THE BOOK--Playing The Percentages In Baseball

What is “late break?”

MGL/341

I’m going to guess you’re addressing that question to me regarding my Bedard article.  If it wasn’t addressed to me, I apologize.

“Late break” is the deflection of the pitch due to both spin and gravity in the last quarter-second before it crosses the plate.

The idea comes from Tango as outlined here:
http://www.insidethebook.com/ee/index.php/site/comments/classifying_pitches1/#15

What I mean is that, “Is there early break as opposed to late break or is it simply that some pitches have more break than others due to angle and speed of spin?”

Pitches, except for knuckleballs, have very close to constant acceleration.

When I heard the term “late break” used, I always assumed that the physical reality was that late break was just some constant percentage of total break such that pitches with a lot of break would have more late break as well as more early break and that hitters simply perceived them as having late break because the deflection in the last half of the trajectory is always much bigger than deflection in the first half of the trajectory.  While that makes physics sense, it doesn’t correlate very well with comments by hitters.

However, Tango introduced a novel idea, to me anyway, that the lateness of the break should be measured not in terms of distance traveled but in terms of time.  In terms of deflection over a fixed time period at the end of the trajectory, harder thrown breaking pitches, e.g., 90-mph sliders, might have almost as much break as slower pitches, like a 70-mph curveball that drops much farther during its whole trajectory than does the slider.

Looking at spin + gravity deflection over the last 0.25 seconds traveled is the closest thing I’ve found to what I believe hitters perceive as the break on a pitch.

I’d like to insert this article into the ‘late break’ mix: 
http://www.livescience.com/health/060420_baseball_perception.html

“In the last few feet before the plate, the ball reaches an angular velocity that exceeds the ability of the eye to track the ball,” Fuld told LiveScience. “The best hitters can track the ball to within 5 or 6 feet of the plate.”

Sometimes players will abandon eye contact mid-way through the pitch and move their line of sight to where they anticipate the ball will cross the plate. Batters often “take” the first couple pitches of an “at bat” in this manner to try and calibrate the movement and speed of a pitcher’s offerings.

and

But a hitter is at the mercy of what the pitch does in those last few feet. That’s when their eyes have left the ball and a nasty 12-to-6 curveball--a pitch named after the face of a clock and which drops top to bottom--can make even the best hitters swing out of their shoes. The pitch looks innocent enough, but during the instant the hitter is blind to the ball, a good curveball will have dropped a foot or more, and the batter will likely swing over the pitch.

The FSN show Sports Science covered this as well, saying that Normal human anticipatory reaction time is 0.19 sec. and:

Major league baseball hitters never see the bat contacting the ball. A 95-mph fastball becomes invisible 25 ft from home plate. The closing velocity of a pitch is so fast that you literally cannot see it when it reaches you, Brenkus says. When you think you see it, it’s really just your brain projecting where it believes the ball to be.

Mike checks in with Johan Santana.

I’d like to Mike Fast and Greg Rybarcyzk speaking to each other.  Since Greg had the BIP data on Torii Hunter, the Twins must be one of the teams where he has extensive data.

A merging of Mike’s Twins data with Greg’s data would be nirvana.

***

Mike, somewhere else, you asked about LWTS values by count.  I’ll get that to you in short order.

Thanks, Tom.

The link to the Santana article is here:
http://mvn.com/mlb-stats/2008/01/09/tales-of-the-changeup-an-analysis-of-johan-santana/

Mike, thanks for putting the link.

***

If you go here:
http://www.insidethebook.com/ee/index.php/site/comments/hitting_by_count/

You can take the “pass through” counts and convert them into linear weights.  Just remember that to convert wOBA to runs, you just divide by 1.15.  The league average in that sample is .332.  So, you end up with the following:

Through Count LWTS
Through 3-0 0.207
Through 3-1 0.137
Through 2-0 0.097
Through 3-2 0.062
Through 2-1 0.035
Through 1-0 0.034

Through 0-0 0.000
Through 1-1 -0.016

Through 2-2 -0.037
Through 0-1 -0.043
Through 1-2 -0.083
Through 0-2 -0.104

This means that at count 3-0, your linear weights is +.207 runs.  Of course, each pitcher (and hitter) will have his own LWTS.  For Santana, it’ll be a bit lower.  For a hitter, it should max out at .32 runs or so.  After all, why let him tee off on you, if you can just walk him at that count.

