*TSN.ca (Canada’s Sports Leader) posted the following story on their website last night:*

*[hat tip to Steven Trainor]*

*The story draws upon The Wages of Wins and the WoW Journal. And it also reports part of a table (analyzing the Raptors at the midpoint of this season) from the column The Third Way of Bryan Colangelo. The story reads like something written for this forum (except the writing by the unidentified TSN.ca staff person is better). So rather than write a post this morning, I thought I would just re-post the TSN story.*

*But before I could get this posted, though, the story was updated this morning with three additional paragraphs on John Hollinger’s Player Efficiency Rating. This additional material is in italics below.*

**Judging who the Most Valuable Player in the NBA is has always been a tricky task. To begin with, the term “valuable” can be vague and subjective.**

Is the MVP the best player in the league? If that were the case, surely Kobe Bryant would have won the award by now. Is the MVP the most valuable to his team? Or is the MVP the most valuable in the league?

In their book The Wages of Wins, economists David Berri, Martin Schmidt and Stacey Brook have attempted to make it easier to determine what it means to be valuable. The trio has established a formula that attempts to determine a player’s true value to his team.

The Toronto Raptors are a good example that numbers might give some better insight into a team’s play.

Forward Chris Bosh is clearly the most talented player on the Raptors. Bosh is the only player on the team to have made an All-Star team and he is widely regarded as one of the best young players in the league. Nevertheless, according to Berri’s research, point guard Jose Calderon has actually produced more wins for his team than Bosh and, arguably, is the more valuable player.

Berri’s analysis of the first half of the Raptors’ season shows that after 41 games Calderon’s Wins Produced value is 8.5, while Bosh’s is 5.7.

__Wins Produced for Selected Toronto Raptors__

Player | Wins Produced after 41 games | Predicted Wins Produced after 82 games |

Jose Calderon | 8.5 | 17.0 |

Chris Bosh | 5.7 | 11.5 |

Carlos Delfino | 3.6 | 7.2 |

Anthony Parker | 3.6 | 7.2 |

Jamario Moon | 3.0 | 5.9 |

T.J. Ford | 1.6 | 3.1 |

Jason Kapono | -0.3 | -0.6 |

Andrea Bargnani | -3.5 | -7.0 |

To get these values, Berri and his team decided to look beyond simply scoring numbers – a stat his research has shown to be greatly overvalued.

In his own words: “productivity in the NBA is not strictly about how many points you score. Rebounds, turnovers, steals, and shooting efficiency matter.” With that said, a player that scores a lot with a low shooting percentage may not be as valuable as a player that scores a little less, but has a higher shooting percentage and a higher turnover average.

To arrive at those numbers, Berri first began by calculating Calderon and Bosh’s Win Score. Again, Berri in his own words:

“Our research indicates that the relative value of a point, rebound, steal, turnover, and field goal attempt … is equal. Assists, blocked shots, free throw attempts, and personal fouls … are each worth less.”

So in order to measure a player’s performance, Berri and his tream created the following simplified formula:

Win Score = Points + Rebounds + Steals + ½Assists + ½Blocked Shots – Field Goal Attempts – Turnovers – ½Free Throw Attempts – ½Personal Fouls

Turnovers, missed field goals, missed free throws and personal fouls are all things that could turnover the ball and give the opposing team an opportunity to score.

Berri then tweaks this number slightly to account for other factors, such as player position, to determine how many Wins Produced a player has earned.

Berri’s research has been remarkably accurate. For the 2003-04, he and his team added up all the wins predicted by his formula and compared it to the teams’ actual win total – Berri’s formula was an average of just 1.67 wins off.

Looking back at Berri’s formula, it becomes clear why Calderon is valued so highly. Maintaining possession of the ball is a key component of Wins Produced. Calderon’s low turnover rate is well known, but what haven’t gotten as much attention have been the Spaniard’s incredible shooting percentages. Calderon is hitting 50.7 percent from the field, 43.4 percent from behind the arc and 91.2 percent from the free throw line. Steve Nash is the only other player in the league shooting better than 50% from the floor, 90% from the line and 40% from 3.

Not only is Calderon effectively getting his teammates the ball, but he’s also doing it at an incredibly efficient level. A highly efficient player, particularly a point guard, can limit the number of possessions and scoring opportunities the other team gets. In other words, the Raptors’ best defense might just be Calderon’s offense.

Calderon is on pace to generate 17.0 Wins Produced this year. As a comparison, San Antonio’s Tony Parker only marked 10.1 Wins Produced last year and the Pistons’ Chauncey Billups notched 13.3 Wins Produced last year – should Calderon maintain his level, he would join some pretty good company.

