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Today's victims subjects are the PIttsburgh Pirates, a team that has seemed, well, hopeless for a while. However, they have a bright from office with Neal Huntington in charge and widely admired saberist Dan Fox on board. The future looks bright, but the the present is, um, hey, the future looks bright! The 5-15 runs gained from an optimized lineup is as valuable to one team as to the next, and the Pirates .321 team wOBA isn't at the bottom of the National League. On the other hand, it doesn't look like they'll be getting much better than that this season. As always, remember that the "Lousy" might not necessarily refer to the lineup, but to the optimization procedure, or, as the "Optimizer," me... With that said, let's take a look.

[Previous installments: Kansas City Royals, San Diego Padres]

Lineup Optimization by The Book

This is the third in an occasional series I will be writing from time to time on lineups. The general principles are largely drawn from The Book, which is worth checking out on this and many other topics. Sky Kalkman gives a good, brief rundown in this article. So there os good stuff out there, but I've wanted to do these for myself.

Here are a few of the guidelines (with my own twists). Yes, there is a lot of stuff here... Feel free to skim or skip this stuff entirely if you want and browse down to the "Getting to the Point" section, although it will make more sense if you've at least skimmed over the following.

• "It's all relative." Although this isn't directly stated in The Book or in any of the summaries I've seen, I think it's worth noting: the appropriate sport in the batting order for any particular player is relative. People talk about having a "true leadoff man" or a "#4 hitter" or that a player has a swing that's just perfect for hitting #2 or whatever. But the truth is, a player's "best" place in a lineup depends on his skills relative to the other players.
• Where should the best hitter hit? Obviously, you want your best hitter to get the most plate apperances. You want to try to get your best five hitters (by wOBA or equivalent stat (e.g., not OPS) in the top five spots. Of those 5, generally, the best hitters will be in the #1, #2, and #4 spots. Ideally, of these three the hitter in the #1 spot will have the best OBP, the #4 hitter will have the most power, and the #2 hitter will be somewhere in between (relative to the #1 and #4 hitters). The best hitter will probably be inthe #2 or #4 spot. The fourth and fifth best hitters will be in the #5 and #3 spots, respectively. Yes, you read that right: the #3 hitter's onlly advantage in run expectancy over #5 is in home runs. Of the top five spots, this is where you want your low-OBP slugger. As we'll see, platoon issues can make getting the best into the ## 1,2 and 4 slots tough, but getting them into the top 5 is pretty close.
  
• The other half: In slots ##6-9, simply go in descending order of hitter quality, keeping in mind:
  
• Platoon issues: Separating lefties takes a certain precedence, since this prevents the opposing team from leveraging LHPs against your lefties, who generally have bigger platoon splits. Moreover, given platoon splits (more on how these are generated in the next section), different batting orders against RHP and LHP are in order (har har).
• Can pinch hitting help? Note that in the chapter on platoons, the authors of The Book show that pinch hitting to gain the platoon advantage really doesn't solve this and other problems since the penalty pinch hitters suffer from the difficulty of  hitting off of the bench offsets the platoon advantage they might gain.
• Speed on the bases: Baserunning and basestealing are important, but are difficult to place, since often (but not always) the same players are good at both. In general, you want good baserunners (aside from stealing -- those good at taking the extra base, scoring from first on a double, etc.) in front of good contact hitters who can "move them over." Basestealers are best leveraged in front of poor hitters who have trouble moving them over. In both cases, if possible, avoid putting these players in front of high-power hitters, since this negates the advantage of those skills. So while your good baserunner might best be utilized at the top of the order (in front of a #2 hitter with moderate power), your best basestealer will likely be best utilized in further down the order in front of poor hitters -- say, in the #5 or #6 spot.
  
