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Correlation

Posted by SBG on Thursday, December 29th, 2005 at 4:04 pm

The Tony Batista signing has brought out some interesting comments throughout the Twins blogosphere.

Over at Twinkie Town, the masses have been engaging in a long running discussion about the value of Mr. Batista, given his ability to hit home runs and make a huge number of outs. One regular poster even wrote this:

Batista is significantly better than any right handed hitter the Twins have, including Rondell White.

Wow. Better than Hunter? You are kidding with that, right? Better than Stewart (last year's bad season notwithstanding)? Better than Castillo (I know he's a switch hitter)? Hell, is he better than Cuddyer? I wonder if he's better than Juan Castro, at this point.

Let me start with the basics. On offense, the number one objective is to score runs. Sounds simple, doesn't it? Given that premise, who would you rather have, a guy who hits 35 home runs a year or a guy who hits 2 home runs a year. All else being equal, you'd take the guy with 35 home runs, right? Of course. But, the qualifier "all else being equal" is an important qualifier.

I think that we can all agree that it does not require a home run to score runs. In fact, most people would agree that a guy who hits 2 home runs a year but gets on base over 40% of the time can be more valuable than a guy who hits 35 home runs a year, but only gets on base 25% of the time. I say most people, because some still do not get that making outs is the enemy of scoring runs (see the comment from Twinkie Town, above).

Enter Tony Batista. I looked at his three year splits (actually his numbers are for two years 2003-04, as he was so good that he played in Japan in 2005) and found out that he hit 58 home runs in 1237 at bats and 1320 plate appearances, which is 21.32 at bats/home run, which is 4.69 home runs per 100 at bats. He also hit a combined .238/.271/.424/.695.

Michael Cuddyer, over the last three seasons has hit 28 home runs in 863 at bats and 966 plate appearances, which is 30.82 at bats/home run or 3.24 home runs per 100 at bats. He hit a combined .261/.333/.430/.763. In other words, Cuddyer has a better batting average, a better on base percentage, a better slugging percentage and a better OPS. But, Batista will hit one more home run per 100 at bats. And that's enough for some people to proclaim loudly and repeatedly that he is a significant upgrade over Cuddyer. Hogwash.

Let's normalize the numbers to 500 plate appearance for each. This is what the lines look like.

Player PA Outs AB R H 2B 3B HR RBI BB SO BA OBP SLG SH SF HBP GDP
Cuddyer 500 304 447 61 116 25 4 14 49 47 96 0.261 0.332 0.430 2 2 4 17
Batista 500 381 469 58 111 19 1 22 79 20 68 0.238 0.270 0.424 2 6 3 13

Yes, you'll get the 8 more home runs from Batista. Cuddyer provides you with 5 more hits, one more extra base hit and 27 more walks. Batista provides you with 74 more outs. We already know that Cuddyer has better batting average, OBP, and SLG. The only thing that Batista does better is hit home runs and strike out less. Those advantages are more than negated by everything else. He even hits into a lot of double plays, Cuddyer's big bugaboo last year.

[Update: As I mentioned above, I screwed up Cuddyer's outs. He actually averaged 356 outs, not 304. Thus, Batista made only 25 more outs per 500 plate appearances. That mistake does not change the analysis of Batista with respect to his comparision to anyone else or the OPS' or GPA analysis. Also read the post above to understand what OUTS means. -- SBG, December 31, 2005.]

Oh, and Batista has more RBIs, but RBI totals are more about who is hitting in front of you and your opportunites more than anything. Don't believe me? Let's add another player to the table above.

Player PA Outs AB R H 2B 3B HR RBI BB SO BA OBP SLG SH SF HBP GDP
Cuddyer 500 304 447 61 116 25 4 14 49 47 96 0.261 0.332 0.430 2 2 4 17
Batista 500 381 469 58 111 19 1 22 79 20 68 0.238 0.270 0.424 2 6 3 13
Bonds 500 223 330 102 115 21 2 39 82 160 43 0.348 0.564 0.774 0 2 8 5

Look! Bonds only delivers 3 more RBI per 500 plate appearances! Batista is almost as good of a run producer as Barry F'n Bonds! If you believe that, I've got some choice 50 yard line seats for the Vikings playoff game coming up next week. I'll start the bidding at $200 a piece.

I've done some research on correlation (actually I've read a couple of articles). At Baseball Prospectus, they discussed why they use their statistic Equivalent Average. The reason why is that it provides a better correlation to runs scored. Of the statistics that we usually look at, OPS has the best correlation to runs scored. Cuddyer's OPS over the last three years is .763. Batista's is .695. Juan Casto's is .667. Luis Rivas' is .690. There you have it. Tony Batista = Luis Rivas.

