Swing Area Compactness and Positive Aggressiveness, an attempt to quantify plate discipline and consistency of players’ decision making in baseball
By: Julien Demeaux
Tags: Statcast, MLB, Dataviz, Baseball, Analytics

Swing Area Compactness and Positive Aggressiveness, an attempt to quantify plate discipline and consistency of players’ decision making in baseball Julien Demeaux Jun 3, 2020·12 min read

1. Abstract

When it comes to hitting a baseball, most coaches emphasize what they call Quality At Bats (aka QAB) against Batting Average or other well known batting metrics. If the definition of QAB can differ from one baseball program to another, the common trait that coaches instill in their players is the right mental approach. “Have a plan” and “Attack your pitch” are common creeds you hear around baseball fields across youth programs.

What is a good approach? Have a plan, choose your pitch and attack it, stay inside of the ball, aim for outside FBs until you have 2 strikes is a pretty common approach to teach kids. The situation and approach change when there are 2 strikes in the count and/or when runners are on base. Thus the ‘no one on base, less than 2 strikes’ situation is the main situation in which players can develop their very own strategy.

Good players understand this process and master it in their way to become consistent hitters at professional levels.

Using Statcast data for the MLB 2019 season, I will examine players’ consistency in their approach and plate discipline and I will attempt to answer the following questions: “Can data help quantify plate discipline?”, “Who are the most disciplined players?”, “What part of the strike zone do they prefer?”, “How aggressive are they into their observed power zone?”.

To do so I will start focusing on what I called Swing Zone Compactness for the purpose of this study. I will then try to quantify if players tend to be more aggressive at the heart of what should be their power zone.

2. How to assess plate discipline?

Between 2006 and 2010 David Appelman with Fangraphs created new metrics to assess plate discipline. Those metrics are mostly based in computing swinging rates on pitches inside or outside the strike zone. Many angles were taken and dug into during this span and a wrap up web page allows to explore his work (1).

In 2007, Dr. Carleton (@pizzacutter4) refuted that the K/BB ratio used to assess plate discipline was relevant. In a nutshell Dr. Carleton demonstrated that a free swinger could avoid being struck out if he could make contact consistently. On the other hand a patient hitter is simply at the mercy of pitchers’ command and should not be considered a “disciplined hitter” if he couldn’t swing at good pitches.

Dr. Carleton proposed new metrics “based on the concept of signal detection theory, a concept originally developed for medical epidemiological studies which has been used extensively in the fields of cognitive psychology” (2).

Another approach to assessing plate discipline came from Neil Paine with FiveThirtyEight.com where he used a model which considers that players make good decisions when they swing at strikes and take balls. The model produces a “Good Decision ratio” that allows to compare players to one other.

Even though there is some relevancy in those approaches I can see a couple of bias in each model.

Using the result of actions (ball in play, swing and miss, foul ball, etc.) to assess what is supposed to be a decision making process doesn’t seem relevant enough because they also involve players’ ability to make contact. This choice of approach from the authors may specifically be due to lack of data granularity at the time.

Plus those approaches to quantify plate discipline consider the totality of pitch seen no matter what the situation is. A strike in the heart of the zone can be taken as a result of a steal sign given by the 3rd base coach with a speedy runner at first. A ball way outside can be swung at as a result of a given sign. Those situations would negatively tamper the assessment of players’ discipline if we consider that it is bad swinging at a ball or to take a strike. This is quite the opposite in these specific situations when the result of the pitch seems to be negative for the player when he showed discipline. The process matters more than the result when assessing plate discipline.

This is why I will focus on the aforementioned situation -no one on base, less than 2 strikes- and pitch location (which was not necessarily possible when the previous articles were written) to assess players’ decision making independent of other variables.

The first question could be: “Do players attack more fastballs or off speed pitches?”

Using fangraphs definitions, four seamers (FF), two seamers (FT), cutter (FC), split-fingered (FS) and sinker (SI) will all be considered as fastballs. All other kinds of pitches will be considered off speed pitches.

Fig.1 — Distribution of types of pitches swung at with no one on base and less than 2 strikes. Data: Statcast

The MLB 2019 regular season saw a total of 731,728 pitches thrown. Of this total, 296,117 came with no one on base and less than 2 strikes with 118,988 being swung at.

As the chart above shows 56% of these swings were made at fastballs while 44% were made at off speed pitches.

I would have naively thought that FBs would sit around 75% here. Do pitchers deceive this often hitters? Do hitters not chase only FBs in the studied situation? Do hitters gamble the kind of pitch that is coming according to the count? Probably a mix of these assumptions are correct to explain this 44% mark.

My initial assumption is to say that a common and strong approach to hitting a baseball is to hunt FBs. So I first considered keeping only FBs for this analysis but the distribution tells otherwise so I’ll keep this FBs/Off Speed categories .

Considering these 2 types of pitch family, the next question is how compact is the zone when players swing at the ball?

The main hypothesis here is that the more compact the swinging zone, the more disciplined the player.