• The Jim Rice Effect. Some spots have a greater odds of facing double play situations. The spot that sees the most DP situations is #3 by far, followed by #2. Therefore, try to avoid having high GDP players in those spots. The spot that sees the least (particularly in the NL) is the leadoff spot. So some times if you have an excellent hitter who also hits into a good number of DPs, even if he is slow, it might be worth it to move him into the leadoff spot.
• Movin' on up: The "second leadoff hitter" theory has some validity -- having a #9 hitter who can "set the table" for the top of the order does increase run expectancy, so putting the worst hitter 8th sometimes helps. However, this worst hitter has to be really, really horrible in order for the advantage to obtain. In other words, in National League parks, hitting the pitcher 8th is the smart move according to The Book, although it is worth noting that Tom Tango wrote the chapter on lineups, and Mitchel Litchman (aka "MGL") is more circumspect regarding the value of the pitcher hitting 8th.
  
• Remember that who is in the lineup is much more important that what order it goes in. So relax -- despite my nitpicking and worry over two points of wOBA (see below) here and there, it really doesn' t matter that much.
  

Projected Stats, Sources, and Ground Rules for this Series

• Who gets in? As I wrote above, ultimately, who is in the lineup is more important than what order they go in. Having said that, in this occasional series my focus is opposite issue -- the order. So I'm going to accept whatever group of players the manager is throwing out there, whether I think it is the right group or not.
• Where are those numbers coming from?, the basics: For each posts raw batting stats, I'll either use projections from one or more of the more popular projection systems (CHONE, ZiPS, PECOTA, or maybe even in-season Marcels), or if it's a "reader request" and the requester wants to submit his or her own numbers, that's fine, too. I was going to use ZiPS for this post, then I remembered that Brian Cartwright, the creator of Oliver, is (I believe) a Pirates fan. Oliver doesn't project stolen bases (or the totals weren't on FanGraphs), so for the Pirates, I used Oliver, with ZiPS for stolen bases. Don't get caught up in the specific projections though -- they aren't mine, anyway. If they get the relative qualities of the hitters right, that's good enough for out purposes.
  
• Who is the better hitter? From these stats, I will generate a wOBA (if it isn't done already, such as at FanGraphs) for each player. wOBA (weighted on-base average), for those who don't know, is the total offensive value stat that has taken the baseball internet by storm. Introduced by the authors of The Book and invented by Tom Tango, wOBA takes care of all the problems OPS had in terms of the weighting of OBP and SLG, doubles and home runs. It's roughly on an OBP scale, so something between .330-.340 is about average. For the version used at FanGraphs, .330 was about the MLB nonpitcher average in 2008.  You can read more around the 'net, but in short: if one player has a better wOBA than another, he's a more productive hitter, period. wOBA for players can be found at FanGraphs and Stat Corner, for now, and probably more places as time moves on...
• What about platoon splits? As The Book  also explains (I'm telling you, you really should read it!), while each player has his own platoon split, it takes a lot longer than you would think to establish it -- it takes about 2,000 PAs against LHP for right-handed hitters to be able to say with some degree of confidence what their platoon split is -- so that's means only guys in the league a long time. For left-handed hitters, since there is more variability, it doesn't take as long -- about 1,000 PAs. Still, only veterans really get that far. Until then, most players should be assumed to have the league average platoon split. So, following the procedure used in by the authors for earlier years, I took the average wOBA and  OBP splits for the 2005-2008 AL (it was easier to exclude pitchers that way) and applied them to each player. The only stats I will be adjusting this for are wOBA and OBP. BA, SLG, ISO are the generic ones, just to get a sense of the "kind" of hitter a guy is, obviously, those will change, too. but are harder to adjust for generically. In the "vs. RHP" and "vs. LHP" lineups, the wOBA and OBP figures are adjusted for league-average splits, and are thus italicized. [For more on estimating platoon skills, read this.]
  
• What about Stolen Bases? I took the linear weights SB/CS runs projected and prorated for ~600 PAs.
• And baserunning? A bit more complicated... I looked at different options, and finally used Baseball Prospectus'  EQBRR stats minus the stolen basees component, and did a primitive Marcels-type projection with them, without age adjustments, but with regression to the mean incorporating the Speed Score listed in the CHONE projections. Only two years of data so far, so take them with a grain of salt, but it's something. The listed numbers are projected baserunning runs above/below average per 600 PAs.
  
