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

By Wayne Winston | Go to book overview

31
NBA LINEUP ANALYSIS

In chapter 30 we described the methodology for creating Adjusted + /— ratings. These are helpful to teams in making decisions involving players such as trades and salaries. During the season, however, few players are traded and a team's major concern is how to win more games with their current roster. The most important decisions coaches make during the season are which lineups to play when. For example, should a team try to go small against the 2006–7 Suns' “small ball,” or should they go big and push the ball inside?

On average a team plays 300–600 different lineups during the course of a season. Is there any rhyme or reason to coaches' lineup choices? Lineup ratings can help a team win more games: play better lineups more and worse lineups less.

Once we have player ratings it is easy to develop lineup ratings. Suppose we want to rate the Indiana Pacers' lineup of Jermaine O'Neal, Danny Granger, Jamaal Tinsley Troy Murphy, and Mike Dunleavy. Let's call this lineup Pacers 1A During the 2006–7 season this lineup played 326 minutes (more than any other Pacer lineup). They outscored their opponents by 11 points. This means that Pacers 1A played 326/48 = 6.79 games and has a Pure + /— of 11/6.79 = 1.61 points per 48 minutes. Then we look at each minute Pacer 1A was on the court and average the total abilities of the opponents (adjusting, of course, for the league home edge of 3.2 points). We find this lineup played against opposition lineups averaging in ability 1.89 points better than league average. This means that Pacers' 1A should have an Adjusted + /— rating of 1.61 + 1.89 = 3.5 points. In short, this means that Pacers 1A would beat an average NBA lineup (a lineup where the sum of the five player ratings is 0) by 3.5 points per 48 minutes. The amazing thing is that many teams play inferior lineups many more minutes than they do their better lineups. For example, in 2006–7 the Charlotte Hornets played the lineup

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