Weighted Plate Discipline Index (wPDI): A Refresher

Introduction

Last year, I introduced a new (yet simple) pitcher metric. Weighted Plate Discipline Index (wPDI) arises from the core ingredients of plate discipline from the point of view of the pitcher – control, deception, and contact.

wPDI looks at the following basic binary events:

  • Was the ball thrown in the strike zone?
  • Was the ball swung on?
  • Did the batter make contact with the ball?

That’s all.

Weighted Plate Discipline Index (wPDI) does not look at generated bat speed, exit velocity, pitch speed, or quality of contact, etc. wPDI doesn’t even focus on walk rates or strikeout rates, or any other plate appearance result. wPDI focuses solely on the pure components of a pitch. Is the pitch in the zone? Is the batter swinging at pitches in the zone? Is the batter swinging at pitches outside of the zone? Is the hitter contacting the pitch?

That’s all.

In this series of articles, I will be refining and expanding upon what I had started last year. I will look at wPDI’s effectiveness and predictability. Along the way, I shall highlight both pitchers and hitters who catch our eye based on great (and poor) plate discipline performance.

Some pitchers excel due to their raw swing-and-miss ability. Some pitchers succeed because of their impeccable control. One especially useful biproduct of the Weighted Plate Discipline Index is that it allows us to delve into the specific components of what pitchers do well – yet, at the same time, wPDI combines plate discipline metrics into one all-encompassing leaderboard metric.

Let’s first quickly refresh our memory as to how wPDI works.

The Five Plate Discipline Metrics

First, let’s review some FanGraphs terminology. For every major league player, a number of plate discipline metrics are available. Full definitions can be found here in our library, but let’s talk about the ones which power wPDI.

There are five key quantities which will help us enumerate the plate discipline outcomes:

  • Zone%
  • Z-Swing%
  • O-Swing%
  • Z-Contact%
  • O-Contact%

The 1st metric – Zone% – answers the question of is the pitcher throwing strikes?

Zone% = Pitches in the strike zone / Total pitches

The higher the value, the more strikes a pitcher is throwing. Generally speaking, pitchers who have a high zone% have more pitch control. In 2019, the top qualified starting pitchers for Zone% were:

Zone% – 2019 Leaderboard – Starting Pitchers
Rank Name Zone%
1 Lucas Giolito 47.2%
2 Reynaldo Lopez 46.8%
3 German Marquez 46.6%
4 Walker Buehler 46.5%
5 Mike Fiers 46.0%
6 Zack Wheeler 46.0%
7 Mike Leake 45.8%
8 Max Scherzer 45.6%
9 Rick Porcello 45.5%
10 Joe Musgrove 45.5%
11 Justin Verlander 45.2%
12 Gerrit Cole 45.2%
13 Brett Anderson 45.1%
14 Charlie Morton 45.1%
15 Kyle Hendricks 44.7%
All qualified starting pitchers for 2019.

Most of these pitchers, you will instantly recognize as pitching aces or near-aces. Some others, like Kyle Hendricks, are known for their tight control.

The 2nd and 3rd metrics – Z-Swing% and O-Swing% – answer the question of is the pitcher generating swings? wPDI goes a bit further than traditional swinging strike metrics – in that it looks at swings both in and out of the zone independently. Typically, you will only see swinging strike rates disseminated in total. However, the degree of a pitcher’s deception can be better characterized by observing whether the batter is swinging at would-be strikes or would-be balls.

Z-Swing% = Swings at pitches inside the zone / pitches inside the zone

O-Swing% = Swings at pitches outside the zone / pitches outside the zone

Below are the Z-Swing% and O-Swing% starting pitcher leaderboards for qualified pitchers in 2019:

Z-Swing% – 2019 Leaderboard – Starting Pitchers
Rank Name Z-Swing%
1 Jacob deGrom 74.7%
2 Lance Lynn 72.4%
3 Max Scherzer 72.3%
4 Noah Syndergaard 71.9%
5 Julio Teheran 71.7%
6 Clayton Kershaw 71.6%
7 Madison Bumgarner 71.4%
8 Jeff Samardzija 71.2%
9 Reynaldo Lopez 71.1%
10 Tanner Roark 70.8%
11 Joe Musgrove 70.6%
12 Homer Bailey 70.5%
13 Jon Lester 70.3%
14 Masahiro Tanaka 70.2%
15 Sandy Alcantara 70.1%
All qualified starting pitchers for 2019.

