Trey Hillman, undoubtedly pondering a batting order that would make Tom Tango proud.

In August, 1972, with the Detroit Tigers in a terrible slump, manager Billy Martin decided to "shake things up," but instead of benching players or pushing over the buffet, he put the names of his starters in a hat, and wrote the batting order down in the order he randomly picked the names out. The Tigers famously won the first game of the doubleheader in which they used this lineup.

You may or may not have heard or read that story before (I first read it in Baseball Between the Numbers). You probably have heard, and rightly so, that batting order doesn't matter, or, more precisely, that it doesn't matter all that much. Research has shown that even the stupidest move, like hitting the pitcher cleanup, only costs a team about 16 runs over a season on average.

Still, if you're anything like me, you can't help but obsess over lineups. And, while the most optimal lineup increases offensive output by about 5-15 runs a year over a traditional lineup, for teams with weak offenses those marginal runs are all the more important. Yeah, it might be more "fun" to figure out if A-Rod or Teixeira should hit cleanup, or if Youkilis should hit second, or how to break of Philadelphia's lefties, but does it really matter that much for those teams? Hence this series on optimizing lousy lineups. Of course, you may get bad because your team makes it in here. You might decide that the "Lousy" in "Lousy Lineup Optimizer" applies to the process, or the person attempting to do the optimization (me). In any event, I'll be doing these from time to time throughout the season. And today, I'll start with the team for which I root: the Kansas City Royals and their (postponed) Opening Day lineup versus the White Sox.

Lineup Optimization by The Book

I've thought of doing a series on lineup optimization for a while, but while I was wrapped up in my series on starting rotations, lineup optimization posts inspired by Tango, Lichtman, and Dolphin's The Book  became "to the 2009 blogosphere as to what pictures of Jenn Sterger were to the 2006 blogosphere," in the words of Royals Review. Even Rany Jazayerli wrote one. You really should read the chapter in The Book to get all the details. Sky Kalkman gives a good, brief rundown in this article. There's good stuff out there, but I've wanted to do these for myself (all the while knowing it doesn't matter that much) 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: Sky doesn't emphasize this too much, and The Book sort of glosses over (despite the excellent chapter on  platooning) that 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 righties and lefties 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 liklihood 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 does exist -- 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.
  
• 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. That's going to be tough with the Royals, but I'll deal with it.
• 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. For the Royals I averaged CHONE, PECOTA, and ZiPS.
  
• 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's 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 playres 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. [Note: If you think that you "know" that a player has a bigger/smaller split than that, fine. The point here isn't the projections, it's getting a sense of batting order. In any case, you'd be surprised... take the Royals, the team I went over first. Probably the two most experienced batters in group are Jose Guillen and David DeJesus. Guillen still falls short of the RH requirement, having only 1433 MLB PAs against RHP. Without looking at his career numbers, but going off of the projections, I came up with a .312 OBP for him against RHP, and .334 against LHP. His career split?.318 and .334. Regression to the mean, folks. DeJesus is a bit closer, a LH with 848 PAs versus LHP. My "generic" split gets a .360 OBP vs. RHP, and .335 vs. LHP. Career? .369 and .340. That's pretty close for a generic split... Career numbers are different than projections, but it's close enough to make the point. Yup, regression to the mean.]
• What about Stolen Bases? I just averaged the linear weights runs from each projection over about 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 Marcels, again. 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. 

Whew... that's a lot of build-up for what will end up not being much information. First, here are the raw, un-platooned stats for the Royals that Trey Hillman seems to be including in his regular starting lineup. This is not the batting order.

