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Producing The Most Valuable Player

At the conclusion of the 2005-2006 NBA season, many predicted Steve Nash would win his second consecutive Most Valuable Player award. On May 7, 2006 it was confirmed. Nash ran away with the award, winning comfortably in the voting over LeBron James who was followed by Dirk Nowitzki, Kobe Bryant, Chauncey Billups, Dwyane Wade, Elton Brand, Tim Duncan, Tony Parker, Allen Iverson, and Shawn Marion.

The purpose of this article is to show who actually was the Most Valuable Player in the NBA this past season. This will not be done through whimsical media voting. Rather, it will be done through a mathematical equation linking individual player?s statistics in relation to team wins, measuring the player?s production of wins, or rather, the player?s marginal product. I call this PPP, or player production points.        
In the past, the IBM award was given to the player who contributed ?most to his team's overall success? (HoopsCorner).  This award was computed by a player's total points, plus rebounds, plus assists, plus steals, plus blocks, minus personal fouls, minus turnovers, plus 10 times the number of his team's wins, times 250 which was then divided by the team's total points, plus field goal attempts, plus assists, plus steals, plus blocks, minus personal fouls, minus turnovers: (Berri)

player pts + reb + ast + stl + bl - pf - to + (team wins X 10) X 250
divided by
team pts - fga + reb + ast + stl + bl - pf ? to

This award was last given out at the conclusion of the 2001-2002 season.  Shortly thereafter, the sponsorship agreement between IBM and the NBA came to an end. Since its existence in the 1983-1984 season, only three times did the IBM winner correlate with the NBA?s Most Valuable Player: Tim Duncan (2002), Shaquille O?Neal (2000), and David Robinson (1995).

PPS, Points per Shot

For my analysis, I came up with an equation which used most of the same statistics and other important ones as well.  I used two statistics which are not officially scored in NBA games. The first is PPS, or points per shot. I computed this by taking the player?s average points per game divided by field goal attempts per game.

In the IBM model, player?s points were taken into account and later divided by team points, which gave the percentage that the individual player scored for his team. This omits field goal percentage and does not deduct points for missed field goals. When solving a player?s PPP, it is necessary to take into account not only points scored, but also field goals attempted. By doing this, a number of things are accomplished. In a sense, field goal percentage is being included as well as free throws. Every time a player gets to the line and sinks a free throw, he scores a point while the clock is stopped without ever taking a field goal attempt. As one can see, PPS is a great statistic which will probably be taken more seriously in the future of NBA analysis.  Out of the 28 players studied, Richard Jefferson averaged the highest points per shot at 1.51 while Chris Webber had the lowest at 1.06.  Although Jefferson was 25th in league at 19.5 points per game, he led the league in points per shot, thanks in part to his 49% shooting and innate ability to draw fouls and hit free throws.

On Court vs. Off Court Plus/Minus Discrepancy

The next unofficial statistic I used was "on court versus off court plus/minus discrepancy," which had been computed by 82games.com.  This is figured out by taking the player?s on court +/- score minus the player?s off court +/- score to attain the net team +/- score.  This statistic shows exactly how the team fairs while the specific player is on the court as well as off. (82games.com)

Out of the 28 players studied, Dwyane Wade had the highest score of 15.8, while Joe Johnson had the lowest at -4.3. When Wade is on the court his team outscores opponents by 8.1 points per game and when he is off the Heat are outscored by 7.7, giving a net total, or opportunity cost, of 15.8.          

The IBM model showed before neglects to include any kind of statistic showing how the team produces with and without the specified player.  This is why the ?on court versus off court plus/minus discrepancy? is so important when figuring out a player?s value to his team.

Basic Statistics

The other statistics used to solve a player?s PPP are rather fundamental.  Minutes per game are included because obviously the more time a player spends on the court the more the team values his play.  Rebounds, assists, steals, and blocks are all included.  A rebound has value because on the defensive end it changes possession.  On the offensive end, it gives the team another opportunity to score.  Assists have value because each one leads to a field goal made which results in 2 or more points.  Steals are valuable because it changes possession and usually leads to fast break points.  Blocks hold value as well because it prevents the opponent from scoring and also gives the team an opportunity to change possession.  Those are the positive basic statistics accounted for.          

