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## Ask me again… Who’s next to 600 home runs?April 10, 2011

Posted by tomflesher in Baseball.
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In an earlier post, I compared Manny Ramirez and Jim Thome and came to the conclusion that Thome would be the next player to hit 600 home runs.

I feel vindicated.

Nonetheless, it seems that some of my assumptions were incorrect. The first was the assertion that Manny and Thome were the same age. Mea culpa – Thome is actually almost two full years older. That came from a relative-age comparison I had run a few posts prior and I just misremembered.

The second is that I used a downgraded rate of production for Thome. He had been hitting at a .053 home run per plate appearance clip over the previous season and a half. If, however, I use Thome’s 2010 numbers, he hit – for the same team he’s playing for now, in substantially the same position – 25 home runs in 340 plate appearances for a rate of .0735 home runs per plate appearance, or approximately one home run every 13 1/2 plate appearances.

Finally, I assumed that Thome wouldn’t be used very often. I assumed he’d make about 2.5 plate appearances per game. However, Thome has played in six of the eight games so far this season and made … 16 plate appearances. (Okay, so this wasn’t too bad.)

I’ll make the totally unwarranted assumption that Thome will play in 75% of games and average 2 plate appearances per game. He needs eleven home runs to hit 600. At his average rate, he’ll take (13.6)x(11) = 149.6, or about 150, plate appearances to do this. That’s about 75 games to play in, or about 100 real-time games, if he continues averaging 75% play time and 2 plate appearances per game. That takes us about 62% of the way through the season. The Twins played game #100 on July 26 last year.

I therefore predict that Jim Thome, barring injury, will hit his 600th home run in the month of July.

## Jim Thome’s Marginal ValueOctober 5, 2010

Posted by tomflesher in Baseball, Economics.
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I’ve alluded to the similarity between Manny Ramirez and Jim Thome quite a bit. They both played in Cleveland for a few years before moving on to other teams. They’re each in the DH phase of their careers. Thome is about two years older than Ramirez, but otherwise they’ve had relatively similar production. That’s why it was so odd for the White Sox to let Thome go a few years back only to pick an injured, probably going-downhill Manny for about a quarter of the season when Ramirez is making about $18 million and Thome’s maximum salary was about$15.7 million. There’s an argument that Manny still has more productive years left than Thome, of course. (I happen to think that argument is wrong, but that’s just me.)

Just for fun, let’s take a look at their production since Manny’s trade.

In the last 24 games he played, Ramirez had 88 plate appearances, a respectable .420 OBP, and a Jeteresque .261 batting average. His win probability added was -.273, for those of you who are into that sort of thing. Meanwhile, over the same number of games, the flagging, decrepit Thome had only 79 plate appearances, with a paltry .333 batting average, and only a .494 OBP.

Thome’s salary this year for the Twins was \$1.5 million.

I think the winner here is clear.

## The 600 Home Run AlmanacJuly 28, 2010

Posted by tomflesher in Baseball, Economics.
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People are interested in players who hit 600 home runs, at least judging by the Google searches that point people here. With that in mind, let’s take a look at some quick facts about the 600th home run and the people who have hit it.

Age: There are six players to have hit #600. Sammy Sosa was the oldest at 39 years old in 2007. Ken Griffey, Jr. was 38 in 2007, as were Willie Mays in 1969 and Barry Bonds in 2002. Hank Aaron was 37. Babe Ruth was the youngest at 36 in 1931. Alex Rodriguez, who is 35 as of July 27, will almost certainly be the youngest player to reach 600 home runs. If both Manny Ramirez and Jim Thome hang on to hit #600 over the next two to three seasons, Thome (who was born in August of 1970) will probably be 42 in 2012; Ramirez (born in May of 1972) will be 41 in 2013. (In an earlier post that’s when I estimated each player would hit #600.) If Thome holds on, then, he’ll be the oldest player to hit his 600th home run.

Productivity: Since 2000 (which encompasses Rodriguez, Ramirez, and Thome in their primes), the average league rate of home runs per plate appearances has been about .028. That is, a home run was hit in about 2.8% of plate appearances. Over the same time period, Rodriguez’ rate was .064 – more than double the league average. Ramirez hit .059 – again, over double the league rate. Thome, for his part, hit at a rate of .065 home runs per plate appearance. From 2000 to 2009, Thome was more productive than Rodriguez.

Standing Out: Obviously it’s unusual for them to be that far above the curve. There were 1,877,363 plate appearances (trials) from 2000 to 2009. The margin of error for a proportion like the rate of home runs per plate appearance is

$\sqrt{\frac{p(1-p)}{n-1}} = \sqrt{\frac{.028(.972)}{1,877,362}} = \sqrt{\frac{.027}{1,877,362}} \approx \sqrt{\frac{14}{1,000,000,000}} = .00012$

Ordinarily, we expect a random individual chosen from the population to land within the space of $p \pm 1.96 \times MoE$ 95% of the time. That means our interval is

$.027 \pm .00024$

That means that all three of the players are well without that confidence interval. (However, it’s likely that home run hitting is highly correlated with other factors that make this test less useful than it is in other situations.)

Alex’s Drought: Finally, just how likely is it that Alex Rodriguez will go this long without a home run? He hit his last home run in his fourth plate appearance on July 22. He had a fifth plate appearance in which he doubled. Since then, he’s played in five games totalling 22 plate appearances, so he’s gone 23 plate appearances without a home run. Assuming his rate of .064 home runs per plate appearance, how likely is that? We’d expect (.064*23) = about 1.5 home runs in that time, but how unlikely is this drought?

