THE BOOK--Playing The Percentages In Baseball

How long does it actually take to warm up a reliever, considering all the “tricks” that teams pull when they desperately need to get their guy in fast?  It seems like in an emergency situation, relievers can be ready in the space of one more batter (if the batter has just reached, a reliever can be ready for the batter after the new one coming up).  Kalk’s FLI assumes two more batters, but as he seems to be mostly talking about sudden high leverage situations, do we really need to assume two batters have batted in the interim and not just one?

I admit that I have not always paid enough attention to how relievers warm up so I could be mistaken.

I ran a clock once.  I figured the reliever needed 30 or 40 pitches to warmup in the bullpen.  I figure you can make 6 pitches per minute, so say 5 or 7 minutes of warmup time.

The game lasts 180 minutes, minus about 25 between inning and between pitcher replacement stoppages of 60 minutes.  That leaves 120 minutes to face about 80 batters, or 1.5 minutes per batter.  After 2 batters, that’s 3 minutes elapsed.  Bring in some wasted time to visit the mound, and 2 batters seems the minimum to me.  You’ll usually find a 3 batter lead is more typical.

But, this was very ad-hoc.

That leaves 120 minutes to face about 80 batters, or 1.5 minutes per batter.

This is on average of course.  Some pitchers slow way down with men on base in any situation.  Surely they could be instructed to do so in an emergency.  With 4 or more pitches in the AB, and 45 seconds per pitch, 2 minutes for other delays (mound visits by the manager to talk to the pitcher, a separate one by the catcher).  I really don’t see why it would always take more than one batter for a team that really wanted to make a quick change.  Obviously, you wouldn’t take such extreme measures unless the leverage skyrocketed all of the sudden, so it wouldn’t necessarily even come into play more than a couple of times a week.

In general you’d want 2 or 3 batters.  But do you really NEED more than 1, especially as you could have warned your ace that he might be needed before the inning started?

Well, if it’s just a one batter look ahead, that’d be a fairly easy LI calculation to make.  You look at all the possible next states, weight them by their frequency, and you get the Future LI (x+1).  Not fairly easy, but doable by hand.

What Josh does is give you x+2, which is more intensive to be sure.

Setting aside if you need 1, 2, or a 3 batter lead, the two LI charts (mine and Josh) gives you pretty much what you want.

For the more basic question you are asking, you can have plenty of 1 or 2 pitch at bats as well, at which point, it’s kinda hard to stretch it.  Maybe 20-30% of the time, all you need is a 1-batter advance.  Maybe.  Two batters just seems more practical.

So why not just use a weighted average of the FLI for 1, 2, and 3 batters hence, guys?  Maybe 25, 50, 25 for the weights.

OTTOMH, from watching umpteen games per season, I would say that 1 batter is a stretch, even in an emergency, unless the pitcher has already warmed up some, NEEDING 3 batters is rare, and 2 is just about right 80% of the time.

I am quite willing to concede 2 batters as it really is not that important to me… just something I was wondering about.  I do however question the effective use of FLI for some of the most important reliever situations.

It seems to me like some of the most important mid-inning baseball pitching changes occur after consecutive batters reach base, very often with 2 outs (as there are more likely to already be runners on base with 2 outs).  In other words, whether justified or not, pitching changes will more often occur after two “worse than average” results than they would after two “average” results.  It seems like looking ahead two average batters is kind of missing the point.

I guess what I am trying to say is that LI itself still seems more useful than FLI for a decision about warming up a reliever.  Were I a manager making these decisions, I would look at the possible LIs for various results of the next couple of ABs that might be the most relevant for my decision (and indeed, as a live-event gambler this is often what I did), rather than looking at a FLI that takes the average LI of all possible results.

Obviously the rules are not intractable, like an IBB perhaps, but, from a sabermetric perspective, you can’t just warm up a reliever indiscriminately or according to the manager’s whim.  There is a price to pay for warming up.

I think that FLI is an excellent way of determining when to warm up a reliever.

Would you ever warm up a reliever with two outs?

The price of warming up varies with the situation.  If there are 2 outs and you are protecting a lead in the 9th, there is virtually no price to pay for warming up your best pitcher, so why not?  For example, you have a 4 run lead and your pitcher has runners on 1 and 2 and 2 outs.  You can warm up your best reliever and then bring him in if the next batter reaches base.  Why not?

The FLI is only important in terms of balancing the price of warming up the reliever.  That (significant price) usually only comes into play in the 7th or 8th innings.