Category: In-Game Decisions

Sunday Morning Quarterbacking Fourth Down Attempts (Part 1)

Abstract:

Arguing with couch-mates about what a National Football League team should do on fourth down has become a nearly equivalent staple to football Sundays as nachos. I analyzed data from 2010 to 2014 to make statistical predictions of the results of the three potential play types—Punt, Field Goal, and Run a Play From Scrimmage (“Go For It”)—as an alternative to the hindsight and anecdotally based arguments that are most frequently used. I divided my research based on where the offense is on the field using the five-yard demarcations drawn on all fields. Overall, the results of the research indicated overwhelming evidence in favor of “Going For It” on fourth down. The advantage to “Going For It” rather than punting ranged from 2.618 to 3.384 average net points resulting from the decision. The advantage to attempting a field goal ranged from 2.702 to -0.193 average net points (potential explanations for negative value explained within).

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3-0 Green Light

If you’ve watched at least two or three baseball games on TV before, you’ve probably heard a play-by-play commentator ask his color commentary counterpart if the hitter should get the “green light” on a 3-0 count. In other words, whether the manager should give his player permission to swing if a pitch looks really good. The opposing arguments in this scenario are as follows: “Player X should be allowed to swing because the vast majority of the time pitchers throw a fastball right down the middle that player X should be able to crush, resulting in an outcome far better than a walk” and “Player X should not be allowed to swing because player X could end up making an out and squander a very advantageous position.” For my money, I highly doubt that there are many situations in which Major League managers do not allow their players to use their discretion in this situation. This dilemma did, however, peak my interest. Does a batter getting the green light in a 3-0 count tend to pay off or not?

My strategy in trying to figure this out was not overly complex and can be explained in three steps. First, I compiled data from all players who had an at-bat in a 3-0 count (ie. they put a 3-0 pitch in play, as walks are not considered official at-bats) since 1988—the first year this data was available. I divided the data into two groups, those with at least 10 at-bats and those with fewer. I did this to ensure that sample size did not skew my results for the 10+ at-bat group, but still see how the less than 10 AB group stacked up. I also compiled data for these players’ performances after a 3-0 count, or in other words, the outcome of all plate appearances in which the count was 3-0 at one point but did not end with the 3-0 pitch.

*Note: I adjusted this data to not include intentional walks, hit by pitches, and reach on errors since those don’t reflect the ability of the hitter.

My next step was assessing value to three different categories of outcomes, 3-0 at-bats (balls put in play in a 3-0 count), 3-0 walks, and post 3-0 plate appearances. To do this I used run values from Tom Tango’s The Book: Playing the Percentages in Baseball. Run values give the average number of additional runs scored in an inning after a given event (eg. a single or a stolen base). One issue I ran into was not having a run value for sacrifice flies or ground into double plays. Exactly how I got around this is not extremely relevant, but I went ahead and explained it at the end if you are interested.

The last step in this process was to compare each player’s performance with the green light to their projected performance had they not had the green light. I added the run value amassed from all 3-0 plate appearances under investigation (ie. not intentional walks, hit by pitches, and reach on errors) to the run value amassed in post 3-0 plate appearances. This sum constituted the player’s performance with the green light.

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Calculating each player’s projected performance without the green light required a few steps. I added all 3-0 walks and post 3-0 plate appearances together, leaving just 3-0 at-bats unaccounted for. I multiplied the number of 3-0 at-bats by the average run value of a post 3-0 plate appearance and added this product to the previous sum of 3-0 walks and post 3-0 plate appearances.

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This entire projection hinges on the following assumption: that no Major League player would swing at a pitch outside the strike zone with a 3-0 count. I’ll go into more detail on this later, but the important part of this assumption is that it means that all 3-0 at-bats, had the player not had the green light, would have resulted in a strike and a subsequent 3-1 count. This situation would be the exact same as all the other post 3-0 plate appearances these players had, so I can accurately project how the player would have done overall in those plate appearances without the green light by substituting a post 3-0 plate appearance for each 3-0 at-bat.