Getting to the Point:

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

Comment: Remember that only the italicized numbers are altered for average platoon splits... After all that about the importance of having a good hitter in the #2 spot, I put a dude with projected .321 wOBA and .330 OBP in there? Ladies and gentlemen, your 2009 Royals offense! Seriously, the "ideal" #1,#2, #4 combination would be DeJesus (OBP_, Gordon (balanced), then Jacobs. Well, not ideal, but better. Maybe Teahen could hit third, Butler fifth... But you can't put all those lefties in a row... Other than Butler, none of the non-lefties project as hitting righties well. So Crisp ends up second, although hardlyon his own merits as a hitter. Still, he does some things well, like baserunning and avoiding the DP. Mike Jacobs isn't your typical #3 hitter, and probably wouldn't be in most lineups. Gordon looks like the best hitter versus RHP in the group, but ends up #5 in stead of #4 or #2 (I thin he'd be a good leadoff hitter with those baserunning numbers and moderate power), but end up #5 because of platoon issues and other player limitations. It's not a bad place for him, as he has  some of the better power potential on the team to drive in lumbering "baserunners' like Jacobs and Butler, while having baserunning ability for the lower powered guys behind him, and the basestealing to help out bad hitters like Jose Guillen, et. al.  Mark Teahen is the 4th best hitter against RHP in this group, but ends up 7th. You could actually make a case for switching Teahen and Jacobs, given that Crisp's speed and his and DDJ's baserunning is a bit wasted in front of an all-or-nothing guy like Jacobs. That, in addition to Teahen's superior skills in avoiding the DP might make him a better choice there, and his baserunning would take better advantage of Billy Butler's contact hitting. It's a mix-and-match thing.

For Opening Day, however, the Royals are facing one of the beautiful people: Mark Buerhle, a lefty. Here is Royals' manager Trey Hillman's Opening Day lineup as posted by the the Mouth of Sauron Royals.com.

Comment: The first thing that stands out to me is that Trey Hillman apparently isn't too worried about having a lefty reliever leveraged against his team,  not even in the first inning. Or about four out of the top give hitters being way below average. But, hey, at least there's good baserunning in front of Mark Teahen, who makes it into the third spot, as I mentioned earlier! Some Royals fans are probably puzzled by those wOBA numbers, since we were reminded again and again about the Royals success against left-handed pitching due to the huge platoon splits of players like Billy Butler, Mike Avilfes, and Jose Guillen. Regression to the mean, my friends...

It's hard to imagine improving on Michael Scott's Trey Hillman's brilliance, but I'll see what I can come up with:

Comment: Yes, I expect this to raise some eyebrows. Leading off with Billy Freaking Butler? One of the worst baserunners in baseball? Well, yes. But look -- the next best projected OBP of these guys against LHP is David DeJesus with .335 -- that's a 30 point gap. More importantly, while Butler could reasonably hit in the second or fourth spots, he projects as a Jim-Rice-esque double play machine, at least so far. The first spot in the lineup sees the least amount of DP situations of any spot, including the ninth. Moreover, Butler doesn't project as all that powerful -- decent power, but not a ton of home runs, so they won't be "wasted" by not having guys on base for him. Moving on, Guillen hits fourth as he's actually projected as pretty okay versus lefties, and with some acceptable power. Mike Aviles his fairly balanced. Neither David DeJesus or Alex Gordon project as good hitters versus lefties, but again, this is what happens with bad lineups and platoon issues -- you get guys hitting in the top half who aren't very good in those spots. Gordon has more power and lower OBP (along with being good at avoding the double play) and so he could hit 3rd here, but the overall slightly higher projected wOBA, along with his good basestealing ability in front of the bad ##6-9 hitters make him a decent choice for #5 in this lineup. Alternating right and left down here messes with the "according to wOBA" order. Yes, I realize that Jacobs has 1 point of wOBA on DeJesus after the split, but that OBP (which actually matches his overall OBP from 2008) is intolerable.  His baserunning doesn't help. In response to all those who "know" that Miguel Olivo will OPS .850 versus lefties this year, I can only ask that they read the section on platoon splits above.

Final Thoughts:

Not much to say. Again, remember, each change is small -- a run is a big difference. The biggest one can be putting a double play machine who is otherwise  good hitter up top, which can save about 2 runs by itself, but in this case, Butler would only be down it against left-handed starters. I welcome comments, mockery, whatever. And if you have requests for lousy lineups you'd like this lousy optimizer to lousily optimize, please let me know the team, and perhaps the lineup and projection system you want me to use.

Let the arguments begin!