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 1^st 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:

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 2^nd and 3^rd 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:

 

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 4^th and 5^th 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:

 

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:

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%).

Weighted Plate Discipline Index (wPDI) for Pitchers

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

wPDI = Index_A * A% + Index_B * B% + Index_C * C% + Index_D * D% + Index_E * E% + Index_F * 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.

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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.