# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

50
COMPARING PLAYERS FROM
DIFFERENT ERAS

In chapter 15 we tried to determine whether it would be likely that Ted Williams would hit .400 if he were to play today. Our analysis required that we compared the pitching and fielding abilities of players from different eras. In chapter 15 we used a fairly simplistic approach and found that it was unlikely that Ted Williams would hit .400 today. In this chapter we use our WINVAL ratings to determine whether the players in the NBA have improved or declined in quality since 2000. The end of the chapter summarizes the results of Berry, Reese, and Larkey who analyzed the change in player quality over time for Major League Baseball, professional hockey, and professional golf1

Analyzing Change in NBA Player Quality, 2000–7

We have WINVAL player ratings for all NBA players for the 2000–7 seasons. For example, if Dirk Nowitzki had a + 10 rating for the 2004–5 season, that would indicate that per 48 minutes, if Nowitzki played instead of an average 2004–5 player, then our best estimate is that the team would improve their performance by 10 points per 48 minutes. We can use our WINVAL ratings to estimate the relative level of player abilities during the 2000–7 seasons. Let's arbitrarily assign the 2006–7 season a strength level of 0. If our model estimates, for example, that the 2003–4 season has a strength level of + 4, that would mean, on average, players in 20034 were 4 points better than players in 2006–7. Each “data point” is a player's WINVAL rating for a given season. We restricted our analysis to players who played at least 1,000 minutes during a season. We used the Excel Solver to estimate:

1Berry, Reese, and Larkey, “Bridging Different Eras in Sports.”

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