Tony LaRussa (TLR to his buddies) is a manager who engenders emotions of either love or hate … okay, perhaps more hate than love, unless you happen to support the Red Birds that is. A visit to Busch III can quickly descend into a snoozefest as LaRussa changes pitchers with impunity: The joke is that if LaRussa were to be fired by Walt Jockerty then AT&T would see a huge dent in its profit.

That LaRussa was caught driving under the influence should have caused far more of an outcry than it did. Such behaviour is abhorrent and irresponsible and as team manager he needs to take his obligations to his players and the fans a lot more seriously. Let me tell you, had a similar incident occurred in EPL Soccer with Manchester United boss, Sir Alex Ferguson, his position would have been untenable. Anyway, that is another debate for a different publication.

Whatever your thoughts about LaRussa as a person there is no doubt that he is a brilliant manager and an astute tactician who inspires players and has been the driving force behind St Louis’ ascent to the pinnacle of baseball. That is why when LaRussa does something that you should stand up and take notice.

And that is exactly what THT proprietor Dave Studeman did when he asked me to have a look at Tony’s latest wheeze, namely the benefit of switching the eighth and ninth hitters (yes, that’s the pitcher) around.

###### The theory

So why on earth would TLR decide to move his worst batter (the pitcher) down the order? Surely it is conventional wisdom that the pitcher should bat last because he is the least effective hitter?

Not so quick. The theory is that by batting the pitcher in the number eight slot then the number nine hitter has a better chance of getting on base and being driven in by the number two to four hitters (or specifically Pujols in this case). Baseball Think Factory had a thread on the issue a few weeks back that talked through the rationale.

###### Tools on the interweb

First it needs to be said that this isn’t an especially new topic. Line-up optimisation has been speculated about for ages and many seminal pieces have been penned on the subject. Tom Tango, MGL and Andy Dolphin found, in The Book, that optimizing the line-up would be worth max a win and half during a season, though the practicalities dictate that it will likely be less than that.

Those of you who want to read more about the topic are invited to point your browsers here, here, here and here.

There is an easy answer to this question and that involves a trip to David Pinto’s excellent Baseball Musings website. David has a line-up tool that we can use to decipher how many runs LaRussa is costing or saving with his batting order shuffle.

###### A new tool from the THT bag of tricks

However, that won’t a column maketh. Over the past few years I’ve been working deep underground in a secret bunker located 14 nautical miles west of Area 51, just before the location of the last sighting of Rumplestiltzkin, building the spreadsheet to end all spreadsheets—it is one small step for a man, one giant leap for Excel.

This spreadsheet takes a batting order, any batting order, and a ton of assumptions for running and fielding and spits out loads of cool things such as a run expectancy, win expectancy (for two teams), run frequency, base-out state frequency, lead-off frequency and Leverage Index, among other things (in a quiet moment it can also make a nifty latte too). Take any batting order and I can tell you all the items mentioned above.

The full version of the model tips the scales at a monstrous 200Mb and is a pain in the ass to use (calculating a bespoke Leverage Index is what does it), however, I do have a cut down 15 meg version that I will be releasing as a compendium to the THT 2008 Annual. Yes, on 1 December this technology will be available to you, Joe Public, for the price of a few sheets of paper plastered with quality baseball analysis.

So what’s all this got to do with Tony LaRussa and his line-up? Everything. I’m going to use my Markov to work out the pros and cons of LaRussa’s strategy.

###### The situation

The St. Louis Cardinals have had a topsy-turvy year for sure. Before we go any further let’s take a look at production from each batting slot.

Slot BA OBP SLG OPS 1st 0.276 0.317 0.339 0.656 2nd 0.301 0.365 0.494 0.859 3rd 0.32 0.422 0.561 0.983 4th 0.253 0.326 0.403 0.729 5th 0.24 0.311 0.354 0.665 6th 0.274 0.328 0.458 0.786 7th 0.257 0.326 0.363 0.689 8th 0.263 0.317 0.341 0.658 9th 0.258 0.301 0.36 0.661

Surprisingly perhaps there isn’t that much difference between the eighth and ninth slots in terms of production. There are two reasons for this. One, LaRussa has batted the pitcher in the eighth hole for some part of the season, and two, St Louis actually has the best hitting pitching in the NL. Check out the table below for cumulative team pitching:

Team BA OBP SLG OPS STL 0.198 0.231 0.245 0.476 LAD 0.148 0.195 0.215 0.41 NYM 0.161 0.203 0.193 0.396 PHI 0.158 0.202 0.19 0.392 MIL 0.152 0.173 0.213 0.386 CHC 0.158 0.171 0.211 0.382 ARI 0.146 0.154 0.226 0.38 COL 0.148 0.205 0.17 0.375 SDP 0.151 0.186 0.188 0.374 ATL 0.156 0.186 0.189 0.375 FLA 0.124 0.17 0.188 0.358 PIT 0.141 0.164 0.165 0.329 CIN 0.12 0.154 0.144 0.298 SFG 0.11 0.133 0.161 0.294 HOU 0.117 0.15 0.14 0.29 WSN 0.104 0.137 0.133 0.27

TLR first swapped his pitcher to the number eight slot on 4 August and the hurler has remained their ever since. To date than means that pitchers have hit at number eight over 50 times this season; let’s try to work out the impact on wins of employing this model (pitcher hitting eighth) since the start of the season.

