Returns to inequality in MLB

Take a look over here if you want to get the background for this series, otherwise read on.

Sports + Numbers Prediction: "This is anyone’s guess. The returns to inequality – after controlling for the wide distribution in overall team salary – might be strong or they might not. I don’t have a good feel for it so this will be more of a fact finding mission."

The data

To see the impact of inequality we will look at each team’s Gini coefficient against their winning percentage, controlling for team spending. The resulting equation gives us an r-squared value of 0.13 with only salary spending being significant (P-value of 0.00001) while the Gini coefficient comes in at a P-value of 0.18.

Payroll vs Winning % - MLB 2008-2012

For every million dollars in team spending the expected increase in winning percentage is 0.000654. For a team that spends $10 million more than a comparable team – all else equal – we would expect them to win an additional game.

Gini vs Winning % - MLB 2008-2012

On inequality the - insignificant - coefficient is -0.14. Within the range of Gini coefficients in baseball (0.35 to 0.66) this would mean a difference of 7 wins from the most equal to the least equal (more wins to the most equal). Not nothing but not exactly a huge impact. The gap in payroll ($19 million to $206 million) projects to a gap of nearly 20 wins.

Payroll vs Gini (color-coded by winning %) - MLB 2008-2012

Returns to inequality in the NFL

Take a look over here if you want to get the background for this series, otherwise read on.

Sports + Numbers Prediction: "I would think the returns to inequality are high here, but not exactly as a proxy for having stars. The NFL’s cap structure essentially forces teams to play rookies and younger, pre-contract extension players heavily and supplement them with selected veterans. The catch is that nearly all teams have a big young player population so the difference between one that works out and one that doesn’t might not be visible in the salary distribution."

The data

To see the impact of inequality we will look at each team’s Gini coefficient against their winning percentage, controlling for team spending. The resulting equation gives us an r-squared value of 0.07 with only salary spending being significant (P-value of 0.0007) while the Gini coefficient comes in at a P-value of 0.57.

Payroll and Winning %

For every million dollars in team spending the expected increase in winning percentage is 0.00417. For a team that spends $15 million more than a comparable team – all else equal – we would expect them to win an additional game.

Gini and Winning %

On inequality the coefficient is -0.17. Even though the P-value tells us this that Gini is insignificant, the fact that the variance from perfect equality to perfect inequality is slightly less than three wins should tell us all we need to know. 

Gini and Payroll, color coded by winning percentage

Returns to inequality in the NBA

Take a look over here if you want to get the background for this series, otherwise read on.

Sports + Numbers Prediction: "My guess is the NBA will have the biggest returns to inequality as a proxy for teams having stars. With those stars they are not able to afford middling salaries for role players and drop quickly down to minimum salary or exception-level players."

The data

To see the impact of inequality we will look at each team’s Gini coefficient against their winning percentage, controlling for team spending. The resulting equation gives us an r-squared value of 0.32 with both terms being significant (P-values of 0.000008 for spending and 0.00004 for Gini coefficient).

Payroll and Winning %

For every million dollars in team spending the expected increase in winning percentage is 0.005. For a team that spends $20 million more than a comparable team – all else equal – we would expect them to win an additional eight games.

Gini and Winning %

On inequality the coefficient is 0.67. In theory this would tell us that a team with a single superstar making all of the money (stay with me, I understand this is not possible under the NBA CBA) would have 55 more wins than a team with all players making exactly the same salary. In practice we have variation within a much smaller band ranging from 0.09 to 0.56 (see table below for details) so the projected difference if those two teams had the same salary would be 25 games. 

Gini and Payroll, color coded by winning percentage

Returns to Inequality: Introduction and predictions

As a follow up to my data dump post on league-level and individual player inequality in sports, I want to go a level deeper in each league and see where inequality makes a difference on the field (or court, or ice). This series of posts will look at each league and run a simple regression of winning percentage against overall payroll and team Gini coefficient.

I expect there will be relatively low correlation between spending and winning in the harder-capped leagues (NHL and NFL) while the NBA and MLB should show some.

The real interesting point will be whether prominent current teams that are more unequal (stars and minimum-salary guys: the Miami Heat or New England Patriots) are successful as a rule or as an exception.

A few predictions before I get started:

NBA – My guess is the NBA will have the biggest returns to inequality as a proxy for teams having stars. With those stars they are not able to afford middling salaries for role players and drop quickly down to minimum salary or exception-level players.

NFL – I would think the returns to inequality are high here, but not exactly as a proxy for having stars. The NFL’s cap structure essentially forces teams to play rookies and younger, pre-contract extension, players heavily and supplement them with selected veterans. The catch is that nearly all teams have a big young player population so the difference between one that works out and one that doesn’t might not be visible in the salary distribution.

MLB – This is anyone’s guess. The returns to inequality – after controlling for the wide distribution in overall team salary – might be strong or they might not. I don’t have a good feel for it so this will be more of a fact finding mission.

NHL – I am guessing that returns to inequality are strong here too, with relatively high leverage of the individual players resembling the NBA more than the NFL or MLB.

NBA draft picks as assets – the triumph of hope over experience?

Zach Lowe had an article up today on Grantland about the current view around the NBA that draft picks are extremely valuable assets for teams to stockpile and use in future trades. He explains:

The word "asset" has never had more currency in the NBA. Draft picks, even in the 20s, are "assets" teams can use to acquire cheap talent, or to grease the wheels in potential mega-trades for star players. The Celtics view the three unprotected picks they nabbed from the spend-spend-spend Nets not just as young players that will don the hallowed green, but as "assets" carrying the lure of the unknown for a rival GM looking to move a disgruntled star.

Luckily for us, someone has already gone to the trouble of valuing NBA draft picks and the results should be sobering to teams clutching likely mid- to late-first round picks and hoping for the next Tony Parker.

Source: ESPN.com

Even teams holding picks they think will be at the top of the draft should look carefully at the rate of team performance mean reversion in the NBA (see this post from last year) and be realistic about where the pick will be.

I can see two primary reasons for the run-up in value of picks relative to real, actual players - besides the momentum of "everyone is doing it."

1. The 2011 CBA – The NBA went to a lot of trouble, and cancelled a lot of games, to get a very owner-friendly collective bargaining agreement in their latest negotiations.