacers...........4-3
Chicago Bulls............4-3
Sacremento Kings........10-8
Cleveland Cavaliers.....10-8
Atlanta Hawks............6-5
Boston Celtics...........7-6
Denver Nuggets...........6-6
Orlando Magic............6-6
Torono Raptors...........3-3
Dallas Mavericks.........5-6
New York Knicks..........4-5
Seattle Supersonics......5-7
Milwaukee Bucks..........6-9
Los Angeles Lakers.......5-8
Washington Wizards.......5-9
Phoenix Suns.............3-5
Philadelphia 76ers.......4-8
Minnesota Timberwolves..4-8
LA Clippers..............2-5
Miami Heat..............3-11
Memphis Grizzlies.......2-11
This certainly does not look as though the best teams had the best record in close games. Unless, of course, you believe that the New Jersey Nets, Golden State Warriors, and Portland Trailblazers are three of the top five teams in the NBA. Also, the Lakers (who are considered to be one of the best teams in the NBA), fared among the worst in these close games. An argument could be made that these are small sample sizes and therefore statistically insignificant. This is not necessarily the case. For instance the Lakers record of 5-8 in close games would only happen by random chance 1.5% of the time. Therefore, it seems clear that in many cases, a team's record in close games has nothing to do with how good the team is.
On the contrary, a team's record in blowouts seems to be a much better indicator of how good a team is. Here are the records of teams in games decided by 10 or more points:
Boston Celtics............45-3
Los Angeles Lakers........37-9
Detroit Pistons..........37-10
Phoenix Suns..............31-9
Orlando Magic............34-12
San Antonio Spurs........31-11
Houston Rockets..........31-11
Utah Jazz................37-14
Dallas Mavericks.........29-11
New Orleans Hornets......37-15
Toronto Raptors..........26-16
Denver Nuggets...........29-18
Golden State Warriors....22-14
Washington Wizards.......26-19
Philadeplphia 76ers......18-20
Sacremento Kings.........17-23
Portland Trailblazers....15-22
Chicago Bulls............19-29
Indiana Pacers...........14-22
Cleveland Cavaliers......10-17
Charlotte Bobcats........12-24
Atlanta Hawks............11-24
Los Angeles Clippers.....10-35
Memphis Grizzlies........10-37
New Jersey Nets...........8-31
Minnesota Timberwolves...8-35
New York Knicks...........6-33
Milwaukee Bucks...........5-29
Seattle Supersonics.......5-37
Miami Heat................4-34
This looks a lot more like a ranking of the best teams. The top twelve teams all made the playoffs. It appears as though the teams that win blowouts are much likely to be better teams than those who win close games.
John Hollinger stated it well in a recent chat on ESPN.com:
Here are the records of teams in games decided by three points or fewer in 2007-2008:
Portland Trailblazers...10-2
Golden State Wariors.....9-2
Houston Rockets..........9-3
New Jersey Nets..........7-3
New Orleans Hornets......8-4
Detroit Pistons..........5-3
San Antonio Spurs........8-6
Charlotte Bobcats........8-6
Utah Jazz................4-3
Indiana Pacers...........4-3
Chicago Bulls............4-3
Sacremento Kings........10-8
Cleveland Cavaliers.....10-8
Atlanta Hawks............6-5
Boston Celtics...........7-6
Denver Nuggets...........6-6
Orlando Magic............6-6
Torono Raptors...........3-3
Dallas Mavericks.........5-6
New York Knicks..........4-5
Seattle Supersonics......5-7
Milwaukee Bucks..........6-9
Los Angeles Lakers.......5-8
Washington Wizards.......5-9
Phoenix Suns.............3-5
Philadelphia 76ers.......4-8
Minnesota Timberwolves..4-8
LA Clippers..............2-5
Miami Heat..............3-11
Memphis Grizzlies.......2-11
This certainly does not look as though the best teams had the best record in close games. Unless, of course, you believe that the New Jersey Nets, Golden State Warriors, and Portland Trailblazers are three of the top five teams in the NBA. Also, the Lakers (who are considered to be one of the best teams in the NBA), fared among the worst in these close games. An argument could be made that these are small sample sizes and therefore statistically insignificant. This is not necessarily the case. For instance the Lakers record of 5-8 in close games would only happen by random chance 1.5% of the time. Therefore, it seems clear that in many cases, a team's record in close games has nothing to do with how good the team is.