As a matter of fact, the decision making process is supposed to be:

Recognize the type of pitch,

Assess the pitch trajectory in or around the strike zone,

Decide whether to swing or not.

Thus, a narrow swinging zone shall be a relevant clue of how well players process those three steps.

To start this study, I have decided to define for every player where the average point of their swinging zone is in the studied situation. I have then considered the distance in feet from this mean point of each pitch swung at during the season. To make up for switch hitters, I have also considered the standing side from which they see the pitch. Thus every switch hitter will be considered as 2 different players: one being a LHB, the other a RHB.

Fig.2 — All pitches seen by Joey Votto in 2019 in the aforementioned situation. Red dots show pitches swung at, grey dots show pitches taken. Black cross shows mean location of pitches swung at. Chart is from catcher’s eyes perspective. Data: Statcast

Fig.3 — All pitches seen by Robinson Cano in 2019 in the aforementioned situation. Red dots show pitches swung at, grey dots show pitches taken. Black cross shows mean location of pitches swung at. Chart is from catcher’s eyes perspective. Data: Statcast

Figures 2 and 3 show Joey Votto and Robinson Cano’s pitches seen in 2019 in the studied situation. Red dots show the pitches players swang at, grey dots show pitches players took. The black cross shows the average location of pitches swung at.

We can start to get a visual clue of how spread out the pitches swung at are for each player and each kind of pitch.

The idea here is to get the coordinates of this black cross and to use it as the reference point.

Once I have defined those reference points (2 for each player-stand: against fastballs and against off speed pitches), I worked on 2 different metrics to assess the consistency of players’ decision making.

The first will consider the mean distance of each pitch swung at to define the compactness of the swing area.

The second will consider an area of approximately the size of 2 baseballs around the reference point to compute the swing rate in this area. This metric — being called Power Zone Aggressiveness — will show how aggressive are players in what is supposedly their power zone.

3. Swing Area Compactness

The first step to compute the Swing Area Compactness is to get the distance between each pitch swung at and the reference point.

Fig.4 — The distance between each pitch swung at and the reference point is computed to define the average distance from the center of the area. Data: Statcast

The Swing Area Compactness consists then in computing the average distance. The smaller the average distance, the more compact the swinging area. The more compact the swinging area, the more disciplined the player. In a nutshell, we can consider that the player is more disciplined to swing in or around his power zone when the average distance to it is smaller.

The 2019 dataset contains a total of 973 players-stand (remember that switch hitters are considered as 2 different hitters). Two different Swing Area Compactness are computed for each of those player-stand, one when facing fastballs, one when facing off speed pitches. This brings the pool of player-stand-pitch type to 1816 individuals.

From there I have filtered out players who have seen less than 100 pitches (the average amount of pitches seen in the pool is 93) which lowered the studied pool to 893 players.

Here are the top 30 players in Swing Area Compactness

Fig.5 — Top 30 players in Swing Area Compactness in 2019. Data: Statcast

According to Swing Area Compactness Greg Garcia (San Diego Padres) emerges as being the player with the most compact swinging zone in MLB. The average distance where he swings fastballs from his reference point is 6.64 inches which represents a little more than the width of two baseballs.

For comparison purposes, the Pool Swing Area Compactness average of the pool is 8.76 inches, which is almost the size of three baseballs.

For a moment I considered using the median distance instead of the average distance to make up for outliers that could simply be brain farts. But in the end this is the player who decided to swing the bat and no randomness is supposed to be involved in this process so I decided to stick with the average distance.

Another thing to notice is that we find only one player, Luis Arraez (Minnesota Twins), who makes the top 30 while facing off speed pitches. His Swing Area Compactness is also pretty good against fastballs at 7.53 inches.

Fig.6 — All pitches seen by Luis Arraez in 2019 in the aforementioned situation. Red dots show pitches swung at, grey dots show pitches taken. Black cross shows mean location of pitches swung at. Chart is from catcher’s eyes perspective. Data: Statcast

Visually Arraez’s pitch chart is pretty impressive with very few swings at pitches outside of the strike zone.

On the other end of the Swing Area Compactness scale we find players who could be called free swingers.

Fig.7 — Bottom 30 players in Swing Area Compactness in 2019. Data: Statcast

The first thing to notice when looking at the bottom 30 players in Swing Area Compactness is that Off Speed Pitches are over represented which kind of makes sense if we consider that hitters are more oftenly deceived by breaking balls and off speeds in general than by fastballs.

It is also somehow surprising to see MVP caliber players like Yelich or Arenado. One might consider that a good plate discipline, as well as pitch recognition and ability to make contact, is mandatory to become an efficient hitter.

Maybe the latter is more important and Yelich’s incredible results are more connected to his technique and contact ability than to his plate discipline. Another way to see it may just be to consider that his power zone is the entire strike zone!

Which brings us to the second point of this article: how aggressive are players into their power zone?

4. Positive Aggressiveness

First of all to define what the Power Zone is for every player, I have decided to create an area representing the size of 2 baseballs around the reference point.

