Wrapping up the McCarver discussion

I wanted to spend another post on the Tim McCarver lead off walk/lead off home run discussion in order to wrap it up.

Let's do this bullet point style!

• I was surprised at how close the two outcomes were with respect to multi-run innings, about a 2-4% difference historically. One of the great things about studying baseball is that you are surprised by the results and you learn things. That's part of why I write this blog. If I wasn't leaning anything, I would just be up here pontificating. In this case, I found that I was guilty of attributing more import to the home run than it deserved. Obviously, the home run is far more valuable because it is one guaranteed run, but with respect to multi-run innings its value is marginalized relative to the walk. I did not recognize this, and thus my initial approach to the problem was incorrect.
  
• We can definitely conclude that Tim McCarver is totally wrong. Whether we examine the problem from the perspective of history or probability, both correct ways of examining the problem, the weight of evidence is greatly against him. Even thought the difference in probabilities is seemingly small, it's over such a large set of samples that it takes on much significance. It's nearly impossible to conceive of a scenario in which the walk is more valuable than the home run, which was McCarver's basic assertion.
• We reaffirmed a basic baseball truth: outs are your most precious commodity. The difference between the two events with respect to multi-run innings has nothing to do with their relative value to each other from a run expectancy point of view. The home run is more valuable with respect to multi-run innings not because it scores a run, but rather because it precludes the possibility of an out.
• Finally, we provided a tad more evidence for the Markov property in baseball. The conjecture about the walk being more likely to lead to big innings is largely based on the assumption that indicates more about the game state than it actually does. Baseball is largely dependent only on the current state of the game, not on how each state was reached.

Screw Peter Abraham

I take back every nice thing I ever said about him and his blog. The following is an ignorant, misinformed, bullshit, throw-away blurb of which he ought to be completely and utterly ashamed (emphasis mine).

3. Think about how much money it could cost the Yankees to retain Jorge Posada, Mariano Rivera and Alex Rodriguez. Over the lifetime of their contracts, you could be talking an investment of at least $250 million. That’s a lot for a 36-year-old catcher, a 38-year-old pitcher and a guy who never played in the World Series.

That's what A-Rod is to you, Pete? Go to hell.

The McCarver Strikes Back

Today, during the Indians-Red Sox game, as I was watching live, McCarver again reiterated the not-so-surprising not-so-revelation that your chances of a multi-run inning are higher after a lead off home run than a lead off walk. Why does this surprise Tim McCarver?

Here's how it works. In the game state with no one on base and no one out (hereafter abbreviated 0-000), you have a probability of scoring exactly zero runs from then on (P0), a probability of scoring exactly one run from then on (P1), and the probability of scoring more than one run from then on (P2+ = 1 - P0 - P1). Conversely, the probability of no multi-run inning is P0 + P1 = 1 - P2+.

After a lead off home run, you return to the 0-000 game state. Only now, in order for there to be a multi-run inning, you only need to score one more run. Therefore, the probability of no multi-run inning is now just P0. The probability of a multi-run inning has become P1 + P2+.

After a lead off walk, you enter the game state 0-100 (man on first, no one out). You still need to score two more runs. As before, you have a probability of scoring zero runs P0', one run P1', and two or more runs P2+'.

In order for the lead off walk to be more valuable, P0 would have to exceed P0' + P1'.

Now, P0 is roughly 0.72. P0' is roughly 0.58. P1' is roughly 0.25. Therefore, P0' + P1' is equal to roughly 0.83. Therefore, the probability of scoring one run or more from state 0-000 is 0.28. The probability of scoring two or more runs from state 0-100 is 0.17. (All of these numbers are based on Keith Woolner's "An Analytical Framework for Win Expectancy" from Baseball Prospectus 2005.)

The difference is roughly 11%. Most (all?) of this will be accounted for by the fact that the man on first can be doubled off and the man who hit the lead off home run can't.

So that's the math. But do you really need it? A home run is one guaranteed whole run that no one can take away. The lead off walk increases your odds of scoring exactly one run by roughly 14%. The lead off home run increases those odds by ONE HUNDRED FREAKING PERCENT.

**EDIT** As pointed out in comment number one, referencing the probability of scoring one run is misleading, as scoring one run and scoring zero runs both count for nothing for the purposes of counting multi-run innings. The ninth-inning analogy is apt: it's the second runner scoring that is important and neither the lead off walk nor the lead off home run will have a great affect on what that second runner does. What is important is that the lead off home run eliminates the probability of the double play and the lead off walk does not. In other words, it is the out that is important, not the run. Point well taken. **END EDIT**

Tim, do us a favor and stop bringing this up as if it's surprising. You will sound a whole lot more intelligent and we I will be a whole lot less aggravated.