On the contrary, a team's record in blowouts seems to be a much better indicator of how good a team is. Here are the records of teams in games decided by 10 or more points:
Boston Celtics............45-3
Los Angeles Lakers........37-9
Detroit Pistons..........37-10
Phoenix Suns..............31-9
Orlando Magic............34-12
San Antonio Spurs........31-11
Houston Rockets..........31-11
Utah Jazz................37-14
Dallas Mavericks.........29-11
New Orleans Hornets......37-15
Toronto Raptors..........26-16
Denver Nuggets...........29-18
Golden State Warriors....22-14
Washington Wizards.......26-19
Philadeplphia 76ers......18-20
Sacremento Kings.........17-23
Portland Trailblazers....15-22
Chicago Bulls............19-29
Indiana Pacers...........14-22
Cleveland Cavaliers......10-17
Charlotte Bobcats........12-24
Atlanta Hawks............11-24
Los Angeles Clippers.....10-35
Memphis Grizzlies........10-37
New Jersey Nets...........8-31
Minnesota Timberwolves...8-35
New York Knicks...........6-33
Milwaukee Bucks...........5-29
Seattle Supersonics.......5-37
Miami Heat................4-34
This looks a lot more like a ranking of the best teams. The top twelve teams all made the playoffs. It appears as though the teams that win blowouts are much likely to be better teams than those who win close games.
John Hollinger stated it well in a recent chat on ESPN.com:
Will (NYC): I agree that some close games are 50/50 but those are in the minority. A big part of being a great team is the ability to show heart and win the close games. It's called performing under pressure and that is something that Boston showed they may be lacking greatly. That is why people are less confident in their chances.
John Hollinger: A lot of people believe that, but the evidence it isn't true is just overwhelming. Look at any team that was together for a number of years, even the great ones -- Jordan's Bulls, for instance -- and you'll find that the closer the score, the closer they are to .500. In other words, in games decided by two points or less they'd be almost exactly .500, even a team like the Bulls; in games decided by 15 points or more they'd be nearly 1.000. It's a fallacy that the good teams win the close games; the good teams win by 20. The lucky teams win the close games. There is no team in history that's been able to defy the correlation between scoring margin and wins over an extended period.
5.14.2008
So What is Going to Happen in the Utah-Los Angeles Series?
Here is a quick analysis of the Jazz-Lakers series and what I believe will occur in the remaining three games...
I calculate something called an Offensive Quotient and Defensive Quotient, which is a measurement of how each team performs in comparison with the average team over the course of 100 possessions. The resulting number represents the amount of points a given team is better (or worse) than the "average" NBA team. I use these numbers to calculate the outcome of any given game.
In the Jazz-Lakers series, it is clear that the teams are pretty close to equal.
Offensive Quotient:
Utah.........6.01
LA Lakers....5.46
Defensive Quotient:
Utah.........0.65
LA Lakers....1.71
These numbers demonstrate that the Jazz are about a half a point per game better than the Lakers on offense and about a full point worse than the Lakers on defense. However, both teams made major acquisitions during the season. Here are the numbers for the Jazz after acquiring Kyle Korver and the Lakers after acquiring Pau Gasol.
Offensive Quotient:
Utah..........7.85
LA Lakers.....7.43
Defensive Quotient:
Utah..........0.60
LA Lakers.....0.27
Both teams were absolutely ridiculous on offense after their trades and still slightly better than average on defense.
In the previous four games of the series the home team won. The question then is how the numbers play out if we use home-road splits (using numbers from the entire season):
HOME
LA Lakers
Offensive Quotient.......6.29
Defensive Quotient.......3.24
Utah Jazz
Offensive Quotient.......10.43
Defensive Quotient.......5.03
ROAD
LA Lakers
Offensive Quotient......4.63
Defensive Quotient......0.15
Utah Jazz
Offensive Quotient.......1.70
Defensive Quotient......-3.68
Obviously, each team is considerably better at home, especially the Jazz. This is nothing new. So how does this play out for the series?
