In the top of the 1^st inning of the June 28, 2009 Mets Yankee game Derek Jeter led off the first inning with a double. Then Nick Swisher hit a ground ball to Mets first basemen Dan Murphy. Surprisingly, Murphy eschewed the safe play of retiring the batter at first and threw to 3^rd base in an attempt to nail Jeter, who was trying to advance to 3^rd. The ESPN announcers criticized Murphy for allowing the possibility of a big inning. Murphy threw late to 3rd so Jeter was safe at 3^rd and Swisher was of course safe at first. The Yankees went on to score three runs in the first inning and won the game 4-2. In hindsight, it is clear that Murphy’s gamble backfired, but when the ball was hit to him how should he have decided whether or not to throw to 3^rd base?

                If Murphy throws to third then in all likelihood one of the following will occur.

• Jeter is out and Yankees have a runner on 1st with one out. In this situation MLB teams average scoring .55 runs.
• Jeter is safe and the Yankees have runners on 1^st and 3^rd with none out. In this situation MLB teams average scoring 1.86 runs.

If Murphy takes the safe play and retires Swisher at 1^st base, then Jeter moves to 3^rd base and the Yankees have a runner on 3^rd base with one out. In this situation MLB teams average scoring .98 runs.

Let P = probability that Murphy gets Jeter out at 3^rd base. If

P(.55)+ (1-P)1.86> .98

then the Mets are better off (on average)with Swisher throwing to 3^rd. A little algebra shows that Murphy needed around a .67 (or 2/3) chance of nailing Jeter to make throwing to 3^rd the right play. While watching the game my gut feeling was that Murphy had around a 50-50 chance of nailing Jeter, so if I were in Murphy’s shoes I would not have thrown to 3^rd. The point is that if the Mets had worked through this analysis Murphy would have been able to translate his personal view of the probability of a successful play into making the proper decision. Chapter 6 of my book Mathletics has many examples of how basic probability theory can be used to help baseball teams make better in game decisions.

While we work for the Dallas Mavericks rating players and lineups, after our Mavs were eliminated I rooted hard for LeBron and the Cavs. Like many others, I was very upset that the Cavs lost to the Magic and LeBron and Cleveland endured another year of frustration. The Cavs did not have to lose this series. The following two pieces of information tell us why they lost the series:

1. In the 57 minutes during which Ben Wallace played and Joe Smith did not the Cavs were clobbered by 58 points. Adjusting for the strength of the Magic players in the game during this time, the Cavs played 40 points (per 48 minutes) worse than an average NBA team.
2. In the rest of the series the Cavs dominated the Magic by 43 points in 236 minutes and played 18 points (per 48 minutes) better than average.

If the Cavs had played Joe Smith more with Wallace or had played Wallace less minutes, the NBA’s dream Cavs-Lakers series might have become reality.

Most followers of the NBA think LeBron James and Kobe Bryant are the two best players in the NBA. Well, there is pretty convincing evidence that Kobe Bryant may not be the best player on his own team? If you look at how the Lakers play with various combinations of Odom and Bryant in and out of the game during the 2009 playoffs it becomes clear that if Odom is not as good as Bryant, he certainly is an outstanding player. Look at the following numbers:

• With Bryant and Gasol in and Odom out the Lakers were outscored by3 points in 320 minutes. After adjusting for the strength of opponents faced, the Lakers played 4 points better than an average team (per 48 minutes) during these 320 minutes.
• With Bryant out and Gasol and Odom in during the playoffs the Lakers outscored their opponents by 21 points in 86 minutes! After adjusting for the strength of opponents faced the Lakers played 13 points better than an average team (per 48 minutes) during these 86 minutes.
• As expected, with Kobe, Gasol and Odom in during 535 minutes the Lakers outscored their playoff opponents by 165 points, playing 23 points (per 48 minutes) better than an average team.

So it looks like the fantastic Kobe Bryant could not make the Lakers outscore playoff opponents with Gasol in unless he had Odom in. On the other hand Odom and Gasol easily dominated their opponents without Kobe. Makes you question the  “conventional wisdom”!

My book Mathletics is for everyone who wants to know how professional baseball, football and basketball teams use math to improve their team’s performance. The book develops all needed math so it is entirely self contained. If you’ve wanted to know the math behind Moneyball, or how to evaluate NBA players and lineups this book is for you. Many topics are covered such as how to evaluate the effectiveness of running and passing plays and how to rate sports teams. Finally, we have an extensive section on the mathematics of gambling on football, basketball and baseball. Mathletics will be available by September 15, 2009!