 

O-Swing% – 2019 Leaderboard – Starting Pitchers
Rank Name O-Swing%
1 Jacob deGrom 37.9%
2 Justin Verlander 37.2%
3 Stephen Strasburg 37.2%
4 Masahiro Tanaka 36.9%
5 Hyun-Jin Ryu 류현진 36.7%
6 Jose Berrios 36.4%
7 Patrick Corbin 35.8%
8 Joe Musgrove 35.5%
9 Martin Perez 35.4%
10 Max Scherzer 35.4%
11 Miles Mikolas 35.4%
12 Zack Greinke 35.2%
13 Kyle Hendricks 35.1%
14 Clayton Kershaw 35.1%
15 Shane Bieber 35.0%
All qualified starting pitchers for 2019.

From the above, it is fairly easy to spot one of the reasons why Jacob deGrom earned his second straight Cy Young award. deGrom sits atop both the Z-Swing% and O-Swing% 2019 leaderboards. Not only do batters swing at deGrom’s electric pitching within the zone almost three-fourths of the time, but they are also tempted to swing at his would-be balls more than any other pitcher in baseball.

The 4th and 5th metrics – Z-Contact% and O-Contact% – answer the question of is the pitcher generating missed bats? Once again, wPDI looks at pitcher deception both for would-be strikes as well as for would-be balls separately.

Z-Contact% = Number of pitches on which contact was made on pitches inside the zone / Swings on pitches inside the zone

O-Contact% = Number of pitches on which contact was made on pitches outside the zone / Swings on pitches outside the zone

For contact rates, the lower the value, the better the pitcher. For those so inclined – you can subtract from unity to obtain the swing-and-miss rate.

Below are the Z-Contact% and O-Contact% leaderboards for qualified starting pitchers in 2019:

Z-Contact% – 2019 Leaderboard – Starting Pitchers
Rank Name Z-Contact%
1 Gerrit Cole 77.1%
2 Lucas Giolito 77.3%
3 Justin Verlander 77.7%
4 Max Scherzer 78.2%
5 Luis Castillo 79.4%
6 Robbie Ray 79.8%
7 Jacob deGrom 80.0%
8 Jack Flaherty 80.6%
9 Lance Lynn 81.0%
10 Mike Minor 81.5%
11 Noah Syndergaard 82.0%
12 Matthew Boyd 82.2%
13 Yu Darvish 82.2%
14 Eduardo Rodriguez 82.9%
15 Reynaldo Lopez 83.1%
All qualified starting pitchers for 2019.

 

O-Contact% – 2019 Leaderboard – Starting Pitchers
Rank Name O-Contact%
1 Gerrit Cole 49.1%
2 Luis Castillo 50.0%
3 Shane Bieber 51.3%
4 Patrick Corbin 52.0%
5 German Marquez 52.3%
6 Max Scherzer 52.4%
7 Sonny Gray 54.0%
8 Lucas Giolito 54.6%
9 Justin Verlander 55.1%
10 Charlie Morton 55.5%
11 Clayton Kershaw 55.7%
12 Yu Darvish 56.0%
13 Matthew Boyd 56.2%
14 Trevor Bauer 56.2%
15 Robbie Ray 56.3%
All qualified starting pitchers for 2019.

The contact rate is where Gerrit Cole shines bright. Cole generated more swings and misses than any other major leaguer – both in and out of the zone. A few other starting pitchers appear on both top-15 lists – Luis Castillo, Lucas Giolito, Max Scherzer, Justin Verlander and Robbie Ray.

Now that we have gone through the basics of the underlying plate discipline metrics, let’s talk about outcomes.

The Six Plate Discipline Outcomes

At the outset of this article, I mentioned that wPDI looks at three very basic binary events:

  • Was the ball thrown in the strike zone?
  • Was the ball swung on?
  • Did the batter make contact with the ball?