Using post-Korver and post-Gasol numbers, you find that in a series of games with even home-road splits (like a 6 game series with 3 home game for each team), Utah would be expected to win 51.30% of the games with an average score of 108.05-107.71. However, as we know, this is a seven game series with the Lakers holding home court advantage. This significantly favors the Lakers (especially with the small sample size of only three games remaining).
The numbers show that in the average home game for the Lakers, they should beat the Jazz 83.23% of the time (Yikes!!). The average score should be 110.48-100.26 (obviously favoring the Lakers). Almost the exact opposite is true for Jazz home games. The Jazz should win home games against the Lakers 84.82% of the time by an average score of 112.39-101.25.
Since the Lakers have two home games to win two games and the Jazz have one home game and two more games to win, the significant advantage goes to the Lakers. Based on these numbers, the Lakers should win the series 74.83% of the time. This is probably consistent with popular opinion. However, if Utah wins tonight, their odds to win the series improve from 25.17% to 87.37%. Needless to say, whoever wins tonight, wins the series.
I calculate something called an Offensive Quotient and Defensive Quotient, which is a measurement of how each team performs in comparison with the average team over the course of 100 possessions. The resulting number represents the amount of points a given team is better (or worse) than the "average" NBA team. I use these numbers to calculate the outcome of any given game.
In the Jazz-Lakers series, it is clear that the teams are pretty close to equal.
Offensive Quotient:
Utah.........6.01
LA Lakers....5.46
Defensive Quotient:
Utah.........0.65
LA Lakers....1.71
These numbers demonstrate that the Jazz are about a half a point per game better than the Lakers on offense and about a full point worse than the Lakers on defense. However, both teams made major acquisitions during the season. Here are the numbers for the Jazz after acquiring Kyle Korver and the Lakers after acquiring Pau Gasol.
Offensive Quotient:
Utah..........7.85
LA Lakers.....7.43
Defensive Quotient:
Utah..........0.60
LA Lakers.....0.27
Both teams were absolutely ridiculous on offense after their trades and still slightly better than average on defense.
In the previous four games of the series the home team won. The question then is how the numbers play out if we use home-road splits (using numbers from the entire season):
HOME
LA Lakers
Offensive Quotient.......6.29
Defensive Quotient.......3.24
Utah Jazz
Offensive Quotient.......10.43
Defensive Quotient.......5.03
ROAD
LA Lakers
Offensive Quotient......4.63
Defensive Quotient......0.15
Utah Jazz
Offensive Quotient.......1.70
Defensive Quotient......-3.68
Obviously, each team is considerably better at home, especially the Jazz. This is nothing new. So how does this play out for the series?
Using post-Korver and post-Gasol numbers, you find that in a series of games with even home-road splits (like a 6 game series with 3 home game for each team), Utah would be expected to win 51.30% of the games with an average score of 108.05-107.71. However, as we know, this is a seven game series with the Lakers holding home court advantage. This significantly favors the Lakers (especially with the small sample size of only three games remaining).
The numbers show that in the average home game for the Lakers, they should beat the Jazz 83.23% of the time (Yikes!!). The average score should be 110.48-100.26 (obviously favoring the Lakers). Almost the exact opposite is true for Jazz home games. The Jazz should win home games against the Lakers 84.82% of the time by an average score of 112.39-101.25.
Since the Lakers have two home games to win two games and the Jazz have one home game and two more games to win, the significant advantage goes to the Lakers. Based on these numbers, the Lakers should win the series 74.83% of the time. This is probably consistent with popular opinion. However, if Utah wins tonight, their odds to win the series improve from 25.17% to 87.37%. Needless to say, whoever wins tonight, wins the series.
Introduction to Adjusted Scoring Margin
This year as I was preparing to fill out an NCAA bracket, I wanted to use something beyond the typical, "I saw North Carolina play, and they look pretty good." As most people who follow sports statistics know, scoring margin is the best predictor of future success. However, with the college game there is so much of a variance in the strength of schedule that pure scoring margin seems like a silly way to evaluate teams.