*NOTE: THE FOLLOWING THREE PARAGRAPHS WERE ADDED TO THE TSN STORY THIS MORNING*

*Update: In all fairness, it should be mentioned that Bosh has a better Player Efficiency Rating (PER) than Calderon, 24.97 compared to 21.78. PER was created by ESPN.com analyst John Hollinger to “summarize a player’s statistical accomplishments in a single number.” *

*The formula for PER is uber-complicated, but, much like Wins Produced, it attempts to balance positive stats, such as scoring and assists, with negative stats, such as turnovers and personal fouls. Hollinger adjusts each player’s PER to account for minutes played and pace of his team (so players on slow-paced teams aren’t penalized). *

*With that out of the way, here is the most interesting part: Bosh’s PER is currently sixth best in the NBA – better than Tim Duncan, Dirk Nowitzki and Yao Ming. *

Bosh is clearly having one of his best seasons, particularly in the last month, but is Calderon more valuable?

*This is where the article ends. For those who are intersted, h**ere is the full table cited above:*

**The Toronto Raptors at the Midpoint of the 2007-08 Season**

*– DJ*

*Basketball Stories*

Lior

January 29, 2008

This argument is clearly bogus. “Wins produced” is linear in the player stats (it’s non-linear in the team totals, but that’s irrelevant). Hence the sum of the individual “Wins produced” for a team is only a function of the team total production (total points, rebounds, total FGA etc). In other words, the fact that the total individual “Wins produced” numbers add up to total wins only says that total team production correlates with wins, but says nothing about whether assigning each player his fraction based on the box score is a good assessment of individual contribution. Perhaps the individual stats of player X were really a function of the greatness of player Y?

The real justification for drawing individual conclusions is that a player’s “WP48” seems to be fairly constant year-to-year and team-to-team. That is, if you keep the player constant but change the team around him his WP48 seems about constant. That leads credence to the fact that “WP48*playing time” is meaningful.

Lior

January 29, 2008

Clarifying my post above, I should have said that “Wins produced” is (almost)

additive with fixed weights. The following is based on the published technical note.Summary of definitions:

Associate to the

ith player a number P_i (PROD in the notes) which is a fixed linear combination of his stats, and a number A_i which only depends on his position. Let T_i be the number of minutes played.To the team associate numbers M48(teammate adjustment) and D48 (team defense adjustment) based on total team numbers.

The player WP48 is then W_i = P_i/T_i – A_i – M48 – D48.

Analysis: consider summing (T_i W_i/48) over all players of the team. The “Production” term adds up to a fixed linear combination of team totals. Since total team minutes is not player-dependent, the “defensive adjustment” and “mate adjustment” terms add up to a team-only number. The only term which doesn’t simply depend on total team stats is the “position adjustment”, and only for a minor reason: the weighted sum of the A_i over player times equals (total minutes played/48) times an average of the adjustment for the different positions, weighted by the total minutes contributed by that position. If every team played on of C,PF,SF,SG,PG each at all times, this number would also be independent of the players. This is not exact, but the departures are tiny.

To conclude: if you multiply each player’s WP48 by minutes played and add over all players, the number you get is almost entirely a function of the total team box score stats, and differs from such a number only via the variation of distribution of playing times among the 5 positions. If this total correlates well with team wins, we only learn that total team wins can be calculated from total team production — we know nothing positive or negative about how to divide this total among the individual players. For that other data needs to come in.

Okapi

January 29, 2008

“…Whatever revelations Morey has found for assessing players, they remain proprietary for now. But at the team level, he said, there are four statistics that are now widely accepted as indicative of a team’s success rate: “effective” field-goal percentage (a combination of 2-point and 3-point percentages), rebounding and turnover rates (which determine how many more possessions a team gets), and free-throw edge (in attempts, not percentage)…”

Animal

January 29, 2008

LIOR, good point. win score is good but it is

not“an average of just 1.67 wins off.” Pythagorean win totals are what are “an average of just 1.67 wins off.”dustin

January 29, 2008

It was the author of the article that made that observation. Not db. DB is very familiar with the pythagorean equality, which is probably why he used it as the basis for his player productivity metric.

Animal

January 29, 2008

dustin, DB has said before win score explains 93% of wins. That 93% figure is what pythagorean win totals explain. Dont get me wrong, I think win score is the best summation of box score statistics. I think it is substantially better than PER. I just don’t like that 93% claim. I think it’s disingenuous.