Extended Pitch Count Estimator (August 4, 2003)
This will be my last full-blown article for a long while. I would have preferred to do more work on this, but, what the heck. Every now and then, it's nice to be the one to leave an honest mess behind for someone else to clean up.
--posted by TangoTiger at 02:08 PM EDT
Posted 5:16 p.m.,
August 5, 2003
(#1) -
bob mong
You gave these formulas (formulae?):
Pitches per BIP = 2.5 x [(1 - BIP rate) ^ 0.08] + 1
Pitches per BB = 1.5 x [(1 - BIP rate) ^ 0.10] + 4
Pitches per K = 1.9 x [(1 - BIP rate) ^ 0.07] + 3
A couple of questions/comments:
First, where did the 2.5, 1.5, and 1.9 #s come from?
Second, where did the 0.08, 0.10, and 0.07 #s come from?
Third, you are using the assumption that a BIP rate of 100% implies 1 pitch per PA - though I admit that this kind of makes intuitive sense, it still seems a big step. What is your justification for this assumption?
Posted 9:10 a.m.,
August 6, 2003
(#2) -
tangotiger
Bob, let's take it backwards. If let's say you construct a model where a pitcher, with every pitch, will do the following to a batter:
make contact for a fair ball: 90% of the time
others (fouls, swing and miss, or called ball/strike): 10%
I think it's easy to see that at some point, that 10% will eventually lead to a walk or a K. So, what value for "others" would I have to set to guarantee that the PA will end with a fair ball? Mathematically, I have no choice but to set "others" to 0%.
Now, this is not exactly how baseball works. Every count offers the pitcher/batter matchup different expectations for the batter to get a fair ball. And in fact, every individual pitcher/batter/count matchup has their own rates.
But, to the extent that I want the BIP rate to be 100%, I have to put the pitches/PA at 1. We also know that the league average is around 3.7 to 3.8 pitches when the BIP rate is around 73 to 76%. So, we have that fixed point. We also have the two sample points provided by Randy Johnson (57%, close to 4 pitches/PA) and Brad Radke (81% and close to 3.5 pitches/PA).
So, given those 4 points (and some other behind-the-scenes work that I'm doing), those equations come out. It maxes out to 3.5 pitches / BIP, 5.5 / BB and 4.9 / K, though I suspect that a pitcher with very high BB and K would probably throw more pitches than I'm showing here (will go to 3-2 more than someone else). It may be that I also need a function for BB that is based on the BIP rate AND the K rate.
In any case, I think what we have here is a reasonable basis to further the research on estimating pitch counts.
Posted 11:57 a.m.,
August 6, 2003
(#3) -
bob mong(e-mail)
(homepage)
That kinda makes sense...but I am still not buying it.
Here's why:
Assumption 1a: There are no swinging strikeouts. From this it must follow that a batter can make contact with every strike.
Assumption 1b: There are no called strikeouts. From this it must follow that there is a big enough incentive for the batter to avoid strikeouts that he will swing at every strike when he has two strikes on him already.
Assumption 2: There are no walks. From this it must follow that the pitcher can throw a strike every time, if he so chooses. And furthermore, there must be a big enough incentive for the pitcher to avoid walks that he WILL choose to throw a strike every time there are three balls.
Certain things follow from these assumptions:
From (1a) the batter knows that under no circumstances can he be struck out. Even if he has two strikes on him, he can always make contact with every possible third strike. So why not take/foul-off a few pitches, wait for the one that is the fattest?
From (2) the pitcher knows that under no circumstances will he give up a walk. Even if the count has three balls, he can always throw a strike. So why now throw a couple of bad pitches early in the count, hoping to get the batter to chase them?
Here is an example of where this situation could exist:
Imagine a slow-pitch softball league of very high quality (where the relevant rules (4-ball walks, 3-ball Ks, etc.) are the same as MLB baseball).
In slow-pitch softball, nobody strikes out, for obvious reasons (those given in (1a) and (1b) above: it is so damn easy to hit a strike and so shameful to strikeout that nobody ever does).
Since we are assuming a very high quality of play, let's also assume that the pitchers are good enough that there are no walks (or so close to zero that it is basically the same).
So we have a league where nobody strikes out and nobody walks - in this league, will the batters always swing at, and put in play, the first pitch they see?
I doubt it - I think that there will be a non-trivial number of foul balls, plus I think batters will be willing to take a pitch or two in order to get the fattest pitch possible, even if they have to go to two-strikes to do so. And the pitcher may be willing to try to get the batter to chase a few bad pitchers, knowing that he has four balls to work with, and that he can always come back with a strike and depend on his defense.
...
I don't really think this affects your model at all (since your model isn't really concerned with that extreme end-point), but I think that it does break down at that end point.
Posted 1:05 p.m.,
August 6, 2003
(#4) -
tangotiger
Bob, what you are saying is that the penalty for the walk is so high that a pitcher would rather finally give a fat one down the middle than to give up a walk.
That a pitcher/batter will work the plate to the point where the pitcher can throw at the corners and risk a ball, or a batter will wait for a fat one and risk a strike.
But, don't forget there are also swinging strikes. If the pitcher has the batter 0-2, it's very possible therefore that he can swing and miss, and thus the strikeout.
What you are saying is that the batter has the chance of swinging and missing on 0-0 and 0-1, but that he cannot at 0-2. Is that because the price of the strikeout is so high that he just absolutely has to get the ball on the bat, rather than take a big cut and maybe get a solid hit on it?
In the "real-world", there are a few pitchers that I estimate had 95% BIP rate (back to the early 1900s). From that standpoint, the pitches / BIP checks in at 3.0. Even at 99% BIP rate, I'm estimating 2.7 pitches / BIP.
So, from 99% BIP to 100%, I'm going from 2.7 to 1.0. I really have no reason to make it go to 1.5 or 2.2 or anything else.
I agree, it's an interesting scenario, but one which we probably don't need to worry about, as you are also saying.
(There were 2 pitchers in the beginnings of baseball with no walks and Ks and at least 150 PA, but they used different rules for balls and strikes.)