Using Regressed Platoon Splits to Isolate Ideal Lineups

One of the things that’s exciting about baseball is hypothesizing on what makes a great lineup.  Conventional wisdom states that you need a fast guy at leadoff, a guy with bat control second, your best hitter third, your best power hitter fourth, a good RBI guy fifth, and then your best remaining hitters in descending order.  As an American League guy we don’t even have to worry about whether to put the pitcher eighth or ninth, but some like the idea of another fast guy in the “second leadoff spot” a.k.a. the nine-hole.  Smart fans mention that you want to split up your lefties and righties to make harder bullpen matchups late in the game.  I personally don’t care for conventional wisdom because it’s often cliche and muttered without thought.

Chapter five of The Book (if you don’t own this, what are you waiting for?) looks at the numbers to sort through the bull and find what actually is important to building a quality lineup.  It’s been a while since I’ve read the thing, and my copy is about 700 miles away, but as I recall they surmised that the difference between the best and worst lineup that you can come up with isn’t very big.  If you do want to take advantage of that Extra 2% (Cha-Ching) then you should start off with your high OBP guys to start with your sluggers in the middle.  The most important spots are 1, 2, and 4 as these guys come up with less than two outs a ton and as you should know, the less outs in an inning the higher the probability of scoring.

I briefly touched on the idea of spreading out your lefties and righties above, but even more important is trying to maintain the platoon advantage against starters.  A team like the Tampa Bay Rays can’t afford to go out and sign guys that maul both types of pitchers. So it makes a lot of sense to get guys with wide platoon splits that can start against those they dominate and come off the bench in high-leverage situations when the opposition plays the bullpen matchup game.  The thing about platoon splits, though, is that you can’t just look at career lines in what generally amounts to smaller samples and project players to perform at that level.  This is where we can regress players to league averages to get a better idea of a players true platoon splits.

Before going on, PLEASE read this tremendous piece by Matt Klaassen.  Matt, or Devil Fingers, is one of my favorite authors for his ability to mix humor with high-level statistical concepts.  I am but, a humble servant compared to him, and I give HUGE  thanks for his help in answering my questions on the intricacies of regressing platoon splits.  I’m going to get my Muffin Man on while you’re reading Matt’s words that I could not phrase better myself:

Ok, feel better or at least smarter?  The takeaway is that you have to adjust players toward the league average in all cases, but especially in the event of a small sample.  Kelly Shoppach should not be expected to be utterly useless against righties and a Demigod against lefties.  The player may show that they are better against one that the other, but like most things, their true talent is neither as bad nor as good as it seems to be over short intervals.  Enough with the teachings, let’s break out with the raw.

Matt broke down how to regress wOBA to league average, but we can apply those same principles to do the same for On-Base Percentage and Slugging Percentage.  First, I’ll give you the summary and then show you how to reverse-engineer this stuff to do it on your own:

I have sorted by wOBA and picked whom I think would best contribute to a lineup depending on which arm the starter throws with.  I assumed Brignac would get all starts at SS, but man, if Sean Rodriguez could show an ability to play average defense at SS, this team could really make some noise.  Now to give you an idea of how we got here and give you fodder to call me names here’s the work broken down by batter-handedness:

Left-Handed Hitters:

Right-Handed Hitters:

Switch-Hitters (I call these Puppy-Ds):

Ok, so you’ve got a bunch of stuff in front of you (download the Excel Workbook or follow along in Google Docs if you want) and aren’t sure what it all means.  Career OBP/SLG/wOBA comes from Fangraphs and is based on the entirety of the players career.  Same with the versus LHP/RHP numbers except that the splits and PA go from 2002 – 2010.  This really only affects Manny Ramirez and Johnny Damon, but it needs to be mentioned.  PA is the number of plate appearances against that type of pitcher and the % is the percent of total plate appearances.

The Platoon Skill section is where we start to get into the nitty-gritty.  Split is based on Matt’s work and you can see this formula as well as all others if you download the Excel Workbook.  Split gives us an idea of how wide a player’s platoon splits are going to be.  It is calculated as the percentage form of the difference between the splits divided by the career number.  The larger the number, the wider the split so if the number is negative you could say the player exhibits a “reverse-platoon” advantage.  This is the non-regressed form, though, so these percentages are under the spell of small sample variation.

We can begin to draw conclusions once we’ve regressed these percentages to the mean.  I have used Matt’s figures of 8.6% and 6.1% for lefties and righties, respectively, for the wOBA calculations.  I replicated his use of Baseball-Reference to come up with the league averages for OBP and SLG, except that I’ve used league-wide data from 2008 – 10.  You can find these averages in the LA tab, but I’ll re-print here.  For left-handed batters, the league average platoon split for OBP and SLG is 7.2% and 5.3%, respectively.  For normal-handed batters the league average is 9.0% for OBP and 11.7% for SLG.  I will give an example from each type of batter so that you can see how the plate appearance and league average adjustments:

Reid Brignac OBP: (23%*74+7.2%*1000)/(74+1000)

You can see that Brignac has an extremely wide split at 23%, but he’s also had very few chances at only 74 plate appearances.  After a heavy dose of regression his 23% observed platoon split comes down to a still highest among lefties 8.3%.