Turnovers and personal fouls are also used in solving the equation, but are considered negatives.  Anytime a player turns the ball over, his team forfeits the chance to score as well as give the other team an opportunity to score.  Anytime a foul is committed, that player is one step closer to being taken out of the game.  If he is out of the game, chances are the team will not do as well as if he was on the court.  

The Basics

A player of MVP caliber is needed on the court as much as possible.  After all, many of these players have high ?on court versus off court plus/minus discrepancy."  If they did not, they would not be considered as valuable.  Therefore, minutes played per game are necessary in figuring out PPP.  The more minutes a player spends on the court, the more likely that team is to win.          

As Vince Lombardi said, ?If winning isn?t everything, why do they keep score??  Winning is everything, and that is why season team win totals are taken into account when solving PPP.  The more wins the team has, the more value the player holds.  If the team does not make the playoffs, how valuable can a player really be to his team?  On the final list of most valuable players, or leaders in PPP, it should be no surprise that the top 15 made the playoffs.

The final statistic used was games played.  Just like minutes played per game, so is the amount of games played in the season.  If the player is injured or suspended, he obviously is not playing.  If he is not playing, the team has less of a chance of winning, if he is valuable.

PPP, Player Production Points

Now that all the statistics for which PPP is solved are understood, the formula will be presented as follows:

pps*10 + oc vs oc pmd + mpg + rpg + apg + spg + bpg + gp ? to ? pf + tw
divided by

This is computed as: points per shot times ten, plus "on court versus off court plus/minus discrepancy," plus minutes per game, plus rebounds per game, plus assists per game, plus steals per game, plus blocks per game, plus games played, minus turnovers, minus personal fouls, plus team wins, which is then divided by the number of games in a season, 82.

I came up with this equation by using the basic official statistics that are recorded by the NBA as well as doing a little research.  It makes sense to include other statistics which the IBM award left out in order to figure out how valuable a player is to his team.  It is not possible to know how valuable a player is to his team unless you know how well the team does when he is on and off the court, which is why I included the "on court versus off court plus/minus discrepancy" statistic.  Also, PPS makes perfect sense to include because it describes the efficiency of the player as well as his scoring ability.  PPS is generally a low number, as described earlier, which is why it is multiplied by 10 in the PPP equation in order to show its value.  Just having a players average points per game in the equation does nothing to show his value.  Any player can score 30 points in a game, but the important question is: how many shots did he take in order to score that amount of points? This is precisely why PPS was used instead.  

After figuring out the PPP equation, I plugged in the numbers for the top MVP finishers for the 2005-2006 season and then included the rest of the top 25 scorers in the NBA.  I was not surprised to find that Kobe Bryant, the leading scorer this season with 35.4 points per game, finished 14th out of the players studied in points per shot with 1.35, because he shot over 27 times per game.  

Some may look at this list and argue that Steve Nash is the Most Valuable Player, because after all he did win the award.  The truth is, Chauncey Billups is actually the Most Valuable Player in the NBA.  He finished second in PPS with 1.48, finished 6th in "on court vs. off court plus/minus discrepancy" with 11.1, and finished ahead of Nash with more minutes, rebounds, and steals per game.  

Sure, Nash averaged four more assists per game then Billups, but Billups? Pistons also won ten more games then Nash?s Suns.  

The Top 28
Chauncey Billups
Dirk Nowitzki
LeBron James
Tim Duncan
Shawn Marion
Dwyane Wade
Tony Parker
Steve Nash
Richard Hamilton
Richard Jefferson
Vince Carter
Kobe Bryant
Pau Gasol
Elton Brand
Antawn Jamison
Gilbert Arenas
Michael Redd
Kevin Garnett
Mike Bibby
Allen Iverson
Ray Allen
Paul Pierce
Jason Richardson
Chris Webber
Rashard Lewis
Chris Bosh
Mike James
Joe Johnson

Feedback may be sent to Jeffrey.Dobin@RealGM.com. Raw data on this formula is available upon request.

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