Anyway, if you are at 1-0, a called ball puts you at 2-0, and that’s worth .063 runs.  A strike puts you at 1-1, or a .050 run change the other way.

If you look at the first chart of that link, the “at 1-0 count”, meaning the PA ended then and there, the wOBA is .388, which is +.015 runs above the “pass through” of .371 at that count.

To summarize for this count:
+.063 ball
+.015 in play
-.050 strike

If you figure the frequency of these 3, you should end up with a number close to 0.

Figuring the in play happens about 20%, the ball happens 35% and the strike 45% (guesses on my part), that gives us a weighted average of .003 (should be zero).

Anyway, that’s the blueprint!  Now, you and Walsh can wow us some more…

UPDATE: Jan 29, 2008.  The numbers in this post are incorrect.  Corrected numbers are lower down in post 17:
http://www.insidethebook.com/ee/index.php/site/comments/pitch_analysis_of_eric_bedard/#17

==================================
ORIGINAL POST:

Using those numbers, here’s what I get:
Count LWTS ball strike inPlay
3-0 0.243 0.087 -0.070 0.113
3-1 0.174 0.156 -0.076 0.064
2-0 0.133 0.110 -0.062 -0.033
3-2 0.098 0.232 -0.398 0.000
2-1 0.071 0.103 -0.071 0.003
1-0 0.070 0.063 -0.050 0.015

0-0 0.037 0.034 -0.043 0.043
1-1 0.021 0.050 -0.067 0.042
2-2 0.000 0.098 -0.300 -0.066
0-1 -0.006 0.027 -0.062 0.055

1-2 -0.046 0.046 -0.254 -0.043
0-2 -0.068 0.022 -0.232 -0.030

I’m fascinated by the numbers above.  Compare the 3-0 and the 3-1 counts.

If you get a called strike, the run value of that strike is the same.  That is, going from 3-0 to a 3-1 count, or from a 3-1 to a 3-2 count is the same marginal change.

But, a ball count at 3-0 is alot less than at 3-1.  And the reason is that at 3-0 you are already pretty close to a walk, and therefore, getting that 4th ball isn’t as valuable as getting one when you are at 3-1 (and a walk is not a given as much).

To counteract that, getting a ball in play with a 3-0 count is enormous, while getting a ball in play on a 3-1 count is still very good, but just not as good.

What you would really like to do is come up with a Linear Weights by count, for each batter and for each pitcher.  That will tell you A GREAT DEAL about how a batter does at each count, compared to an average player.

Tango,

What do you mean that each pitcher (and hitter) should have his own linear weights?  Do you mean that good pitchers, like Johan Santana, suppress run scoring enough that we need to recalculate the Lwts values of the offensive events in a 3.5-run-per-game environment (or whatever) in order to accurately apply them to Santana?

It seems like doing that on a per-pitcher and per-hitter basis would be a lot of work, and I’m wondering if the payoff is worth it compared to using league-average linear weights for everyone?

Actually, my Markov calculator can give you LWTS by quality of pitcher:
http://www.tangotiger.net/markov.html

I’m suggesting also doing it on a per-count basis.  I think you will see a difference, because some hitters have certain strengths that can and cannot be leveraged by the specific counts.  What should a power hitter do on a 3-0 count compared to a slap hitter?  You can only figure that out if you know each player’s overall value.

In short, each player is worth an average of “0”, he’s his own universe.

And no, it’s not that hard.

Instead of “hard”, I probably should have said that the implementation was “complex”, or “straightforward but nontrivial”, as my freshman physics prof would say.

I have done the linear weights on a per-count basis.  I can see the impact there.  There’s a 0.3 run/pitch difference between the best and worst counts and a 0.2 run/pitch difference between the best four and worst four counts--that’s pretty substantial.