I decided to use a formula to determine how well teams performed against a given team based on how the other teams performed against that team. For example, let's take a situation where Team A beats Team B 80-70. Let's also say that Team B typically scores 65 points a game and gives up 85 points per game. Team A scored 80 points, but since Team B typically gives up 85 points, Team A actually performed 5 points worse than the "average" college offense (Offensive Quotient). On defense, Team A gave up 70 points, but since Team B typically only scores 65 points, Team A again performed 5 points worse than the average college defense (Defensive Quotient). By just looking at the game, Team A would get a +10 scoring margin, but with the adjusted scoring margin, Team A gets a -10 rating (the offensive quotient plus the defensive quotient). If you add a team's adjusted scoring margin ("ASM") for each game and divide by the number of games you can rate the teams accordingly. Obviously, a team with a zero ASM is average (negative is bad and positive is good).
So I threw the numbers together and found that Kansas was the best team followed by Memphis, *cough* Duke *cough*, North Carolina, and UCLA. So it seemed that a Final Four with the four number one seeds was likely (not a surprise that the numbers would bear this out). Once the Final Four came around and there were four number one seeds left, I calculated the outcomes of the games for one of my buddies who has a hypothetical gambling problem (to quote the Sports Guy, "if gambling were legal"). I told my buddy that the hypothetical lines were off and to take a Memphis-Kansas final. He made a lot of hypothetical money. Then he had me look at the final and I discovered that Kansas should have been a one point favorite. At the time Memphis was at -2 (hypothetically). So I told him to take Kansas. Shortly thereafter Rose disclosed that he was hurt and the line changed to favor Kansas. My buddy hypothetically took Kansas anyways because I said that they were better. One Mario Chalmers shot later (it was a close game as the numbers demonstrated) and a good overtime for Kansas and my buddy made a lot more hypothetical money.
My eventual design was to translate this to the NBA because it would be more effective since each team plays every other team at least twice. So I use the same system only I calculate how many points an average team would score or give up based on offensive and defensive efficiency. This method is particularly helpful early in the season when strength of schedule varies much more. Using offensive and defensive efficiency to determine strength of schedule is better than W/L record because records are often based on flukes (I will tackle this topic independently some day). The NBA ASM allows me to tell who has played the most difficult schedules (both on offense and defense), the best offensive teams, the best defensive teams and an expected outcome of any game.
I will begin doing a team-by-team assesment of the 2007-2008 season based on these numbers very soon.
I decided to use a formula to determine how well teams performed against a given team based on how the other teams performed against that team. For example, let's take a situation where Team A beats Team B 80-70. Let's also say that Team B typically scores 65 points a game and gives up 85 points per game. Team A scored 80 points, but since Team B typically gives up 85 points, Team A actually performed 5 points worse than the "average" college offense (Offensive Quotient). On defense, Team A gave up 70 points, but since Team B typically only scores 65 points, Team A again performed 5 points worse than the average college defense (Defensive Quotient). By just looking at the game, Team A would get a +10 scoring margin, but with the adjusted scoring margin, Team A gets a -10 rating (the offensive quotient plus the defensive quotient). If you add a team's adjusted scoring margin ("ASM") for each game and divide by the number of games you can rate the teams accordingly. Obviously, a team with a zero ASM is average (negative is bad and positive is good).
So I threw the numbers together and found that Kansas was the best team followed by Memphis, *cough* Duke *cough*, North Carolina, and UCLA. So it seemed that a Final Four with the four number one seeds was likely (not a surprise that the numbers would bear this out). Once the Final Four came around and there were four number one seeds left, I calculated the outcomes of the games for one of my buddies who has a hypothetical gambling problem (to quote the Sports Guy, "if gambling were legal"). I told my buddy that the hypothetical lines were off and to take a Memphis-Kansas final. He made a lot of hypothetical money. Then he had me look at the final and I discovered that Kansas should have been a one point favorite. At the time Memphis was at -2 (hypothetically). So I told him to take Kansas. Shortly thereafter Rose disclosed that he was hurt and the line changed to favor Kansas. My buddy hypothetically took Kansas anyways because I said that they were better. One Mario Chalmers shot later (it was a close game as the numbers demonstrated) and a good overtime for Kansas and my buddy made a lot more hypothetical money.
