When talking about value, who can be more valuable than A-Rod?

What is a Stolen Base Really Worth?
(Or a single, or a double?)

The opinions of both casual fans and serious statistical analysts are both very divided about the true value of a stolen base. It is probably a fair statement to say that some members of each group overvalue the stolen base, and some members undervalue it. In this week’s edition of Statistics 101, I will attempt to apply some heavy-handed analysis of my own to add some new ideas to the discussion.

The basis for this week’s column is the Runs Created, a formula developed by (whom else) Bill James to estimate the value of a hitter’s offensive contribution. I will be using the “stolen base” version of runs created (RC) since it is fairly simple but encompasses most of the numbers I am looking for. The formula is: [(H + BB – CS) * (TB + (0.55 * SB)] / (AB+BB-CS). To learn more about runs created, check Wikipedia, Google, or your favorite statistical web site.

Using this formula, Alex Rodriguez leads the major leagues in runs created with 138 (all statistics are through some of the games on Wednesday, so I apologize if any of the numbers sound strange). Magglio Ordonez ranks second, and you might be surprised to learn that Hanley Ramirez ranks third. However, since we already know that Rodriguez is the best player in baseball, this doesn’t really tell us much. How does A-Rod’s power compare to Magglio’s average and Hanley’s speed? If you just want the simple answer, skip the next paragraph.

Using the runs created formula above, I have broken down the “B factor” (TB + (0.55 * SB) into its individual components. If we assume that the “A factor” (H + BB – CS) is constant, what does each component of the B factor contribute to the overall runs created total? That sounds confusing, but stick with me – I promise it won’t be that bad. The formula for total bases (in case you didn’t know) can be rewritten as [1B + (2B*2) + (3B*3) + (HR *4)]. So if you take A-Rod’s 48 home runs, multiply it by four, and divide by the “B factor” (TB + (0.55 * SB), you will find the weight that his home runs contribute to the overall factor. For A-Rod, that is (48*4) divided by [82 + (2*28) + (3*0) + (4*48) + (0.55*22] or 0.56.

At the end of the day, all that complicated math means that A-Rod has derived 56% of his runs created from his home runs. He has derived another 24 percent from singles, 16 percent from doubles and 4 percent from stolen bases. Compare that to Ordonez, who has earned 37 percent of his value from singles and 34 percent from doubles. Or Ramirez, who has earned 8 percent of his value from stolen bases, 33 percent from singles, 29 percent from home runs, 25 percent from doubles and even 5 percent from triples.

So, to answer the original question of what a stolen base is worth, the answer is, not much. The Mets’ Jose Reyes has derived 14% of his value from his stolen bases, but only Reyes, Juan Pierre, and Reggie Willits have earned double-digit value with their thievery. When even Pierre is only earning 13 percent of his value on the bases, you get an idea of what a stolen base is worth – and keep in mind, the “B factor” doesn’t even include caught stealing!

Of course, the value of a stolen base is different from the value of speed. When you consider both steals and triples, Reyes and Pierre both derive more than 20 percent of their value from their legs before you even consider infield singles or singles stretched into doubles. At 25%, Reyes’ speed value leads the major leagues, but Curtis Granderson (24 percent) moves into second place while Pierre (22%) ranks third.

What about Ichiro Suzuki, you might ask? Ichiro derives a staggering 63% of his value from singles, leaving just 15 percent for steals and triples. And Ichiro doesn’t even lead the major leagues in singles value – Luis Castillo (70 percent), Jose Vidro (66%) and Willits (65%) rank even higher. That makes sense, if you think about it – Ichiro does more than just hit singles, while the others really don’t.

Back to the power categories for a second, it is actually a bit of a surprise to see A-Rod leading the league in home run value (56%) given his average (.312) and steals (22), but he is still numero uno. Number two is Prince Fielder (54%) and Ken Griffey Jr. rounds out the top three at 46 percent. For the truly curious, Casey Kotchman (35%) derives the most value from his doubles, while Granderson (21%) gets the most from his triples.

Clearly, this method of estimating value underestimates the stolen base a bit, but since players like Pierre and Willits also get value from infield hits and triples, it seems to me like their speed is valued fairly. It also seems that singles can be a bit overrated, and it’s almost impossible to overvalue a home run. Bad news for the seven people left on Magglio’s MVP caravan.

The full top 10 list of players deriving the most value from their home runs:

1. A-Rod, 56%
2. Prince Fielder, 54%
3. Ken Griffey Jr, 46%
4. Albert Pujols, 45%
5. Brad Hawpe, 43%
6. Miguel Cabrera, 43%
7. Mark Teixeira, 41%
8. B.J. Upton, 39%
9. Torii Hunter, 39%
10. David Ortiz and Hideki Matsui, 38%

Questions and comments may be sent to johnfranco@sportsgrumblings.com