The difference between the best third and worst third of hitters/pitchers is what?  I would guess less than 0.05 runs/pitch, maybe closer to 0.02.  There are also park/weather effects, that are maybe on the 0.01 runs/pitch level.  There’s also the question of regressing all those values properly to the mean.

It seemed to me that it was safe to ignore everything but the effect of the ball-strike count as a first pass.  IMO, the complexity of introducing the other calculations into my spreadsheet, both in terms of a huge impact to computing run-time and file size as well as the possibility of making an error in the calculations, wasn’t worth the payoff for anything but the count.

There are 12 ball-strike counts, but there are on the order of 1000 hitters and pitchers, and it’s probably not wise to assume that their unregressed 2007 performance reflects their true talent level, so multiple seasons of data would need to be considered.  Am I missing something that would simplify the task of computing a hitter/pitcher-specific run environment?

Remember that I’m setting every hitter and every pitcher as his own universe (everyone at a 0-0 counts has a LWTS of zero).  To that end, we don’t care about park factors!  Isn’t it great?

And, we’ve got two thousand pitches per hitter and three thousand per pitcher, which is fairly substantial.  The bigger worry about the pitch-count LWTS is with the men on base.  Clearly, if 1B is open, the batter and pitcher will approach the PA differently.  Same with man on 3B and less than 2 outs.

Skyking did something very similar with Adam Dunn on his blog, which I linked to from here somewhere.  I’ll look for it in a minute…

Here you go:
http://www.insidethebook.com/ee/index.php/site/comments/hitting_by_count/#14

Post 14.

Tango, I wanted to say thanks for your help on this.  I am working on this linear weights stuff behind the scenes even if it’s not showing up in my published articles yet.  It is very helpful to look at things in terms of run values.

The data in post 9 is incorrect.  Here’s the corrected one:

Count LWTS ball strike inPlay
3-0 0.207 0.123 -0.070 0.113
3-1 0.137 0.193 -0.076 0.064
2-0 0.097 0.110 -0.062 -0.033

3-2 0.062 0.268 -0.362 0.000
2-1 0.035 0.103 -0.071 0.003
1-0 0.034 0.063 -0.050 0.015

0-0 0.000 0.034 -0.043 0.043
1-1 -0.016 0.050 -0.067 0.042

2-2 -0.037 0.098 -0.263 -0.066
0-1 -0.043 0.027 -0.062 0.055

1-2 -0.083 0.046 -0.217 -0.043
0-2 -0.104 0.022 -0.196 -0.030

It was a sloppy Excel issue.  In Excel, when you sort, the formulas become all messed up.  I could tell it’s a problem because the LWTS value through the 0-0 must be zero, and it wasn’t.

Compare the 0-1 and 2-2 counts.  Both have the same run value (-.04 runs), or basically, an average hitter in these counts hits like Adam Everett at an 0-0 count.  Now you know how he feels.

Anyway, when a pitched ball is contacted, the run value of that pitch is much higher on an 0-1 count than it is on a 2-2 count.  That is, either the pitcher is giving up easier pitches on 0-1 when contacted, or batters approach that count much differently.

The relative value of a called ball to a strike is the same in both counts, except it’s much more magnified with a 2-2 count.  In effect, we can create “Leverage Index” for the counts by dividing the run value of ball and strike by the ones at the 0-0 count:

Count LWTS ball strike inPlay Liball Listrike
3-0 0.207 0.123 -0.070 0.113 3.6 1.6
3-1 0.137 0.193 -0.076 0.064 5.7 1.8
2-0 0.097 0.110 -0.062 -0.033 3.3 1.4

3-2 0.062 0.268 -0.362 0.000 7.9 8.5
2-1 0.035 0.103 -0.071 0.003 3.0 1.7
1-0 0.034 0.063 -0.050 0.015 1.8 1.2

0-0 0.000 0.034 -0.043 0.043 1.0 1.0
1-1 -0.016 0.050 -0.067 0.042 1.5 1.6

2-2 -0.037 0.098 -0.263 -0.066 2.9 6.2
0-1 -0.043 0.027 -0.062 0.055 0.8 1.4

1-2 -0.083 0.046 -0.217 -0.043 1.4 5.1
0-2 -0.104 0.022 -0.196 -0.030 0.6 4.6

At a 2-2 count, a called ball has three times more impact than at an 0-0 count, while a strike has 6 times the impact.

