How often did Thor go to that grip in 2015, and what factors influenced his decision to do so? (Image source) 
Since we're already well into the offseason, I'm sure you've already seen a lot of analysis looking back at the 2015 Mets, but my goal here has always been to try and bring you something you won't see elsewhere, so let's dig into some pitch sequencing data. I’m looking at Noah Syndergaard today, and I’ll work my way through rotation over the next few weeks. There’s a lot of information about a pitcher that can be obtained by looking at pitch sequences, and I won’t be reviewing every detail from the tables and graphs posted below, so you might notice something I haven’t, or think of a question I haven’t addressed, in which case share it with me in the comments or on twitter. If you want to get your own PitchFx data, you can download it from Baseball Heat Maps.
It took a little
longer than some people predicted,
but Noah Syndergaard made an amazing major league debut in 2015: 166 K: 31 BB
in 150 IP with an 88 ERA/84 FIP/75 xFIP. His 97.1 MPH fastball was the
fastest of any pitcher who threw at least 150 innings in 2015, and his
curveball whiff/swing rate was 2 standard deviations above league average, per Brooks Baseball. As if that wasn't
nasty enough, he also threw a high 80's changeup that produced whiff/swing and
GB/BIP rates more than a standard deviation above league average, and started
mixing in a nasty slider at the end of the season. Brooks can give you tons of
information about Syndergaard's pitch usage and outcomes from the 2015 season,
but I haven't seen pitchsequencing data available anywhere yet. Also, while
I've seen some great discussions on this topic around the web (The Hardball Times is a great place to
start on the subject), most have had a leaguewide focus, and I'm interested in
looking at the individual level here. Below I show how and when Syndergaard
mixed his pitches, and then investigate how well they played off of each other.
Syndergaard threw
2,380 pitches to 603 batters in 2015 with two intentional walks issued, which
leaves us with 1,769 pitch sequences worth investigating. The first graph below
is the distribution of those sequences with a minimum count of 75 (I combined
sinker's and fourseamer’s into one FB category for this graph), and the fill
breakdown is by the ballstrike count when the second pitch was thrown. Below
that I've included a table of the relative frequency of each sequence by count,
which also includes the 'FBSL' and 'SLFB' sequences. If all sequence types
were included in that table, each row would add up to 100%.
Aside from being pretty,
the first graph gives us some clues about pitch usage tendencies without overloading
us with numbers. For example, the CUCU sequence to LHB's has no purple hues,
which indicates that he never doubled up on curveballs to lefties if the count
went to 3 balls. The same column in the RHB table suggests that he might double
up on the curveball early or when ahead in the count, but was much less likely
to do so later in the count. As expected, curveballs are more frequent vs.
RHB’s, and changeups more frequent against LHB’s. The table below it might
overwhelm with numbers at first, but the numbers give us an even better idea of
Syndergaard's tendencies. First, the rightmost column with the smaller numbers
represents the count for each row so you can get an idea of sample size. By
looking at the CHFB column you can see that Syndergaard was more likely to
throw his fastball after a changeup if that changeup put him behind in the
count. Also, as expected from what we already knew, he's more likely to throw
consecutive curveballs early in the count, and the fastball in any count. While
the above charts give a good visual representation of how Syndergaard mixed his
pitches in 2015, it doesn't consider how the change in count influenced
Syndergaard's decision. Say Syndergaard just got ahead 12 with a fastball to a
lefty, how likely was he to throw a changeup with his next pitch? That's what
the tables below will tell you. We could take it further too, breaking it down
by times through the order, runners on base, whether or not it was a close
game, whether or not the Mets were winning... but the samples start getting
small quickly, and I don't want all those tables here anyway.
Naturally, if the
previous pitch was a ball, the count can't possibly be 01 or 02 (same for
previous pitch strikes and 0 strike counts). From the table above, you can see
that Syndergaard was more likely to throw a changeup to a lefty after a
fastball for a ball than after a fastball for a strike in nearly all counts.
Also, if he just got ahead 02 against a RHB with a fourseamer, it was a coin
flip as to whether he'd double up on the fastball or use the curveball.
From the curveball
table, you can see that Syndergaard often doubled up on the curveball after
falling behind 10 against righties, or getting ahead 02 against lefties.
One could keep
inspecting the above usage tables for trends and outliers in the data, but
right now we're only looking at one dimension of the pitch, its type. A
convenient metric for considering multiple dimensions of the pitch (velocity
and location) is effective velocity. Effective velocity (EV) is Perry Husband's
concept that the more jammed a batter is, the less reaction time he has to get
good wood on it, so the pitch is effectively faster than its radar gun value.
Alternatively, the farther low and outside the pitch is, the longer a batter
has to wait on it, and so the pitch is effectively slower. As a result, there
is an imaginary line from the batters feet to shoulder high and outside where
the effective velocity of a pitch is equal to its actual velocity, and for
every 6 inches away from that line on the horizontal axis, the effective
velocity gains or loses 2.75 MPH. Pitchers are already looking to disrupt a
batters timing by changing speeds and location pitchtopitch, effective
velocity just gives them a blueprint for maximizing that timing disruption between pitches
in a PA. (For more on the subject, check out this great SBNation
piece written by Jason Turbow for a full background and better understanding
than you’ll get from my 3 sentences, or this Dan Weigel piece from Beyond
the Boxscore that tracks EV changes throughout a few PA's with Trevor Bauer on
the mound).
Considering the speed
variation in his impressive repertoire, Syndergaard was already near the top of
the league in average change in velocity, but he's even better by average
change in EV. I haven't seen a standard approach to calculating EV, but my
numbers match up pretty well with this site, which
has posted deltaEV data on all pitchers who threw at least 150 IP over the
past 3 seasons (and takes a similar approach as Weigel, except with Collin
McHugh as the main subject). By radar gun velocity, Syndergaard averaged a change of ~7 MPH
from pitchtopitch, but by EV that change increases to ~11.3 MPH. Intentional
or not, Thor is increasing his average delta EV with his breaking ball and
changeup usage, as you can see from these Brooks Zone Profiles.
Zone Profiles of Thor's soft stuff, catchers POV (from Brooks) 
Soft stuff is mostly
down and outside, and it kind of looks like the strike zone is split in half
diagonally across the strike zone. His fastball usage is more scattered against
righties (as it should be for a pitch thrown so often), but he rarely came
inside with the heat against lefties, which suggests he wasn't using the EV
concept to influence his pitch decisions. Still, he's probably going to have to
start coming inside more against lefties in the future, even if just as a
'showme' pitch, because otherwise they'll be sitting on the outside corner.
And if he does, it should only benefit his average EV gap.
Let's
wrap this up by comparing the results of the second pitch of a sequence given the first. Ideally we'd use linear weights/100 pitches for
comparison, but the samples are too small for that here, so instead we’ll look
at the swinging strike rate, batted ball profile, and wOBABIP (wOBA on balls in
play). The graphs below are grouped by the first pitch of the sequence, and is
looking at swinging strike rate on a per pitch (not per swing) basis. For a
baseline, here are Thor's overall swinging strike rates by pitch type:
Pitch
Type