• How about grounding into double plays? I thought this would be easier, but the data was hard to find for opportunities and stuff... In short, the new Baseball Reference came out with information on GiDPs, opps, league averages and stuff. So I was able to do a three year pseudo-Marcel. The number listed is the GiDP runs above (avoided) or below (grounded into ) average per 600 PAs, normalized for the average number of opportunities seen over 600 PAs from 2005-2008. 

First, here are the raw, un-platooned stats projected by Oliver (with a bit of ZiPS for SB/CS) and myself for the Pirates.  This is one  of the most frequent batting orders that  Baseball Reference records the Padres used the most this season so far. I don't know if there are any platoon situations I'm missing here or not -- I'm just gong to use this set of players for orders vs. LHP and RHP, and hopefully there is enough information here and above for people to put their own orders together. Or you can post in the comments section, and we can discuss what order the alternate lineups should go in.

Getting to the Point:

What's that? You actually want to see an optimized batting order?

[Only the columns in italics are adjusted for league-average platoon splits.]

Comment: Despite the obvious lack of punch in this lineup considered as whole, for optimization purposes, the Pirates have a nice advantage in that their best three hitters vs. RHP are not all lefties. Thus, I was able to get them in the "top three" spots -- #1, #2, and #4. However, when I originally went through and did this, I had McLouth hitting first to take advantage of his speed, then realized that with Morgan hitting 9th, that woudl be two lefties in a row. That is the short/long version of why Ryan Doumit is leading off. It's not that bad, though, as McClouth probably hits for more power versus RHP anyway, and can "drive him along," and McClouth's ability to avoid the double play is more useful in the #2 spot than leading off. When a team has a... less-than-great group of hitters, you end up with situations like Freddy Sanchez hitting #5. Remember, generally, the #5 hitter will be better than the #3 hitter. While Andy LaRoche's superior power might be better served in the #3 spot, Sanchez is better at avoiding the double play, and moreover, Sanchez's superior contact abilities better leverage McClouth's good baserunning. Adam LaRoche is a no-brainer for the #4 spot here. It would be nice to be able to get Brandon Moss up higher, but again, back-to-back lefties are to be avoided, which is also why Jack Wilson hits 7th and Morgan hits at the bottom. This bothered me, as did other things, and I finally worked my way around to a different batting order vs. RHP that got Moss into the top 5 and Doumit out of the leadoff spot if that really bothers people, although it has other "interesting" consequences... so here it is, presented with next to no comment.

[Only the columns in italics are adjusted for league-average platoon splits.]

Next to no comment: Which do you prefer? Discuss. No, I won't be doing this for every team...

[Only the columns in italics are adjusted for league-average platoon splits.]

Comment: Another case of a team whose best hitters are lefties, and thus have to get shuffled around vs. RHP. Sanchez and Little LaRoche are up top with the best projected OBPs, with Doumit, the best projected hitter vs. LHP, hits cleanup. Although Big LaRoche is a better hitter than McLouth, and thus seems like a better fit for the #5 spot, I switched them because of his greater power in the #3 spot, which sees the most PAs with two outs, and also because McLouth's basestealing and baserunning are better leveraged in from of bad hitters like Jack Wilson and (in this situation) Moss. I can see it both ways.

Final Thoughts:

Remember that these are just suggestions based. If you have different projecitons, obviously the best lineups will change. And with any set of projections, as can be seen above, you can try different combinations to see which seems best.

As has been noted, and you've probably read elsewhere, versus a traditional lineup an optimized lineup only gains a team 5-15 runs a season. It's more important to get the right players into the lineup than what order they are placed in. Still, given than 5 runs/half a win costs about $$2-3M on the free agent market, so it isn't nothing, particularly for a team with the Pirates' budget.