But at 0-1, it’s fairly close to 0-0.

Overall however, you get the same run value.

Tango, I think your numbers in #17 are still off.  I get the same overall values for each count as you do, but I disagree with some of the specific values, particularly for balls in play.  Some of your values are illogical, so I’m pretty sure you have an error.  For example, it doesn’t make sense that hitters would do better on balls in play at 0-1 as compared to 0-0 or on 2-1 as compared 2-0.

Here are the values I got, using 2007 AL data:
Count Total Ball Strike InPlay
3-0 0.205 0.324 0.148 0.277
3-1 0.148 0.324 0.060 0.215
2-0 0.101 0.205 0.038 0.070
3-2 0.060 0.324 -0.305 0.060
1-0 0.039 0.101 -0.013 0.047
2-1 0.038 0.148 -0.039 0.038
0-0 0.000 0.039 -0.044 0.041
1-1 -0.013 0.038 -0.079 0.022
2-2 -0.039 0.060 -0.305 -0.102
0-1 -0.044 -0.013 -0.108 0.012
1-2 -0.079 -0.039 -0.305 -0.115
0-2 -0.108 -0.079 -0.305 -0.137

Hmmm… your numbers are definitely smoother.  I’ll check it tomorrow.

Ok, I see where I went wrong (really bad mistake) on BIP.  However, I see where you went wrong too.  A ball thrown on a 3-0 count cannot be worth .324 runs.  The run value at 3-0 is already .205, as per your numbers.  Therefore, a ball in that case will bring it up to 4-0 (.324 runs), and therefore you need to take the difference, or +.119 runs.

Tango, I can see that now that you point it out.  I made a similar mistake with the strikeouts, which should be -.305 less whatever the run value of the particular two-strike count is.

When I fix my mistakes from #19, here are the run values:

Count Total Ball Strike InPlay
3-0 0.205 0.118 0.148 0.277
3-1 0.148 0.175 0.060 0.215
2-0 0.101 0.205 0.038 0.070
3-2 0.060 0.263 -0.365 0.060
1-0 0.039 0.101 -0.013 0.047
2-1 0.038 0.148 -0.039 0.038
0-0 0.000 0.039 -0.044 0.041
1-1 -0.013 0.038 -0.079 0.022
2-2 -0.039 0.060 -0.266 -0.102
0-1 -0.044 -0.013 -0.108 0.012
1-2 -0.079 -0.039 -0.226 -0.115
0-2 -0.108 -0.079 -0.197 -0.137

Mike - Maybe I am not understanding your table correctly.  Why would a strike ever have a positive run value (counts 3-1,3-0,2-0) or a ball ever have a negative run value (counts 0-1,1-2,0-2)?

Peter, you are correct.  I was not subtracting out the value of the current state for balls or strikes on any of those counts.

Try these on for size:
Count Total Ball Strike InPlay
3-0 0.205 0.118 -0.057 0.277
3-1 0.148 0.175 -0.088 0.215
2-0 0.101 0.104 -0.063 0.070
3-2 0.060 0.263 -0.365 0.060
1-0 0.039 0.062 -0.051 0.047
2-1 0.038 0.110 -0.077 0.038
0-0 0.000 0.039 -0.044 0.041
1-1 -0.013 0.050 -0.066 0.022
2-2 -0.039 0.100 -0.266 -0.102
0-1 -0.044 0.032 -0.064 0.012
1-2 -0.079 0.040 -0.226 -0.115
0-2 -0.108 0.029 -0.197 -0.137

I have some numbers from 2004-2006.  Just so we are comparing apples to apples are you using all events, all events less bunts, all non-pitcher events, all non-pitcher events minus bunts or some other subset?

Peter, I am using all events except baserunning (stolen bases, caught stealing, wild pitches, balks, etc.).  The numbers I listed above are for the 2007 AL.  I have also generated a set of linear weights by count for the 2007 NL, but I didn’t list them.