There are 3 queries, which each question above having a “yes” or “no” answer. Ordinarily, there would be 23 = 8 possible combinations of outcomes. However, two of these outcomes do not exist. If the batter does not swing – the ball cannot be hit. We can safely eliminate the impossible scenarios of:

  • In Zone / No Swing / Contacted
  • Out of Zone / No Swing / Contacted

What is left are the six plate discipline outcomes:

wPDI: Classifying the 6 Pitching Outcomes
Outcome Outcome Outcome Outcome Outcome Outcome
A B C D E F
Zone? Out of Zone Out of Zone Out of Zone In Zone In Zone In Zone
Swing? Swung On Swung On No Swing Swung On Swung On No Swing
Contact? No Contact Contact Made No Swing No Contact Contact Made No Swing

Using our five metrics above, we can write a formula for each of the six possible outcomes:

Outcome A: (1 – Zone%) * (O-Swing%) * (1 – O-Contact%) = The percent of all pitches which are out of the zone, swung on & contact is not made.

Outcome B: (1 – Zone%) * (O-Swing%) * (O-Contact%) = The percent of all pitches which are out of the zone, swung on & contact is made.

Outcome C: (1 – Zone%) * (1- O-Swing%) = The percent of all pitches which are out of the zone & that are not swung on.

Outcome D: (Zone%) * (Z-Swing%) * (1 – Z-Contact%) = The percent of all pitches which are in the zone, swung on & contact is not made.

Outcome E: (Zone%) * (Z-Swing%) * (Z-Contact%) = The percent of all pitches which are in the zone, swung on & contact is made.

Outcome F: (Zone%) * (1- Z-Swing%) = The percent of all pitches which are in the zone & that are not swung on.

From a pitcher’s perspective, some of these outcomes are better than others. In last year’s original post, I talked about how to rank the outcomes. Each were graded and assigned a weight/index from least desirable (0%) to most desirable (100%).

wPDI: Pitching Outcome Indexes
Outcome Description Index
A Out of Zone / Swung On / No Contact 100%
D In Zone / Swung On / No Contact 90%
F In Zone / No Swing 80%
B Out of Zone / Swung On / Contact Made 65%
C Out of Zone / No Swing 10%
E In Zone / Swung On / Contact Made 0%

Weighted Plate Discipline Index (wPDI) for Pitchers

Below is the generalized formula for wPDI, the Weighted Plate Discipline Index:

wPDI = IndexA * A% + IndexB * B% + IndexC * C% + IndexD * D% + IndexE * E% + IndexF * F%

The idea behind wPDI was to mimic wOBA, in which outcomes are weighted/indexed. Higher values are awarded to the better outcomes via one single value.

Please refer to the original wPDI post for an explanation of how the above weights/indexes of wPDI were generated. In future posts, I will provide statistically revised indexes (more math stuff!), which will harness the full potential of this generalized linear model.

In my next post, I will look at the final wPDI leaderboards for 2019, and associated movement from the prior season. I will also dive into some of the component makeup of certain eye-catching players.





Ariel is the 2019 FSWA Baseball Writer of the Year. He is the creator of the ATC (Average Total Cost) Projection System. Ariel was ranked by FantasyPros as the #1 fantasy baseball expert in 2019. His ATC Projections were ranked as the #1 most accurate projection system in 2019. Ariel also writes for CBS Sports, SportsLine, RotoBaller, and is the host of the Great Fantasy Baseball Invitational - Beat the Shift Podcast (@TGFBI). Ariel is a member of the inaugural Tout Wars Draft & Hold league, a member of the inaugural Mixed LABR Auction league and plays high stakes contests in the NFBC. Ariel is the 2020 Tout Wars Head to Head League Champion. Ariel Cohen is a fellow of the Casualty Actuarial Society (CAS) and the Society of Actuaries (SOA). He is a Vice President of Risk Management for a large international insurance and reinsurance company. Follow Ariel on Twitter at @ATCNY.

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chazzycat
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chazzycat

hey this is really cool stuff! I swear plate discipline metrics are SO underutilized. People still are not understanding the benefit of having more data points (each pitch instead of AB…it’s huge).

I actually put some work into this stuff a couple years back, you might find this interesting: https://www.pitcherlist.com/a-beginners-guide-to-understanding-plate-discipline-metrics-for-pitchers/

Completely nailed Luke Weaver’s 2017 strikeout rate as being an unsustainable mirage.

I love to see more work being done on this front!!