But wait. Other studies have shown that OPS under values OBP. Why is that? Well, OBP is inherently a smaller number than SLG, and thus merely adding them together makes SLG inherently more important in OPS. A better correlation can be found with OPS'. OPS' = 1.4*OBP + SLG. Gleeman has used GPA, which gives OBP a 1.8 multiplier and normalized it to make it look like a batting average. He calls it GPA. His formula: GPA = (1.8*OBP + SLG)/4. Look at this chart:

Player OPS� GPA
Cuddyer .895 .257
Batista .802 .228
Rivas .804 .231
Castro .772 .221
Hunter .914 .261
White .954 .273

Look. Batista is Luis Rivas in terms of his ability to create offense. His "offensive output" is correlates to the type of offense that Rivas puts up. There is more to scoring runs than hitting a homerun every six or seven games. There is getting on base and not making outs. Outs are the enemy of scoring runs.

I'll give Batista this much, though. He's definitely better than Juan Castro at the plate.


This entry was posted by SBG on Thursday, December 29th, 2005 at 4:04 pm and is filed under Uncategorized. It is one of 928 entries by the author. We are no longer accepting Letters to the Editor on this post. Why?

16 LTEs

Neil replied on December 30th, 2005 at 8:57 am

They really are getting their undies in a bunch over there. I think that in some ways it's less Batista-liking than Cuddy-hating. I have a friend, she's hated Cuddy ever since Gardy (unfairly) trotted him out in the ALCS against the Angels. I think that a lot of people can't get over that combined with the fact that he's clearly underperformed.
Why people gotta hate?

 
spycake replied on December 30th, 2005 at 9:03 am

SBG, you didn't really address the RBI difference, other than to say lineup position. I think there might be more to it than that:

1) Cuddyer was an EXTREME groundball hitter last year (1.8 GB/FB ratio) and has always been more GB-oriented than Batista (0.75 career ratio). Hence fewer sac flies, and a greater frequency of double plays.

2) Cuddyer strikes out more than Batista (28 times over 500 PA), meaning fewer advanced runners...?

3) Bunched with other singles/sometimes-doubles/sometimes-walk-type hitters (which includes most Twins), perhaps an infusion of more HR (8 more over a season, by your count) is indeed more valuable than a handful of extra walks and a few doubles. Especially when combined with the benefits of points 1 and 2 above.

I like Cuddyer, and I wish he could get another chance at third base, but something was wrong with his 2005 season, even past the first month, I'm afraid. His 2004 was better, so I have hope, but he's getting older and his career high points thus far have been "better-hitting 2B than Luis Rivas" and "better third baseman than Terry Tiffee".

 
SBG replied on December 30th, 2005 at 9:20 am

Oh, but I did. Batista will give you four more SF over 500 at bats than Cuddyer. Cuddyer will hit into 4 more double plays over 500 at bats. The numbers are there.

Since when do fly balls advance runners and ground balls don't? How many fly balls to left and center advance runners? We've documented the four more SFs. How about to third? Or second? Not worth mentioning. Unless Batista, a dead pull hitter, starts hitting a lot of flies to right, well, I won't accept that he advances more runners than Cuddyer.

This post is not to talk about how great Cuddyer is. This post is a response to the ridiculous pimping of Batista. He's the best right handed bat we have? Really? Everyone should welcome this signing? Really? When we have the worst offense in the league, we should applaud this? I'll applaud White and Castillo, but this one is a huge thumbs down. I don't care if his contract isn't guaranteed. It's not about the $.125 million. It's about upgrading the team.

This is no upgrade. At all. We've, in effect, put Castillo at 2B and moved Luis Rivas to 3B.

 
SBG replied on December 30th, 2005 at 9:23 am

One more thing. Cuddyer strikes out more, but there's no getting around the fact that Batista provides 74 more outs. Since the notion of productive outs has been all but completely debunked, I can't see how it matters that Cuddyer strikes out more.

 
spycake replied on December 30th, 2005 at 10:31 am

If your argument is that Batista is not the best RH bat on the team, you're preaching to the choir.

But, "the numbers are there" is hardly definitive proof of your Cuddy comparison. You're averaging two very different seasons by Cuddyer -- which one is going to show up in 2006? Also, you're averaging two different seasons by Batista -- one where he had a career low in XBH output (2003) and one where his power more closely matched his career levels (2004). Which TFB shows up in 2006? And your numbers or estimations seem to be off -- you claim "Batista will hit one more home run per 100 at bats" than Cuddyer, but your 500 PA data shows him with 8 more homers...? If you just compare their most recent ML season, TFB has a prorated edge of roughly 10 fewer GIDP, 10 more HR, 5 more SF, etc.