Evan Longoria SLG: (-4.0%*536+11.7%*2200)/(536+2200)

Evan had a platoon split that was about half of B.J. Upton, and almost 1/12th of Kelly Shoppach.  After regressing, we can see that Evan has a true split of 8.6% for his SLG%.

Ben Zobrist wOBA: (6.2%*1201+0*600)/(1201+600)

Puppy-Ds are one area where the book wasn’t completely clear, though as Matt stated, after about 600 plate appearances we have a pretty good idea of where a switch-hitter stands.  We’ll work under this assumption for the remainder of this exercise.  Also, I should point out that Elliot Johnson was our most heavily-regressed player as he only has 19 plate appearances at the MLB level.  Essentially, the regression treats his platoon split as that of a league average player.

The next step was what Matt called “centering” the split.  This took me a bit to figure out, but what I’ve found is that you can multiply, or weight, the % of pitches from southpaws with your true, regressed split.  I did this for the dominant side of the platoon and then subtracted this figure from the true regression number to come up with the weaker side adjustment.  With our adjustment to each side in place we can now use projections to get an idea of what a players regressed platoon splits should look like for the coming year.

First we need a projection, and I chose The Hardball Times Forecasts which I have been using for the last few weeks and on which I based the offensive component of my Team Win/WAR Projections posts.  The forecast column shows what THT thinks will be the overall number for that player for that stat on the year.  We then apply our adjustments to come up with the numbers in yellow under vLHP and vRHP.  These are the numbers that you should expect for the player, though you should know by now that the relatively small sample of just 2011 might dictate otherwise.

Recall, that four hours ago when you started reading this I started off by stating that every fool with a mouth can come up with their idea of an optimum lineup.  Well this fool decided to use these regressed splits to see if perchance a program could do all the legwork for him.  My idea of a good lineup leverages solid OBP early with better SLG in the middle-to-bottom.  With the Rays, I worry less about splitting up my lefties and righties, because if a player is going to be exposed in a matchup, it’s highly likely that there’s a better option on the bench that can come in if the leverage is high enough for Mr. Maddon to make that call.  Basically, I don’t care if we have eight righties in a lineup against a lefty starter, because they’re all going to do work and can be subbed out later if/when his opposite-handed counterpart needs to make an appearance.

Recall this table:

I have placed a position next to players that I think should start versus that type of pitcher.  Like I mentioned earlier, if Sean Rodriguez shows that he’s not an absolute hack in the field (or even Elliot Johnson shows that he can give comparable defense while providing a slightly better bat) then I wouldn’t hesitate to bench Reid Brignac against lefties.  Sorry if you root for players, but I root for laundry and see players as inputs, not human beings.  I love Brignac and hope he can become a four WAR player year-in and year-out, but his glove better be a tremendous upgrade or he better show that he’s isn’t a complete feeb against lefties.  Rant over, apologies to those that are sensitive.

We can take these OBP and SLG numbers and plug them in over at Baseball Musings Lineup Analysis tool.  The idea is that you plug in nine players and their accompanying OBP and SLG and the tool tries every possible combination of how you could line them up.  Additionally, it will compile the expected Runs Per Game (RPG) based on the input OBP and SLG numbers.  Here’s a look at the top-10 lineups versus left-handed pitchers output by the tool:

The ideal lineups are just a tick under five and a half runs per game and almsot all of them feature Ben Zobrist leading off and Longo in the two-hole.  You can sort through this on your own to find what you like and what you don’t.  I think it’s a neat tool, but certainly not gospel.  The upshot to having Zobrist and Longo that early in the lineup is that they’re always getting up with few outs and they can rack up plate appearances at an extreme rate.  Meanwhile there would still be good batters behind them that can kick butt with runners on.  Here’s a look at the top-10 versus right-handed pitchers:

How sick would it be to watch a lineup start off with Manny and DanJo?  I honestly hope to see this lineup at some point so that the goobers can point a stick at what a crazyman Mr. Joe Maddon is.  Again, this is just an automated tool and I know many folks that aren’t behind this thing at all, but I think it’s a neat look for an extreme whatif question.

I hope you enjoyed this long, rambling piece.  Now that I’ve given you a calculator to regress platoon splits I’d love to see what others come up with for their team.  Simply download the Excel file HERE and plug in the plate appearances and splits where appropriate.  Don’t mess with the formulas, but it might not hurt to take a look at them to get a better feel for what you’re actually doing.  Personally, I can’t wait to see the Rays take a run at scoring five runs a game this year.  If they can do that and pitch the way they’re capable of, then all these big dreams I’m having might become reality.

Thanks for reading if you’ve made it this far, have a great one.