No, Todd Helton. You are wrong.

From Mr. Todd Helton, following the Rockies' amazing comeback win over Trevor Hoffman and the San Diego Padres in the National League's Wild Card Elimination game yesterday:

"I can't believe it," Helton said. "Can you believe it? We were down. We battled back. We did it against the best closer of all time."

Umm, Todd? Mariano Rivera says "Hi."

One of these things is not like the other

Buried deep in Buster Olney's most recent blog entry at ESPN is this note:

The Marlins will consider all options this offseason, perhaps even the trade of Miguel Cabrera. Marlins executives should know Cabrera and his habits better than anyone, and they have to ask themselves this question: Do they think that the 24-year-old Cabrera will get a handle on his physical condition and expanding waistline?

If they don't believe he will, they should look to move him ASAP, while his trade value is still extraordinary. If he arrives in spring training appearing heavy and has any kind of physical breakdown in 2008, his trade value will plummet, because rival talent evaluators will attribute his problems to his conditioning.

The Marlins' working model for this situation should be Kevin Mitchell, a staggering talent who hit 47 homers and drove in 125 runs at age 27, and then was basically finished as an everyday player within two years because of his condition. Cabrera could be one of the greatest hitters of his generation, but at some point, he will need to make an adjustment.

Let me begin by saying that I do not mean to quibble with Olney's chief assertion. It is entirely possible, more so than with most Major League Baseball players, that Miguel Cabrera will eat himself out of the Hall of Fame. Furthermore, it may indeed be the right idea for the Marlins to trade him, because he would certainly fetch a ginormous bounty. I don't believe either of these events are likely, but they certainly should be scenarios of which the Marlins should be aware.

No, my quibble is with the astonishing choice of comparison for Mr. Cabrera: Kevin Mitchell. This is a very bizarre and inaccurate selection. Kevin Mitchell is nearly the poster child for an above average baseball player's career path: breaks into the majors in his mid twenties, peaks at age 27, and then slowly declines for 5 or 6 years. I will admit that I do not know the details of Mitchell's career and that the chief reason for his decline is not a decrease in his rate of production, but in his playing time.

However, to compare him to Cabrera is astonishingly foolish. Let's look at Cabrera and Mitchell year by year using WARP3:

Age:        20    21    22    23    24    25    26    27    28
Cabrera:   2.5   6.7   9.4  11.5  10.9   ???   ???   ???   ???
Mitchell:  N/A   N/A   -0.1  N/A   4.1   5.7   6.7  12.8   8.6

            29    30    31    32    33    34    35    36 
Cabrera:   ???   ???   ???   ???   ???   ???   ???   ???
Mitchell:  5.3   3.8   4.8   8.0   0.3   2.2  -0.1  -0.1

Folks, Miguel Cabrera has had one of the best starts to a career ever. He broke in as a rookie for the Marlins' World Series run in 2003, serving as a huge lift and a big threat for the latter half the year. He then made himself a perennial MVP candidate by the age of 22. Simply great baseball players do not do that. Alex Rodriguez does that. Ken Griffey Jr. does that. Barry Bonds does that. Inner circle Hall of Famers do that.

Kevin Mitchell wasn't a regular until he was 24, and even then didn't play in 140 games until he was 26. Miggy has played in 150+ games since his first full season. Heading into his age 25 season, Miggy has roughly 40 WARP3. Mitchell had 4 WARP3 at that point. He had only 61.9 for his whole career.

Essentially, Kevin Mitchell is a bad comp for Miguel Cabrera. In fact, just about every ballplayer ever is a bad comp for Miggy (those named Mantle, Mays, and Rodriguez excepted). Miguel Cabrera is on track to be one of the greatest baseball players who ever lived. Kevin Mitchell was never even close to that. Ever. Busting out at age 27 is just far too common to serve as the basis for comparison to a man who put up MVP numbers at ages 22, 23 and 24.

Miggy may eat his way out of greatness, but the Marlins should absolutely not proceed like Miguel Cabrera is Kevin Mitchell. Indeed, they would be much wiser to treat him as if he were Frank Robinson, Ernie Banks, Eddie Mathews, or Lou Gehrig. Each of these players is more comparable to Cabrera than Mitchell.