Finally, I subtracted the projected performance of a player with the red light from their actual performance and divided this difference by the total number of at-bats they had in a 3-0 count (the total number of times the plate appearance was changed by the fact that they had the green light). I call this value the Green Light Effect.

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To green light or not to green light:

The beauty of this study is it’s incredibly easy to read. Each player’s Green Light Effect is the average increase in runs that can be expected by a player getting the green light. I should clarify that this number is for each time a batter utilizes the green light—puts a ball in play with a 3-0 count—not just when he gets the green light and has the opportunity to swing. So in theory, any player with a positive value should get the green light, as doing so would increase the number of runs his team is expected to score.

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Who are the best (and the worst) players with the green light:

There are two different ways to assess a player’s green light ability, how a player performed when swinging on a 3-0 count and how much better or worse that player did than if they instead had the red light. To figure out just how good or bad these players are I used standard deviations. Below are all the players that who are two or more standard deviations from the mean in either direction.

This first set of data deals strictly with the run value of each player’s 3-0 at-bats, without taking into account how much better or worse this is than their expected performance with the red light. The mean of the data for players with at least 10 3-0 at-bats was 0.0959 runs and the standard deviation was 0.155 runs. The middle column is the average number of additional runs that the player’s team is expected to score after their 3-0 at-bat. The right column shows how many standard deviations each player was from the mean.


Cumulative Run Value of 3-0 At-Bats

Best

Player                          Green Light Runs                       Standard Deviations

Nelson Cruz……………….  0.765 ………………………… 4.31

Jose Hernandez………….   0.550 ………………………… 2.93

Ben Broussard…………….  0.511 ………………………… 2.67

Nomar Garciaparra……… 0.463 ………………………… 2.36

Eduardo Perez…………….. 0.459 ………………………… 2.34

Matt Wieters……………….  0.438 ………………………… 2.20

Worst

Player                          Green Light Runs                       Standard Deviations

Casey McGehee……………  -0.352 ………………………… 2.89

J.J. Hardy…………………..  -0.299 ………………………… 2.55

Adrian Gonzalez………….  -0.281 …………………………  2.43

Andruw Jones…………….   -0.269 ………………………….  2.36

Gerald Perry………………   -0.269 ………………………….  2.36

James Loney…………….    -0.258 …………………………   2.28

Charlie Hayes…………….   -0.241 …………………………   2.17

Manny Machado…………  -0.229 …………………………. 2.09

This next set of data deals with the advantage/disadvantage that the green light presents, that is, the difference in runs that is expected from having the green light. The mean of this data was -0.156 runs and the standard deviation was 0.150 runs.

 

Run Value Compared to Expected Run Value with Red Light

Best

Player                          Green Light Effect                     Standard Deviations

Nelson Cruz………………… 0.479 ……………………….. 4.22

Jose Hernandez……………. 0.326 ……………………….. 3.21

Ben Broussard……………… 0.256 ………………………… 2.74

Nomar Garciaparra……….. 0.185 ………………………..   2.27

Eduardo Perez……………… 0.175 ………………………..   2.20

Matt Wieters……………….. 0.162 .……………………….   2.12

Mike Napoli………………… 0.158 .……………………….   2.09

Paul Konerko………………. 0.151 ………………………..   2.04

 


Worst

Player                          Green Light Effect                     Standard Deviations

Adrian Gonzalez…………. -0.569 ……………………….. 2.76

Casey McGehee…………. -0.514 …………………………. 2.39

Vladimir Guerrero…….   -0.492 …………………………. 2.24

Ichiro Suzuki…………….   -0.477 …………………………. 2.14

Andruw Jones……………  -0.476 …………………………. 2.13

James Loney……………..  -0.473 …………………………. 2.12

Charlie Hayes……………   -0.471 …………………………. 2.10

Gene Larkin………………   -0.462 …………………………. 2.04

These are the 3-0 at-bats of the top 3 best and worst hitters based on both Green Light Runs and Green Light Effect:

Player AB H 2B 3B HR GIDP SF
N. Cruz 10 9 3 0 3 0 0
J. Hernandez 17 12 4 0 5 0 1
B. Broussard 15 9 3 1 4 0 0
C. McGehee 11 0 0 0 0 1 0
J.J. Hardy 10 0 0 0 0 0 0
A. Gonzalez 11 1 0 0 0 1 0
V. Guerrero 35 11 4 0 1 2 0

 

The big assumption:

As I explained my process I made a passing reference to the crucial assumption that I made. I assumed that no Major League players swung at 3-0 pitches outside the strike zone. This assumption is necessary because my study assumes that all 3-0 pitches that are swung at would have resulted in a 3-1 count anyways if the player did not have the green light. Under this assumption, each player drew the maximum number of 3-0 walks possible (either with the red light or by taking all 3-0 pitches outside the strike zone with the green light). Thus, swinging on 3-0 did not give up the opportunity to walk on that pitch. As a result, it’s possible to project how each plate appearance would have gone without the green light by substituting the average result of that player’s plate appearances after a 3-0 count. Thus, swing and misses and foul balls don’t need to be accounted for because whether the player took the pitch or amassed a strike by swinging, the count would be 3-1. By no means can I guarantee that this assumption is correct, but it makes intuitive sense because Major Leaguers are extremely selective with 3-0 pitches—even 3-0 strikes—so I have to image they are disciplined enough to not swing at ball four on a 3-0 count. It actually turns out that there is a PITCHF/x metric called O-Swing % that measures the percentage of pitches outside the strike zone that are swung at. The problem is there is not public O-Swing % data (to my knowledge) for batters as opposed to pitchers, nor is there data for specific counts. With this data I could easily replace the generic projection value originally given for any 3-0 pitches outside the strike zone with the walk run value when calculating Overall Expected Red Light Performance.

 

Sac Fly and Double Play Run Values:

There were two events that I wanted to account for that did not have a given run value—sacrifice flies and ground into double plays. These don’t make up a very big part of the outcomes under investigation, so I came up with a makeshift solution for each without worrying too much about it. For sacrifice flies I took a weighted average of the change in run expectancy when an out is made and a runner on third base scores (assuming, somewhat arbitrarily, no advancement by trailing baserunners) weighted by the frequency of each scenario. For ground into double plays I added the run value of an out to the run value of a pickoff. My rationale was that the outcome of a double play, two outs and the loss of a baserunner, is the same as combining a pickoff, which results in an out and the loss of a baserunner, with an additional out. Furthermore, in both scenarios the majority of the eliminated baserunners were on first base before the pickoff/GIDP.

 

The survivor effect:

One of the questions I had going into this study was whether the survivor effect was a factor, in other words, whether players with more 3-0 at-bats performed disproportionately better with the green light. It would have made sense for players who performed well swinging on a 3-0 count to do so more often, and those who had poor 3-0 results early on to do so less. This would have affected results, as it would look like everyone did well with the green light, while in fact only those who did well had the minimum number of 3-0 at-bats to be studied. To check this I plotted all of the data, regardless of number of 3-0 at-bats, on the same graph. On this graph the independent variable was 3-0 at-bats and the dependent variable was Green Light Effect. A general upward trend would indicate that players with more 3-0 at-bats typically did better and the survivor effect was a factor. As it turned out there was no real sign of an upward trend.

This is a graph of every player with a 3-0 at-bat. The red line is the mean value for all players with fewer than 10 at-bats (-0.172). The majority of points with an x value of 10 or greater would need to be above that line to indicate the presence of the survivor effect.

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I recopied the same graph, limiting the x-axis to 50 at-bats to make it easier to see.

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