My eventual design was to translate this to the NBA because it would be more effective since each team plays every other team at least twice. So I use the same system only I calculate how many points an average team would score or give up based on offensive and defensive efficiency. This method is particularly helpful early in the season when strength of schedule varies much more. Using offensive and defensive efficiency to determine strength of schedule is better than W/L record because records are often based on flukes (I will tackle this topic independently some day). The NBA ASM allows me to tell who has played the most difficult schedules (both on offense and defense), the best offensive teams, the best defensive teams and an expected outcome of any game.
I will begin doing a team-by-team assesment of the 2007-2008 season based on these numbers very soon.
Points Saved
Dan Rosenbaum of 82games.com sums up the difficulties of quanitfying defense with traditional statistics nicely:
In order to make an attempt to better measure defense, I have developed a relatively uncomplicated statistic called "points saved." This differs from John Hollinger's points saved statistics because I measure it based on a per-possession number and quantify it over the course of the season. I do this because a guy who plays great defense for 80 possessions per game over the course of a season is more valuable than a guy who defends equally as well, but only plays for 20 possessions a game.
Points saved is calculated by comparing the defensive efficiency of a team when a player is in with the defensive efficiency of a team when the player is sitting on the bench. The number represents the amount of points a team saved (or lost, if the defender is poor) by playing a particular player instead of the other lineups that do not include the particular player. The second number is the amount of points saved per 100 possessions. This represents the amount of points saved by playing the player for an average NBA game instead of other lineups without the player.
There are a couple of major flaws with this system and for these reasons, this stat (like any other) should be taken as an incomplete measure of defensive prowess. First, if a player is on a bad defensive team, and he is a good defensive player, his numbers will be skewed to make him look like the greatest defender of all time (we'll call this the Raja Bell syndrome). Conversely, if the player is a good defender on a good defensive team, this stat will make him look worse than he actually is (Kevin Garnett syndrome). Also, this stat is heavily influenced by a player's backup -- if a player's backup is good, he is replacing the player with good defense which will skew the stat (Dwight Howard syndrome). So, it is important to keep in mind the context from which the stat is derived. Also, small sample sizes will mess things up. For instance, AI is on the floor virtually all the time and therefore there is a small sample size of Nuggets defenses without him.
Without further ado, here are the points saved totals for the 2007-2008 Denver Nuggets (only players playing 1000 possessions or more this season):
Eduardo Najera.................186.53
Allen Iverson..................144.82
Yakouba Diawara.................47.64
J.R. Smith......................38.87
Marcus Camby.....................7.68
Kenyon Martin..................-44.75
Linas Kleiza...................-58.89
Anthony Carter................-140.66
Carmelo Anthony...............-299.84
Points Saved/100 Possessions
Eduardo Najera..................5.42
Yakouba Diawara.................4.20
Allen Iverson...................2.04
J.R. Smith......................1.31
Marcus Camby....................0.13
Kenyon Martin..................-1.00
Linas Kleiza...................-1.51
Anthony Carter.................-3.42
Carmelo Anthony................-5.14
Here are the defensive efficiencies of the Nuggets when these players are in the game:
Yakouba Diawara................102.56
Eduardo Najera.................103.02
J.R. Smith.....................105.35
Allen Iverson..................105.91
Marcus Camby...................106.15
Kenyon Martin..................106.64
Linas Kleiza...................106.99
Carmelo Anthony................107.70
Anthony Carter.................107.91
Surprisingly, Eduardo Najera seems to be the best defensive player on the Nuggets. Also, there are none of the warning indicators that are discussed above: his backups are not particularly good or bad, he played about 40% of Nuggets possessions, and the Nuggets are neither a really good nor really bad defensive team. So there is a chance that he is a really good defender. This is probably because he is quick for a big guy and tries his tail off.
