Monday, August 18, 2014

Thoughts on Lineup Construction Part II

I'm going to start this post with a fairly simple mathematical exercise using hypothetical lineup models.  First, we'll start with 2 assumptions:  You want your the best hitter in the lineup hitting as often as possible.  2.  You want the best hitter in your lineup hitting with runners on base as often as possible.

First, lets take a situation where your the first 3 batters in your lineup all have an OBP of .333 or each one gets on base 1/3 of the time.  What you want to know is the probability that the following batter will come up with at least 1 runner on base.  The leadoff batter, of course, has a .333 chance of getting on base, so the #2 hitter has a 100% chance of batting in the first inning AND he has a 33.3% chance of batting with at least 1 runner on base.

In order to know the probability that the #3 hitter will come up with at least 1 runner on base, you first have to calculate the "off-base percentage" of the first 2 hitters or the probability that neither of them will reach base.  You can calculate it directly, but it's easier this way unless you know the formula and have a good calculator.  At any rate, the "off-base percentage" for the first two batters comes out to 2/3 X 2/3= 4/9=44.4%.  Now, if there is a 44.4%  chance that neither batter reaches base, there is a 100-44.4 = 55.6% chance that at least one of them will reach base.  Of course, there is a 100% chance that the #3 hitter will come to the plate in the first inning.

For the 4'th batter, there is a 2/3 X 2/3 X 2/3= 29.6% chance all 3 of the #1-3 batters will make an out and he will not come to the plate in the first inning.  Of course, that means he would lead off the 2'nd inning.  On the other hand, it also means there is a 70.4% chance he will come to the plate in the first inning with at least 1 runner on base compared to only a 55.6% chance of coming up with at least 1 runner on base if he was hitting 3'rd in the order.  That is why the 4 spot is known as the "Cleanup Hitter."

When you add all this together, including the 18 fewer PA's over the course of the season when moving down from #3 to #4 in the order, I believe there is a small, but significant advantage to putting the best hitter on your team in the 4 hole.  Of course, the probability of coming up at all in the first inning drops off significantly after the 4 hole, so you do not want your best hitter any lower than #4 in the order.

Now, lets do the same exercise using 3 hitters in the 1-3 slots who all have OBP's of .400.  The "off-base percentage" for the first 3 batters then becomes 0.6 X 0.6 X 0.6= 21.6%.  The chances of the "Cleanup Hitter" coming up in the first inning with at least 1 runner on base becomes 78.4% or almost 10% better than with the first 3 batters whose OBP's are all .333.

Conclusions:  1.  The best hitter in your lineup should bat cleanup rather than #3.  2.  OBP is the single most important parameter for all of the first 3 batters in your lineup if your goal is to maximize the effectiveness of your best hitter who bats 4'th.


  1. A few problems with your math...

    1) You are discounting double plays by the #2 and #3 hitters.

    2) You are discounting the first 3 hitters scoring before the #4 hitter comes to the plate.

    Both of these scenarios decrease the effectiveness of the #4 slot in the lineup in the first inning because they both decrease the total number of runners on base he will have during the season.

    I realize you are trying to simplify it, but the higher the SLG of the #2 and #3 hitters (still assuming a .333 OBP) decreases the effectiveness of the #4. If a team has 2 STUDS, wouldn't it make sense that the better of the two STUDS hits #3 instead of #4? Additionally, if you have an Aubrey Huff type player (lots of GDPs) who has a highish OBP, wouldn't you also want to hit your best guy #3?

    1. If you have an outlier in GIDP's then, of course you would have to take that into consideration and drop him in the order if it is too much of a drain on collective OBP. Most of the time, GIDP differences are going to be negligible.

      There is no downside to the first 3 batters scoring before the cleanup hitter comes up, but you still want your 3 highest OBP guys hitting 1,2,3 unless, of course one of them is also your best overall power hitter then you have him in the 4-hole.

      In other words, if you leadoff batter homers and the next two guys make outs, it's better than if he singles and the next two batters make outs. On the other hand, if the leadoff hitter homers too often, you probably want him hitting more often with runners on base, so you would move him down in the lineup.

    2. Just looked it up: Morse has the most GIDP's of any Giants hitter this season with 17. Posey is second with 13 and Pabs has 11. Everybody else is in low single digits. For that and other reasons, you would probably not want Morse hitting in the top 3 in the order and probably not cleanup either.

      Ha! Didn't AJ Pierzynski have almost 40 one year? LOL!

    3. Nope, it was 28. Still, talk about an outlier!

  2. 1) Do you factor in stolen base or contact hitting as good attributes for leadoff or #2 batters?
    2) Watching Mike Trout makes me wonder if he is a better leadoff or #2 batter. Your thoughts?

    1. We will address other factors including speed/SB's, "bat control", GIDP, etc in Part III when we look at each individual position in the order.

      To me, Trout is the best hitter on the Angels team. I would bat him 4'th, although with Pujols on the same team, it gives them some choices.