This approach is totally arbitrary but makes sense considering the ‘Attack your pitch’ mantra that coaches usually teach. The strike zone width represents more or less 5 to 6 baseball width so this so-called Observed Power Zone would make for about one third of it.

Back to Joey Votto and Robinson Cano, here are their respective Observed Power Zone according to this method.

Fig.8 — Joey Votto’s observed Power Zone facing fastballs and off speed pitches. Data: Statcast

Fig.9 — Robinson Cano’s observed Power Zone facing fastballs and off speed pitches. Data: Statcast

Something to notice here is that Cano’s Observed Power Zones might be questionable. Maybe using the average location of pitches swung at is not the right approach, especially for free swingers, as their Swing Area is wide. Maybe another approach based on density could be explored to define this reference point but I’ll stick with the average location for now.

Once the Power Zone is defined, the idea is to focus on the swing rate into the Power Zone which I called Power Zone Aggressiveness (PZA%). To make sure the results are relevant I have filtered out players who faced less than 100 pitches total and less than 15 into the Observed Power Zone.

Fig.10 — Top 30 players in Power Zone Aggressiveness in 2019. Data: Statcast

Tim Anderson, Shohei Ohtani, Raimel Tapia, Khris Davis and Jay Bruce emerge here with a 100 PZA%, meaning they swing everything that is thrown into their Power Zone. Other names are worth mentioning here and made me realize that there is bias in this approach. Free swingers are aggressive anywhere and everywhere in and around the strike zone. So having a high PZA% doesn’t necessarily mean that the player has a positive aggressiveness.

Thus I decided to compare PZA% to the swing rate outside of the Power Zone considering that the bigger the difference is, the more the player is in control with his aggressiveness.

Going down that road I came up with the Positive Aggressiveness metric that shows the difference in swinging rate inside and outside the Power Zone.

Fig.11 — Top 30 players in Positive Aggressiveness in 2019. Data: Statcast

So Joey Gallo swings 65.4% more often when a fastball is thrown into his power zone than when a fastball is thrown outside of it.

Josh Donaldson swings 53.4% more often at off speed pitches when they are thrown into his Observed Power Zone which shows an impressive eye.

Even if some names are worth highlighting here, don’t forget that this metric is meant to assess decision making to swing or not (which in a nutshell is plate discipline) and does not consider at all players’ ability to make contact. Thus I wouldn’t expect any kind of correlation with results minded metrics like BB/K ratio or Batting Average.

Fig.12 — Joey Gallo swings and takes in and out of his Observed Power Zone. Data: Statcast

Gallo shows a real aggressiveness into his Observed Power zone but also has a relevant share of swings elsewhere in the strike zone. The positive is that the swings almost disappear outside of the strike zone and the Positive Aggressiveness metric seems to tell a relevant story.

On the other end of the metric, it is interesting to notice that 19 players swing more often outside of their observed Power Zone than inside of it.

Fig.13 — Bottom 30 players in Positive Aggressiveness in 2019. Data: Statcast

Only 2 of these 19 players have seen more than 200 pitches so we may take those results with a pinch of salt.

Ben Zobrist for example has the worst Positive Aggressiveness of the pool when it comes to FBs (-30.2% out of 154 pitches seen) when he has the best Pos.Ag. percentage of off speed pitches (76.4% out of 114 pitches).

Sample size definitely matters so it would be interesting to find out where the threshold lies when it comes to the amount of pitches seen and the amount of pitches into the Power Zone needed to draw conclusions.

5. Going further

At this point I’d be happy to get some feedback about these metrics (Swing Area Compactness and Positive Aggressiveness) as I stayed in the descriptive area of things.

Do they make some kind of sense?

From a coaching perspective, I’d say they do but there might be limitations.

How could they be improved? What’s missing? Is the approach correct from a data science point of view? How to effectively use them?

There are also some potential bias to overcome:

Is there a better way to define the reference point? Would density or any other approach be more accurate than the average location?

Is the way to define the Observed Power Zone relevant? Would there be a more scientific approach to define it?

Once those hurdles would be cleared, I believe it would be interesting to assess the edge gained or potentially gained by players who have a better Positive Aggressiveness and/or smaller Swing Area Compactness.

It would also be interesting to see if these metrics provide relevant results over time. So exploring other seasons will be mandatory at some point.

Finally the last question I can see at this point is if and how we could extrapolate the same kind of approach to other game situations because decision making has to be assessed in high leverage situations as well.

Special thanks to Garrett Smith and John Edman for your invaluable help and advices in writing this article.

(1) Plate Discipline, fangraphs.com, Steve Slowinski, February 18th, 2010: https://library.fangraphs.com/offense/plate-discipline/

(2) The Adam Dunn debate: Defining plate discipline, MVN.com, Dr. Carleton, May 24th, 2007: https://web.archive.org/web/20080911225907/http://mvn.com/mlb-stats/2007/05/24/the-adam-dunn-debate-defining-plate-discipline/

(3)The Most Disciplined MLB Batters, fivethirtyeight.com, Neil Paine, April 25th, 2014: https://fivethirtyeight.com/features/the-most-disciplined-mlb-batters/