Anthony Carter is a bad defender. This may come as a surprise to George Karl, who played him all season because of his defense. Don't get me wrong, I LOVE Carter as a player (for his heart and determination), but he is not a very good professional basketball player. I don't know if I will be able to take it when I calculate his offensive numbers.
Carmelo is a VERY bad defender. This should surprise no one. The strange thing, is that I am not entirely sure he is that efficient on offense either. Maybe we should trade him before someone figures this out.
I believe that AI's numbers are skewed because the Nuggets rarely played without him. He is typically considered a poor defender. The numbers look a little more normal when calculated per 100 possessions, but I bet that this season was a fluke (at some point I will compare these numbers to previous seasons).
The 2007 Defensive Player of the Year is an average defender. This could be because he cannot guard big players by himself and because he only cares about blocks and rebounds instead of "defense." Or it could be because he has played the entire year with a fork sticking out of his back. At least he took the entire year off on offense in order to make the All-Defense 1st team again. That should look nice on his resume. Too bad it doesn't help his team. He is another trade candidate.
J.R. Smith is not bad considering he was benched for half the season because George Karl did not think he played any defense. Oh well.
Yakouba Diawara plays really good defense. This shouldn't surprise Nuggets fans. This could be the perimeter defender the Nuggets are looking for, however, I believe his offensive numbers may be poor. Surprisingly, the lineup the Nuggets used the second most often this season included Diawara (remember he played a lot early in the season) and it outscored their opponents by 60 points in only 169 minutes.
Please feel free to leave any comments or criticisms.
UPDATE: I am working on a formula to take into consideration the overall effectiveness of the team on which a player plays. This will make cross-team comparisons possible.
Defense is all about keeping the other team from scoring. A player can be a good defender by getting a steal, a block, or a defensive rebound, but those stats offer only a snapshot of how effective a player is on defense. A player can also be an effective defender by denying the ball to an efficient scorer or by letting an inefficient scorer shoot more. Or by providing help defense in a way that does not expose other good scoring opportunities.
In order to make an attempt to better measure defense, I have developed a relatively uncomplicated statistic called "points saved." This differs from John Hollinger's points saved statistics because I measure it based on a per-possession number and quantify it over the course of the season. I do this because a guy who plays great defense for 80 possessions per game over the course of a season is more valuable than a guy who defends equally as well, but only plays for 20 possessions a game.
Points saved is calculated by comparing the defensive efficiency of a team when a player is in with the defensive efficiency of a team when the player is sitting on the bench. The number represents the amount of points a team saved (or lost, if the defender is poor) by playing a particular player instead of the other lineups that do not include the particular player. The second number is the amount of points saved per 100 possessions. This represents the amount of points saved by playing the player for an average NBA game instead of other lineups without the player.
There are a couple of major flaws with this system and for these reasons, this stat (like any other) should be taken as an incomplete measure of defensive prowess. First, if a player is on a bad defensive team, and he is a good defensive player, his numbers will be skewed to make him look like the greatest defender of all time (we'll call this the Raja Bell syndrome). Conversely, if the player is a good defender on a good defensive team, this stat will make him look worse than he actually is (Kevin Garnett syndrome). Also, this stat is heavily influenced by a player's backup -- if a player's backup is good, he is replacing the player with good defense which will skew the stat (Dwight Howard syndrome). So, it is important to keep in mind the context from which the stat is derived. Also, small sample sizes will mess things up. For instance, AI is on the floor virtually all the time and therefore there is a small sample size of Nuggets defenses without him.