My numbers above in #25 are wrong.  You wouldn’t think this would be that hard to get right.  I inadverently left out two-strike foul balls, which I need to go calculate, and I didn’t adjust the in-play numbers for the expected value of the count.  Sigh.

I have away from my computer on other work for the last couple of days but I will try to get you my numbers later today.  Queries are all written (15 of them) but I have to run them again to collect the data and that takes some time since they are pretty complex but I’ll try to get it done today.

These are the values I got for 2004-2006 all MLB.

Count Total
3-0___0.201
3-1___0.135
2-0___0.092
3-2___0.015
1-0___0.032
2-1___0.034
0-0___0.000
1-1__-0.014
2-2__-0.070
0-1__-0.040
1-2__-0.104
0-2__-0.123

Peter, did you include foul balls in your two-strike numbers?  It looks to me like you did for 3-2 but not for 0-2, 1-2, or 2-2.

Here are the numbers I get when I adjust for two-strike foul balls (and fix some stupid spreadsheet stuff regarding how I had split the formulas into two pieces).

Count Total Ball Strike InPlay
3-0 0.201 0.118 -0.055 0.071
3-1 0.146 0.173 -0.127 0.065
2-0 0.100 0.101 -0.063 -0.028
1-0 0.038 0.062 -0.051 0.007
2-1 0.037 0.109 -0.066 0.000
3-2 0.019 0.300 -0.319 0.040
0-0 0.000 0.038 -0.044 0.042
1-1 -0.012 0.049 -0.051 0.041
2-2 -0.029 0.048 -0.271 -0.071
0-1 -0.044 0.032 -0.044 0.056
1-2 -0.063 0.034 -0.237 -0.054
0-2 -0.088 0.025 -0.212 -0.052

The values for ball, strike, and in play are relative to the overall run value for that count.

Your 3-2 LWTS looks mighty low.

Can you post your full data in a spreadsheet?  Something like this:

AtCount,ball,strike,2strikeFoul,inplay,out,1b,2b,3b,hr,roe

where,
ball+strike+2strikeFoul+inplay = 1.00
and represents the frequency of the pitch thrown

and
out+1b+2b+3b+hr+roe = 1.00
and represents the frequency of a ball put in play

And if you can, include “PA” in each row, that shows the number of times that count was entered.  It’s not necessary, but it’s nice to have.

Tango, I will work on getting the data formatted that way so I can share the spreadsheet.

However, I should note that my numbers are lwts/pitch and not lwts/PA.  Lwts/PA ignores 2-strike fouls, but I want to consider them.  At least I think that’s the right thing to do if I want to evaluate the effectiveness of a pitch.  Foul balls are pitches with zero (or near zero) value, but I don’t think it makes sense to ignore them.

For the 3-2 count, the breakdown is roughly 22% balls, 16% strikes, 34% in play, and 28% foul balls.

Perhaps rather than posting a spreadsheet, I’ll just say that the source of my numbers was this page at Baseball Reference:
http://www.baseball-reference.com/pi/bsplit.cgi?lg=AL&team=TOT&year=2007

Then I added the following number of two-strike foul balls:
0-2: 3531
1-2: 5947
2-2: 5783
3-2: 4076
Those numbers came from the MLB Gameday data and are only approximate (within 100 or so, I’d say).

For my table I parsed the Pitch Sequence data in Retrosheet.  I removed all extraneous data (throws to a base, those little dots, anything that wasn’t a pitch to a batter). Then I looked at at each pitch in order and the count that resulted after each pitch.  I summed the RVA for the at bat that contained a particular count. So after the first pitch there were 269434 at bats that started off 0-1 and those at bats had a total RVA of -10681 runs.  There were 237270 at bats that started off 10 and those at bats resulted in a RVA of +7681 runs.  Dividing the runs by the at bats gives the average linear weight for that count.  I took the count out 8 pitches.  If a batter had a 1-2 count after pitch 3 and he hit foul balls on pitches 4 through 7 I counted his final RVA all 5 times.  I ignored the few 3-2 and 2-2 counts that were left after the 8 pitches.