A Proposal for Regression Analysis of a Four-Seam Fastball

Hello, I am new to this, and this is my first post. I think I should introduce myself first. My name is Daniel Fendlason, and I am a first year graduate student at Tulane University, New Orleans, Louisiana, and I  am studying Economics, which is very fun stuff. I did my undergraduate studies at Northeastern University, Boston, Massachusetts, which is where I majored in Finance and minored in Economics.

Ok, now on to the point for doing this in the first place. I am taking Econometrics this semester, and it requires a research paper researching something that we find interesting. Since I am interested in baseball I decided to do my research paper on baseball. A proposal is due in a few days, and below is that proposal. Please read and tell me what you think. I will follow up and submit the full paper when it is due, which is in December. So, without further digressions, enjoy.

Proposed Title: “The effectiveness of the speed and movement of a four-seam fastball”

In my investigation, I would like to better understand the sport of baseball by answering the following questions: is it more difficult to hit a faster moving four-seam fastball than one that is slower moving? Also, is it more difficult to hit a four-seam fastball if it is moving in a more horizontal manner or a more vertical manner? My hypothesis is twofold: if a pitch is faster, it will be more difficult to hit, and if a pitch moves more, it will be more difficult to hit. If my hypothesis is true, then more speed and more movement will make a ball more difficult to hit. The ball from a specific pitch is difficult to hit if a skilled batter swings his bat and does not make contact with the ball, or the contact that is made is poor and results in the batter making a strike, if he swings and misses, or an out, if he puts the ball in play.

Independent Variables

A pitcher can throw many types of pitches. The pitcher can try to deceive the batter by throwing a pitch that has a lot of movement, like a curveball or slider, or a pitch that is slower than it looks when the ball leaves the pitcher’s hand, like a change-up. But the four-seam fastball is the only pitch the pitcher is not trying to intentionally deceive the hitter with movement or deception-of-speed. When a pitcher throws a four-seam fastball he is simply trying to throw it as hard, and as accurate, as he can.

Even though a pitcher is not trying to induce movement when he throws a four-seam fastball, the ball still moves—in fact, the ball can move horizontally, vertically, or both horizontally and vertically. This unintended movement has an effect on the batter to make contact, which means that there will be three independent variables: speed, vertical movement plus horizontal movement, and total movement plus speed. Since there are three independent variables, to analyze this situation three models will need to be created. This should not be difficult, as all that has to change is the variable on the left side of the equation; the dependent variables will remain the same for each model. 

Dependent Variables

The dependent variables will be all of the possible per-pitch outcomes that involve the batter attempting to hit the pitch by swinging his bat; this excludes pitches that an umpire calls a strike or a ball. These two outcomes are excluded, because the batter did not swing his bat, which means that the speed or movement of the pitch having any effect on avoiding contact, or inducing poor contact, cannot be discerned.

In addition, because the outcomes are per-pitch, the walks and strikeouts are excluded, because those outcomes are already accounted for. More specifically, if the batter walks, then he did not swing at the pitch and is therefore excluded. If the batter strikes out, then he swung and missed, which is accounted for with the swinging-strike outcome, or the umpire calls him out which is excluded, because the batter did not swing his bat.

The included outcomes are: swinging strike, foul ball, ground-out, infield fly-out, outfield fly-out, line-out, single, double, triple, and home run. I’ve included many types of outs, because each type of out can tell us what type of contact was made. For example, if the contact was poor, then the result will either be a ground-out or an infield fly-out. If the contact was solid, but the batter still made an out, then the result will be a line-out, or an outfield fly-out. If the contact did not result in an out, then it will be assumed that the contact was solid.

Error Term

The error term will include the sequencing of the previous pitches, the count, the base-out state, the location of the pitch, and the quality of the defense.

Each pitch will be context neutral; the pitches that preceded it will not be accounted for. This can affect the outcome of the pitch, because the absolute speed of the pitch may not matter as much if the previous pitches that a batter has seen in an at bat have been much slower than that of the four-seam fastball.

The count of the at bat can affect the outcome of the pitch, because batters know that, in some counts, pitchers are more likely to throw a four-seam fastball. In this case, the batter may be anticipating the four-seam fastball, which will give the batter an advantage. The base-out state can affect the outcome of the pitch, because it can dictate what pitch a pitcher is more likely to throw. The location can affect the outcome of the pitch, because some locations are more difficult for a batter to reach with his bat when he swings. The quality of the defense can affect the outcome of the pitch as well, because it can turn hits into outs, if the defense is good, or it can turn outs into hits, if the defense is poor.

Data

The data will be collected from www.baseballsavant.com. This website contains data on every pitch thrown from the seasons of 2008 to 2014. The website allows the user to apply filters, which means that the data can be filtered by pitch type, and pitch outcome.

The data will include every four-seam fastball that was thrown in seasons 2008 to 2014. Statistics for the fastballs will include speed, horizontal movement, vertical movement, and all outcomes except walks, strikeouts, called strikes, and balls. Since the outcomes are not numerical values, a numerical code will need to be assigned to each outcome. Table 1 illustrates the numerical code that will be used in this study.

Each year’s worth of data contains approximately 50,000 lines of data. Hence, the initial assumption is that the data is normally distributed and linear. Since there are seven years of data, each model can be run seven different times. This will render a much more unbiased coefficient for each dependent variable.