Swinging
Strike rate

Fourseamer

10.9

Sinker

8.9

Changeup

16.9

Slider

24.5

Curveball

19.2

The
pitch type above each graph represents the first pitch thrown in the sequence. From
the results above, you can see that the swinging strike rate on Thor's
fourseamer increases after a changeup or breaking ball and that the curveball
is least likely to get a swinging strike when following a curveball.
Interestingly, the changeup's swinging strike rate is best when Thor doubled up
on the pitch, and the curveball has a higher whiff rate when thrown after a
sinker than after a fourseamer. Here is his batted ball profile by pitch type
for a baseline comparison for the following graphs:
Pitch
Type

BIP%

GB%

FB%

LD%

PU%

Fourseamer

16.5

6.7

4.5

4.4

0.9

Sinker

21

11.3

4.9

3.9

0.9

Changeup

16.3

9.6

3.6

2.3

0.8

Slider

10.5

5.8

4.7

0

0

Curveball

11.1

4.1

2.1

2.9

2.1

The number above each set of bars represents the count for that sequence. Here
you can see that Thor's sinker had a higher groundball rate when following a
soft pitch than when following a hard pitch. The highest fly ball rate came on
fastballs that followed a changeup, and it's not even close. The highest popup
rate came on curveballs following a sinker, and that sequence also had a higher
than average swinging strike rate. Lastly, here is Thor’s wOBABIP by pitch type
for a baseline comparison for the following graphs:
Pitch
Type

wOBABIP

Fourseamer

.383

Sinker

.358

Changeup

.301

Slider

.431

Curveball

.379

The
numbers represent the BIP count, and considering the small sample sizes, I
almost didn’t post this graph. But for what it’s worth, these final graphs
confirm that Thor’s sinker and curveball complemented each other extremely well
last year.
This
is just some of the information that one can find while digging through pitch
sequence data, so I think it’s easy to understand why THT is taking their time
to define
the pitchsequencing question before looking for an ‘answer’. It’s only one
season of data on Thor, so we have no way of knowing how reproducible these
results will be for him, but we still learned a few new things about 2015 Thor.
We can see exactly what his tendencies were with the ‘Probability of Next
Pitch’ tables, and while a few trends stick out, it appears like he keeps a
pretty consistent approach regardless of count. We saw that Syndergaard had one
of the largest EV gaps from pitchtopitch, and that he could increase the gap
by coming inside more often (especially to lefties). Finally, the last three
graphs suggest that his curveball and sinker complemented each other best last season,
which is interesting since it's often suggested that fourseamer’s
complement the curveball better  although, again, the sample sizes got pretty small.
"Women in the History of Variable Star Astronomy" by Dorrit Hoffleit, 1993 PDF online https://t.co/ipfM3Sygv2 pic.twitter.com/FmIBSQl7LV
— History of Astronomy (@HistAstro) January 7, 2016
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