Without further ado, here are the points saved totals for the 2007-2008 Denver Nuggets (only players playing 1000 possessions or more this season):
Eduardo Najera.................186.53
Allen Iverson..................144.82
Yakouba Diawara.................47.64
J.R. Smith......................38.87
Marcus Camby.....................7.68
Kenyon Martin..................-44.75
Linas Kleiza...................-58.89
Anthony Carter................-140.66
Carmelo Anthony...............-299.84
Points Saved/100 Possessions
Eduardo Najera..................5.42
Yakouba Diawara.................4.20
Allen Iverson...................2.04
J.R. Smith......................1.31
Marcus Camby....................0.13
Kenyon Martin..................-1.00
Linas Kleiza...................-1.51
Anthony Carter.................-3.42
Carmelo Anthony................-5.14
Here are the defensive efficiencies of the Nuggets when these players are in the game:
Yakouba Diawara................102.56
Eduardo Najera.................103.02
J.R. Smith.....................105.35
Allen Iverson..................105.91
Marcus Camby...................106.15
Kenyon Martin..................106.64
Linas Kleiza...................106.99
Carmelo Anthony................107.70
Anthony Carter.................107.91
Surprisingly, Eduardo Najera seems to be the best defensive player on the Nuggets. Also, there are none of the warning indicators that are discussed above: his backups are not particularly good or bad, he played about 40% of Nuggets possessions, and the Nuggets are neither a really good nor really bad defensive team. So there is a chance that he is a really good defender. This is probably because he is quick for a big guy and tries his tail off.
Anthony Carter is a bad defender. This may come as a surprise to George Karl, who played him all season because of his defense. Don't get me wrong, I LOVE Carter as a player (for his heart and determination), but he is not a very good professional basketball player. I don't know if I will be able to take it when I calculate his offensive numbers.
Carmelo is a VERY bad defender. This should surprise no one. The strange thing, is that I am not entirely sure he is that efficient on offense either. Maybe we should trade him before someone figures this out.
I believe that AI's numbers are skewed because the Nuggets rarely played without him. He is typically considered a poor defender. The numbers look a little more normal when calculated per 100 possessions, but I bet that this season was a fluke (at some point I will compare these numbers to previous seasons).
The 2007 Defensive Player of the Year is an average defender. This could be because he cannot guard big players by himself and because he only cares about blocks and rebounds instead of "defense." Or it could be because he has played the entire year with a fork sticking out of his back. At least he took the entire year off on offense in order to make the All-Defense 1st team again. That should look nice on his resume. Too bad it doesn't help his team. He is another trade candidate.
J.R. Smith is not bad considering he was benched for half the season because George Karl did not think he played any defense. Oh well.
Yakouba Diawara plays really good defense. This shouldn't surprise Nuggets fans. This could be the perimeter defender the Nuggets are looking for, however, I believe his offensive numbers may be poor. Surprisingly, the lineup the Nuggets used the second most often this season included Diawara (remember he played a lot early in the season) and it outscored their opponents by 60 points in only 169 minutes.
Please feel free to leave any comments or criticisms.
UPDATE: I am working on a formula to take into consideration the overall effectiveness of the team on which a player plays. This will make cross-team comparisons possible.
5.13.2008
2007-2008 Defensive Efficiency
The following is a ranking of teams according to their defensive efficiency in the 2007-2008 NBA season. Defensive efficiency measures the average amount of points a team gives up per 100 possessions (an average NBA game). This is a significantly better way to measure the defensive prowess than simple points per game because it is not affected by how fast a team plays (for instance, the Nuggets play faster than every team in the NBA, so their defensive ppg is skewed to make their defense look worse than it actually is and their offensive ppg is skewed to make their offense look better than it actually is).
Boston Celtics.......................98.54
Houston Rockets.....................101.02
San Antonio Spurs...................101.27
Detroit Pistons.....................102.26
New Orleans Hornets.................105.01
Los Angeles Lakers..................105.03
Orlando Magic.......................105.39
Dallas Mavericks....................105.46
Philadelphia 76ers..................105.57
Utah Jazz...........................105.74
Cleveland Cavaliers.................105.92
Denver Nuggets......................106.19
Toronto Raptors.....................106.43
Chicago Bulls.......................106.47
LEAGUE AVERAGE......................106.96
Indiana Pacers......................107.09
Phoenix Suns........................107.42
Portland Trailblazers...............107.78
Atlanta Hawks.......................108.15
New Jersey Nets.....................108.57
Washington Wizards..................108.63
Los Angeles Clippers................108.68
Golden State Warriors...............109.12
Charlotte Bobcats...................109.16
Sacramento Kings....................109.33
Seattle Supersonics.................109.41
Miami Heat..........................109.58
Minnesota Timberwolves..............110.91
Memphis Grizzlies...................111.13
New York Knicks.....................111.45
Milwaukee Bucks.....................112.06
There are a couple of interesting things to note about this list.