The binomial distribution is used to model strings of successes and failures in tests where we can say clearly whether each trial ended in a “yes” or “no.” We don’t need to break out that tool here, though – if the probability of a home run is .064, the probability of anything else is .936. The likelihood of a string of 23 non-home runs is

$.936^{23} = .218$

It’s only about 22% likely that this drought happened only by chance. The better guess is that, as Rodriguez has said, he’s distracted by the switching to marked baseballs and media pressure to finally hit #600.

## 600 Home Runs: Who’s Second?July 25, 2010

Posted by tomflesher in Baseball, Economics.
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Alex Rodriguez is, as I’m writing this, sitting at 599 home runs. Almost certainly, he’ll be the next player to hit the 600 home-run milestone, since the next two active players are Jim Thome at 575 and Manny Ramirez at 554. Today’s Toyota Text Poll (which runs during Yankee games on YES) asked which of those two players would reach #600 sooner.

There are a few levels of abstraction to answering this question. First of all, without looking at the players’ stats, Thome gets the nod at the first order because he’s significantly closer than Driving in 25 home runs is easier than driving in 46, so Thome will probably get there first.

At the second order, we should take a look at the players’ respective rates. Over the past two seasons, Thome has averaged a rate of .053 home runs per plate appearance, while Ramirez has averaged .041 home runs per plate appearance. With fewer home runs to hit and a higher likelihood of hitting one each time he makes it to the plate, Thome stays more likely to hit #600 before Ramirez does… but how much more likely?

Using the binomial distribution, I tested the likelihood that each player would hit his required number of home runs in different numbers of plate appearances to see where that likelihood reached a maximum. For Thome, the probability increases until 471 plate appearances, then starts decreasing, so roughly, I expect Thome to hit his 25th home run within 471 plate appearances. For Manny, that maximum doesn’t occur until 1121 plate appearances. Again, the nod has to go to Thome. He’ll probably reach the milestone in less than half as many plate appearances.

But wait. How many plate appearances is that, anyway? Until recently, Manny played 80-90% of the games in a season. Last year, he played 64%. So far the Dodgers have played 99 games and Manny appeared in 61 of them, but of course he’s disabled this year. Let’s make the generous assumption that Manny will play in 75% of the games in each season starting with this one. Then, let’s look at his average plate appearances per game. For most of his career, he averaged between 4.1 and 4.3 plate appearances per game, but this year he’s down to 3.6. Let’s make the (again, generous) assumption that he’ll get 4 plate appearances in each game from now on. At that rate, to get 1121 plate appearances, he needs to play in 280.25 games, which averages to 1.723 seasons of 162 games or about 2.62 seasons of 75% playing time.

Thome, on the other hand, has consistently played in 80% or more of his team’s games but suffered last year and this year because he hasn’t been serving as an everyday player. He pinch-hit in the National League last year and has, in Minnesota, played in about 69% of the games averaging only 3 plate appearances in each. Let’s give Jim the benefit of the doubt and assume that from here on out he’ll hit in 70% of the games and get 3.5 appearances (fewer games and fewer appearances than Ramirez). He’d need about 120.3 games, which equates to about 3/4 of a 162-game season or about 1.06 seasons with 70% playing time. Even if we downgrade Thome to 2.5 PA per game and 66% playing time, that still gives us an expectation that he’ll hit #600 within the next 1.6 real-time seasons.

Since Thome and Ramirez are the same age, there’s probably no good reason to expect one to retire before the other, and they’ll probably both be hitting as designated hitters in the AL next year. As a result, it’s very fair to expect Thome to A) reach 600 home runs and B) do it before Manny Ramirez.

## How much should Manny’s stats have dropped?June 8, 2010

Posted by tomflesher in Baseball, Economics.
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In an earlier post, I used Manny Ramirez‘s differential line to make the case that discontinuing use of performance-enhancing drugs was largely responsible for his drop in production. That’s vulnerable to the criticism that Manny is 38, and that even the best 38-year-old player’s stats drop from his 37-year-old stats.

With that in mind, I queried Baseball-Reference.com’s Play Index to find the stats of players from 1961 to 2009 who, like Manny, played 50% or more of their games in the outfield or as a designated hitter (where Manny might be if he played for an AL team). On average, the 37- and 38-year old players played about 105 games, so I scaled Manny’s drop in stats over the first 27 games to 105 games in order to make the comparison clear. The differential line is behind the cut.

## Manny’s First 27 Games (or, the Marginal Product of Drug Use)June 4, 2010

Posted by tomflesher in Baseball, Economics.
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Last year, Manny Ramirez was suspended for 50 games on May 6. The suspension came after his 27th game of the season. On May 25th of this year, Manny played his 27th game of 2010. That means we can take a look at the first 27 games of each season, when he was using performance-enhancing drugs (in 2009) and when he wasn’t (presumably, this year). The differential line is behind the cut.

## Manny bidding MannyJuly 16, 2009

Posted by tomflesher in Academia, Baseball.
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There’s been some debate as to whether Manny Ramirez should have been allowed to make his rehab starts in AAA Albuquerque before returning to his Major League club, the Los Angeles Dodgers, after a 50-game suspension for drug use. Behind the cut, I’d like to think about some of the reasons behind the punishment and propose a solution.