By The Numbers: What Is The Power-Speed Number?

What players best "combine" sheer power with blazing speed? Is there a way to measure the meshing of these talents? One metric that can be used is called the "Power-Speed Number" (PSN). It was introduced in the 1982 edition of the Bill James Baseball Abstract by the author himself. The PSN is defined as follows:

where HR represents homeruns, SB denotes stolen bases and the product of HR and SB is indicated by juxtaposing the two terms, using parentheses instead of an "X" symbol.

Before giving examples of what this statistic reveals, we point out a few mathematical properties of this metric:

• If a player has 0 HR, then his PSN = 0, no matter how many SB he has amassed. The same is true if he has accrued 0 SB and, say, 50 HR. This is because a zero in the numerator gives a value of zero to the PSN. For example, in 1961, when Roger Maris blasted 61 HR, he had a PSN of 0, because he did not steal a single base!
• The PSN measure is symmetric: HR and SB are weighed equally. That is, for example, let us assume a player had 30 HR and 40 SB. In this case his we have

  rounded off to the nearest hundredth. The exact same PSN figure is assigned to a player with 40 HR and 30 SB. Because of this, we see that this statistic renders SB just as valuable as HR.

• If a player has the same number of HR as SB, then his PSN is precisely that number. This is why we have a "2" in the numerator; it ensures this very outcome. For example, let's assume a player had career totals of 300 HR and 300 SB. Thus, his lifetime PSN number is:

  

• Finally, by the very nature of this statistic, the longer a player is active, the more likely are his chances for his HR and SB totals to increase and, thus, his PSN would also rise.

The top four lifetime leaders for PSN are:

where the numbers for Rodriguez are included through the first week of September of this year.

The career PSN of some Hall of Famers are: Hank Aaron (364.22), Ty Cobb (207.00), Mickey Mantle (238.05), Joe Morgan (385.90), Babe Ruth (209.85) and Honus Wagner (177.24).

For some recently retired sluggers, we have the following PSN: Jose Canseco (279.15), Mark McGwire (23.52) and Sammy Sosa (338.10).

The top four PSN seasons were obtained by Alex Rodriguez (43.91 in 1998), Alfonso Soriano (43.36 in 2006), Eric Davis (42.53 in 1987) and Rickey Henderson (42.36 in 1986). Note how close these four PSN numbers are in the seasonal case and how spread out they are (613.90 to 402.00) for PSN career totals.  By the way, in 1982, the year Henderson had 130 SB, his PSN was 18.57. And in 2001, when Barry Bonds hit 73 HR, his PSN was 22.07.

As a final comment, it is clear that the PSN measure is simple to compute. When making a sabermetrical argument, the PSN would be very useful as a supporting statistic in conjunction with other metrics. By itself, however, it does not take into consideration the times a runner is caught stealing (CS) and by putting SB on equal footing as HR, one may infer that two players with equal PSN statistics have equal values as players.

Next Blog: Is the Bunt Worth It? One Fan's Opinion…

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