###### Pinto is at the plate

First up is David Pinto’s lineup tool. This is not David’s tool per se; rather he coded it based on work by Cyril Morong at Beyond the Boxscore. The concept is simple. You enter the OBP and SLG of all nine players and the algorithm spits out the runs per game for each batting combination.

For the Cardinals I select the batting stats for each of the first seven slots in the order as they come. The eighth and ninth slots are more tricky as both these include a sprinkling of pitchers. What I did was take the hitting stats for pitchers and from that back out numbers for the remaining at bats in these two slots. This gives a reasonably pure measure of the quality of pitcher batting and also a true representation of the production from the number 8 slot in the classic sense of the term. I elected not to omit pinch hitters because I wasn’t sure how they were distributed across the line-up. Unsurprisingly all the data came from the legendary Baseball Reference website.

Here are the data for each batting position as used in the model:

St Louis Cardinals Slot AVG OBP SLG OPS 1 0.276 0.321 0.339 0.66 2 0.301 0.368 0.494 0.862 3 0.32 0.427 0.561 0.988 4 0.253 0.33 0.403 0.732 5 0.24 0.314 0.354 0.668 6 0.274 0.328 0.458 0.786 7 0.257 0.328 0.363 0.691 8 0.263 0.321 0.341 0.662 9 0.198 0.233 0.247 0.48

If we plug the OBP and SLG numbers into Pinto’s tool we get 4.50 runs per game. What if we swap the eight and nine hitters around (in other words put the pitcher in the number eight slot)?

Runs per game increase to 4.59! Over the course of the season that equates to 14 runs or 1.5 wins just by swapping the pitcher.

In fact, Pinto provides two formulas. The one we used above was based on 98-02 data; the second is based on data from 1959-2004. Interestingly if we use the latter time period we get the opposite conclusion: the classic line-up rpg is 4.543, reverse eight and nine we get 4.539—a drop of 0.6 runs per season. What’s going on?

The explanation isn’t trivial. The 98-02 period was an era of hitting which means that the number nine batter is more likely to get driven in than the number eight batter (the top of the order is coming up), which on the fine margins we’re working with tips the balance. Also the tool is based on regression equations and may lack the accuracy to answer questions as to where you should bat individual hitters, especially at the margins. Let’s turn to the Markov to see if we can substantiate our conclusion.

###### Markov

Before we leap in let’s check the model. The Cardinals have scored 4.56 rpg this season (adjusting for extra innings and home victories). If you plug the batting data into the Markov what do you get? 4.57—a close and credible result. So far, so good.

We must replicate the same adjustment and take out all non-pitcher at-bats from the number nine slot. If we do this rpg (actually runs per nine innings) fall to 4.29. This is considerably beneath Pinto’s number but feels correct in the context of a 4.56 rpg average. Anyway, 4.29 rpg is the baseline we measure other strategies against. (One reason for the discrepancy is that the regression equation used in Pinto’s analysis may correct for the effect of pinch hitting and/or may be skewed by the DH).

What do we get if we swap the number eight and nine hitters? Runs scored edges up to 4.294, which equates to 0.6 runs per season, or 0.06 wins—a small number but an increase none the less.

Okay, what about if we put the hurler in the number seven spot? We get an even higher production—4.299 rpg, for an increase of 1.4 runs per season! Let’s continue. Moving the pitcher to the sixth slot then we are at breakeven compared to the nine hole.

What is going on? Why do we get these odd results?

This is largely a foible of the Cardinals’ line-up. Hitters 4,5 and 6 are woeful compared to what the middle of the order should look like. And as the Cards have the best hitting pitchers the difference in production between the pitcher and the four slot isn’t that great (see table above). The offense revolves around Pujols and there are two factors to contend with. First, Pujols gets on base more than most so you need decent hitters after him to drive him in. Second, we want Pujols up when runners are on base and batting the pitcher ninth is likely to mean fewer runners on for big Al.

In turns out that the optimal sweet spot for these two opposing forces is the number seven spot, to the tune of 1.4 runs per season. This is despite the number seven hitter getting about 4% more at-bats over the course of a season than a number nine hitter does. However, once you add in the effect of pinch hitters then this gap will close some.

Those of you who have read The Book may be jumping up and down at the moment itching to email me and point out that I can’t be right. The Book concluded that for NL teams it did make sense to bat the pitcher eighth to the tune of 1.9 runs per year. Moving the pitcher back to number seven is breakeven.

Looking at the NL as a whole and using the same model that we used for the Cardinals we can replicate (or at least attempt to) these results. My calculations suggest that moving an average pitcher to the eighth hole results in an increase of about 0.7 runs per year, slightly less than what The Book found. Moving the hurler further back to number seven is no different to batting the hurler ninth, which is identical to the conclusion in The Book.

###### What others say?

Anecdotal evidence, for what it is worth, would appear to support the Markov answer. An Rick Ankiel does perhaps he doesn’t need any hitters at all!

**References & Resources**

A big thanks to Baseball Reference and Baseball Musings for the data and tools that made this article possible.

Also due to circumstances out of my control (for instance, as you read this I’ll have been sans Internet for a week) the majority of these data are a week or so old (September 20). However, given where we are in the season the conclusions are still 100% valid (barring some almighty statistical freak phenomenon since writing).

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