First of all, the Boston Celtics are the best defensive team in the NBA. And it isn't even close. John Hollinger of ESPN has stated that this Celtics team is the 3rd best defensivev team of all time.
The Milwaukee Bucks are the worst defensive team in the league. This is not surprising given that Michael Redd is known for being one of the worst defensive players in the league.
The top 13 teams in defense made the playoffs. I believe that I will find that the same is NOT true for offense. Therefore, it would benefit teams to put together teams around defense first. That is, if they wish to make the playoffs.
The Nuggets finished 12th in defensive efficiency. This may come as a surprise to those who believe that the Nuggets play terrible defense and blame defense for their eventual downfall. However, this is not a surprise to those who have noted that the Nuggets were 14th in defensive field goal persentage, 2nd in forcing turnovers, 1st in steals, and 1st in blocked shots. Really, only their horrible defensive rebounding (22nd in the league in defensive rebounding rate) kept them from being a pretty good defensive team. However, since the Nuggets play at a blistering pace, they give up a high amount of points per game. This gives the impression that they are bad at defense when they are really slightly above average.
I guess Kenny "The Jet" Smith can choose a different team about which to make "bad defense" jokes.
Boston Celtics.......................98.54
Houston Rockets.....................101.02
San Antonio Spurs...................101.27
Detroit Pistons.....................102.26
New Orleans Hornets.................105.01
Los Angeles Lakers..................105.03
Orlando Magic.......................105.39
Dallas Mavericks....................105.46
Philadelphia 76ers..................105.57
Utah Jazz...........................105.74
Cleveland Cavaliers.................105.92
Denver Nuggets......................106.19
Toronto Raptors.....................106.43
Chicago Bulls.......................106.47
LEAGUE AVERAGE......................106.96
Indiana Pacers......................107.09
Phoenix Suns........................107.42
Portland Trailblazers...............107.78
Atlanta Hawks.......................108.15
New Jersey Nets.....................108.57
Washington Wizards..................108.63
Los Angeles Clippers................108.68
Golden State Warriors...............109.12
Charlotte Bobcats...................109.16
Sacramento Kings....................109.33
Seattle Supersonics.................109.41
Miami Heat..........................109.58
Minnesota Timberwolves..............110.91
Memphis Grizzlies...................111.13
New York Knicks.....................111.45
Milwaukee Bucks.....................112.06
There are a couple of interesting things to note about this list.
First of all, the Boston Celtics are the best defensive team in the NBA. And it isn't even close. John Hollinger of ESPN has stated that this Celtics team is the 3rd best defensivev team of all time.
The Milwaukee Bucks are the worst defensive team in the league. This is not surprising given that Michael Redd is known for being one of the worst defensive players in the league.
The top 13 teams in defense made the playoffs. I believe that I will find that the same is NOT true for offense. Therefore, it would benefit teams to put together teams around defense first. That is, if they wish to make the playoffs.
The Nuggets finished 12th in defensive efficiency. This may come as a surprise to those who believe that the Nuggets play terrible defense and blame defense for their eventual downfall. However, this is not a surprise to those who have noted that the Nuggets were 14th in defensive field goal persentage, 2nd in forcing turnovers, 1st in steals, and 1st in blocked shots. Really, only their horrible defensive rebounding (22nd in the league in defensive rebounding rate) kept them from being a pretty good defensive team. However, since the Nuggets play at a blistering pace, they give up a high amount of points per game. This gives the impression that they are bad at defense when they are really slightly above average.
I guess Kenny "The Jet" Smith can choose a different team about which to make "bad defense" jokes.
Launch of Nuggets Central
Welcome to Nuggets Central! This site is designed to provide two things: (1) my own statistical analysis of the NBA and (2) Denver Nuggets news and analysis. Any and all comments are welcome.
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