Plus, you still didn't address Batista's specific benefit to the Twins lineup. Singles and walks don't score runs as easily as home runs, and as we learned last year, it's very difficult to count on guys like Ford and Cuddyer to manufacture virtually all of your runs through that method. I think adding TFB's power to the Twins small-ball game could help us more than other teams.

Again, no one here is "pimping" T-Bat, but I think taking a flier on him is a great move (although I would like to see Cuddy and Batista compete for 3B in the spring, and I think that Cuddy will get lost in RF literally and figuratively, but that has nothing to do with TFB).

 
SBG replied on December 30th, 2005 at 10:49 am

I rounded on the one per hundred. If you look at the numbers that I posted, Batista will hit 1.45 more home runs per 100 at bats. So, I should have said a little more than one per one hundred.

If stating that Batista is the best right-handed hitter on the team isn't pimping, I don't know what is. You yourself don't believe it, and I am not accusing you of pimping him personally, but what about that assertion?

Either you believe that making outs 73% of the time negates his power or you don't. He hits a home run every 4.4% of his plate appearances. He makes an out 73% of the time. I believe that his 74 more outs than Cuddyer outweigh the occasional home run.

The use of three years was an attempt to show what likely might happen. Of course, we don't exactly what will happen, but averaging out over three years shows more regression to the mean. Plus, ESPN provides three year numbers for me to use without a tremendous amount of work. One thing that I didn't point out is that Batista is much older, past his prime, and has been trending down. I didn't add his putrid Japanese numbers, which when converted to MLB equivalents would show further decline.

The fact that the Twins took a flier on him shows that they really don't believe in the sabremetric theories of how runs are created. They don't believe in correlation. They don't believe in OPS, OBP, SLG, Runs Created, EqA or any of these other metrics. By any other metric besides AB/HR, Batista is shown to be inferior to Michael Cuddyer. But, the Twins apparently believe that he'll magically time his home runs for when there are guys on base or something.

 
Drake33 replied on December 30th, 2005 at 11:14 am

Twins apparently believe that he'll magically time his home runs for when there are guys on base or something

This is exactly what it looks like to me as well. The 'intangibles' of TFB are going to outweigh the quantifiable Cuddyer.

I don't mind the signing if it was meant to give Cuddyer a 'kick in the ass', or to give the Twins a veteran backup infielder. But to give him the starting third base job, really upsets me.

If Batista performs his 0.240/0.280/0.420 line, AND he gets more Plate Appearances than Cuddyer I will join SBG in hunting down Gardenhire...

 
Cheesehead Craig replied on December 30th, 2005 at 11:31 am

I'm just glad the Brewers didn't sign him

 
TheBentKangaroo replied on December 30th, 2005 at 1:30 pm

Well, if Batista is equivalent to Rivas, at least he seems to give more effort. If a guy is going to suck, at least I want to like him.

 
spycake replied on December 30th, 2005 at 1:44 pm

I meant no one *here* is pimping TFB -- perhaps at Twinkie Town, but for you to refute those claims here is like going on Fox News to bash Democrats...

"The fact that the Twins took a flier on him shows that they really don't believe in the sabremetric theories of how runs are created."

Umm... are you confusing the Twins with that poster over at Twinkie Town? I don't think the Twins view Batista as anywhere near their best RH bat --in fact, the comments from TR clearly acknowledge his limitations. TFB came cheap, and he might be able to fill a need on this team, whether off the bench or at third (although we all know Cuddy deserves a shot there too).

And as long as we're all just speculating about stuff, I'm going to remain optimistic about Batista's potential. He may be past his prime, but not past his usefulness:

1) he signed with Japan because he got a ridiculous contract there (2/15 I've seen reported), not necessarily because he had no reasonable offers here

2) it didn't work out in Japan, contractually and statistically, but this could have been due to an inability to adjust to the different style of play and clubhouse culture over there

3) he only just turned 32

I've also heard speculation that he's way out of shape, but he's generally been a healthy guy, and given his skill set (or lack-of-skill set), his physical condition might not matter all that much.

 
Nick N. replied on December 30th, 2005 at 3:53 pm

OK, I guess that I would fall into the lump of "Batista apologists," because I am certainly tired of all the stat-heads bashing the hell out of him. To say he is better than any right-handed hitter on the Twins is clearly assinine. I don't think he's a very good player, but I also don't think he's a bad signing.

Neil commented above that people's warmth to the signing is more related to Cuddy-hating than it is to Batista-liking. This is somewhat true, at least in my case. Michael Cuddyer had an absolutely awful season, and I don't think it's even quanitifiable through statistics, unless you want to look at his avg with RISP (.204) or with the bases loaded (.214). Cuddy hit 12 home runs last year, and TEN came with nobody on base. He came up 14 times with the bases loaded last year, and struck out 6 times. He is absolutely horrible under any kind of pressure, and not only does he not put the ball in play and drive in runs, but he usually has terrible at-bats and strikes out or grounds into a double play. Oh, and then there's his terrible defense. He's got a strong arm, but he has no accuracy, and has slow reactions and little range. I'm absolutely sick of watching him at third base. As I've said before, it's not like this team has not given him ample opportunity. He was handed the starting right field job to start the 2003 season, and handed the starting third base job last season, and he couldn't hit well enough to hold on to either of them.

I don't think Batista is that great of a player, but I'm ready to give him a try. SBG, you and Gleeman and several others are so eager to insult the Twins for signing Batista, but I have not heard ANY alternate suggestions. What would you have done? Traded away valuable prospects for Blalock? Signed Randa for 4 million? Handed Cuddyer the job again despite the fact that he has shown essentially no improvement over the course of his entire career? If Batista doesn't work out, he will be removed from the lineup and the Twins will go another direction. 1 million dollars, not that huge of an investment.

But to say that Batista is another Luis Rivas is absurd. Rivas wouldn't have been starting on any other Major League club for the past several years, and he will in all likelihood never reach the Majors again at this point. Batista lasted in the league for 9 seasons, played in an All Star Game, and has 214 career home runs.

 
brianS replied on December 30th, 2005 at 5:28 pm

Ok, maybe Batista is not quite Rivas. But I don't think the comparison is absurd.

Here's an itty-bit of stat-headiness: OPS+, which is the version that adjusts for park effects and is normed so that the average player scores 100. Below 100, you are a below-average hitter in OPS terms, above 100, you are above average.

Rivas's last 4 years (working backwards): 68, 82, 80, 86.
Batista's last 4 in the majors (working backwards): 88, 76, 102, 86.

Basically, in three of those 4 years, he was very Rivas-like.

As SBG says, the name of the (offensive) game is to score runs. Batista's negatives offensively outweigh his positives. That makes him different from Rivas, who had no discernible positives. But it doesn't make him noticeably better.

 
SBG replied on December 30th, 2005 at 5:55 pm

I didn't provide any alternatives??? Other than advocating for months that they be bold and trade Hunter and try to turn him into a decent infielder. Plus, trading Hunter could have freed up more money to go after another decent bat.

I applaud the Castillo trade and the White signing, but I thought this team was so bad offensively that they needed to do something drastic. But, the Twins have decided to play it safe.

 
frightwig replied on December 30th, 2005 at 7:03 pm

Until the bitter end, there were fans who believed that Luis Rivas would reward their faith in him, too. What can you say?

Twins management painted itself into a corner by already declaring that Cuddyer would not play 3rd base next year, although he did show improvement both offensively and defensively after the first couple months of this past season. TR then found he couldn't sign a Mueller or Randa to a cheap deal, and his budget is maxed because he can't or won't trade Hunter/Stewart/Lohse and he's giving Jacque's money to Castillo. So now he's forced to take a flyer on a garbage player just to fill an artificial "hole" at the hot corner.

Believe it now or later, fans, but the Twins will have a downgrade at 3rd base next spring if Ass-Batista is the regular starter. If TR had signed Jose Valentin to play 3rd base before last season, would *any* Twins fan have applauded? Well, now we have ourselves a lesser Jose Valentin. Thanks, TR.

 
Nick N. replied on December 30th, 2005 at 7:26 pm

It is impossible to know what types of trades Ryan would have been able to pull off and what types of packages Hunter would have garnered, which makes it difficult to speculate about trades that he should have made.

The fact is that there are still four months before the season starts and Batista has a non-guaranteed contract. He could be gone two weeks into spring training and all we'd be out is a little severance pay, and then we will all feel stupid for all this bickering.

 
ubelmann replied on December 30th, 2005 at 8:22 pm

74 outs? Where on earth is that number coming from?

1-OBP gives you how many outs/PA a player makes (either you make an out, or you get on base). With a .332 OBP against a .270 OBP, that means Batista is going to make 365 outs compared to Cuddyer's 334, for a difference of 31 outs.

Also, with regards to GIDP, Batista's last year in the league, he had a close to league average rate of GIDP 15% of the time there was a DP opportunity. Last year, Cuddyer had a GIDP rate of 25%, one of the very worst in all of MLB. Working backwards from Cuddyer's 17 GIDP number, that works out to about 68 DP opportunities. Over 68 opportunities, Batista would be hitting into about 6.8 (say 7) fewer DPs. (Also, outs with runners on base are worse than outs with no runners on base, check out the closest expected runs matrix.)

Now, we're down to a 24 out difference, and I think the extra power and better defense make Batista at least comparable to Cuddyer as a 3B at that point. At the worst, this is a lateral move, allowing Cuddyer to pursue employment at a position he's more comfortable at.

 

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