# Anatomy of a player: League Average Pitcher

While Pitch f/x has been a wealth of good data, without calculating league averages it is difficult to say just how unique certain pitchers are. If I were to tell you that Brandon Webb‘s sinker only rose two and a half inches more than a ball thrown without spin you would have no way of knowing if this represented a “heavy” sinker or not because you don’t have anything to compare it to. This information is what league averages will provide, a baseline to compare individual players to.

This week we will start by looking at some fastball data, including sinkers and cutters and next week we will focus on off-speed pitches. I have been breaking fastballs up into three categories, which I am labeling fastballs (or regular fastballs), sinkers, and cutters. These three distinctions come from my classification algorithm which has broken down the pitches into these three groups. Most of the pitches in the fastball category are four-seam fastballs, and tend to be fastest of the three fastballs. They also “rise” the most and break into a like-handed batter (e.g. a fastball from a right-handed pitcher tends to break towards a right-handed batter). Sinkers tend to be two-seam fastballs. They sink more than regular fastballs but are thrown a bit slower. Cutters are kind of a mix between sliders and fastballs. They are slower than regular fastballs but break much less horizontally than regular fastballs (thus cutting).

To start out we will look at three variables and calculate league averages. The three variables will be initial speed of the pitch, horizontal break, and vertical break. Horizontal and vertical break represent how much the ball moved compared to a ball thrown without spin. To combine data from left handed pitchers and right handed pitchers we will take the mirror image of the horizontal break for the lefties. This will put all pitchers on equal footing for each variable. To find the league averages we simply will take every pitch thrown that fits a certain category and find the mean. I will also graphically show some of the distributions to give you a better view of what major league pitchers are throwing. Let’s start with the regular fastball.

The image on this distribution probably looks familiar to you. It is that of a bell curve(or normal/Guassian distribution). Whenever you randomly sample a large amount of data you get this type of distribution. Here we have a large sample of well over 100,000 fastballs thrown but we don’t really have a random sample. Our sample is only from major league pitchers, who are the best of the best at their craft. So we didn’t have to end up with a distribution like this but it is nice that it turned out that way.

The average fastball is thrown at just under 92 mph but if you look at the distribution the peak appears closer to 92.5 mph. The reason the actual mean is lower is because the tail of the distribution is larger on the slower end. This is probably due to a couple of reasons. First, there is a shortage of pitchers who can hit 97 mph on the radar gun, but teams still need to fill our their rosters with pitchers, so guys who throw in the upper 80s can find a spot. Secondly, there are many different ways of being an effective pitcher. A grizzled veteran might have lost a few miles per hour on his fastball, but might still be effective. Lastly, if you look closely you will see a blip on the radar around 76 mph. These are mostly the fastballs of knuckleballer Tim Wakefield.

Because we have mirrored the left-handed pitchers here, we have a single peak around -5 inches. If we hadn’t done that we would have a peak around -5 inches and a smaller peak (because there are fewer left-handed pitchers) around 5 inches. The negative break here means the ball is breaking in towards a similarly handed batter. If a pitcher threw the ball completely 12-to-six and imparted only top spin on the ball then the ball wouldn’t have any spin in the horizontal direction.

The vertical break of the ball for the regular fastball is almost twice as much as the horizontal break. This means the spin imparted on the ball is mostly in the vertical axis. If you imagine a pitcher throwing a fastball and the ball rolling off his fingers you can see why this makes sense. The “rise” of the ball is not actually saying the ball rose on the way to the plate, but how much less the ball fell than a ball thrown without spin. For more on this concept you can read John Walsh’s article on sinkers. So to sum up, fastballs tend to be thrown around 92 mph with five inches of break horizontally and nine inches of break vertically. What about sinkers?

I am not going to show distributions for all three variables for sinkers and cutters, but if you are interested here are the speed and the horizontal break distributions. The vertical break is really the most interesting part about sinkers. An average sinker only “rises” about five inches vertically. Now we can go back to Webb’s 2.5 inch rise and see how heavy his sinker really is. Again we see a very large tail in this distribution. In this case though the tail is from pitchers who throw side-arm or even under-handed.

Despite these pitches actually being four-seam fastballs, they generate huge sink and thus are classified as sinkers by my algorithm. The final numbers for sinkers are an average of 90 mph with a 7.6 inch horizontal break and a 4.7 inch rise. So sinker ballers sacrifice a little speed for much less rise on their fastballs. Some of this spin is then moved over to horizontal break so this pitch also bores in to a similarly-handed batter.

Cutters are kind of in between fastballs and sliders. The intent is to get a similar speed as a fastball but with the horizontal break of a slider (which moves away from a similarly handed batter). Here are speed and vertical break for cutters. Mariano Rivera is be best example of a pitcher who throws the cutter almost exclusively. Here the average cutter moves like a ball thrown without any horizontal spin. In reality, this actually is from the combination of the arm angle and the wrist pronation canceling each other out and producing no horizontal spin. The cutter checks in with a speed of just over 88 mph with almost no horizontal break and a 6.6 inch vertical break. Again, speed is sacrificed for break.

The last thing I want to show is something I have been kicking around for a while. A few articles ago I posted some of Albert Pujols‘ numbers against different types of pitches. In that article I only used pitches that resulted in the ball being put into play or pitches that resulted in a walk or strikeout. Obviously, this isn’t a great way of calculating how effective a certain pitch is. For example, if a pitcher throws two straight fastballs for strikes then finishes off a batter with a curveball I would only be crediting the curve. After discussion with many different people I think I have come up with a decent way of crediting all pitches which I am calling pitch OPS or pOPS for short.

Basically, how you calculate pOPS is for every pitch thrown you calculate the change in expected OPS that for what a league average batter who produce in that situation. So for 2007 league average OPS was .753 but league average OPS for a 1-0 count was .853. So if a pitcher threw a fastball for a ball to start the at-bat his fastball would be docked .1 in pOPS. If a pitcher gives up a double then the OPS of 3.0 is subtracted from whatever the league average OPS of the current count. If the pitcher walks the batter or hits him then the pOPS is calculated by only using OBP because there is no slugging average for that at bat. Using this metric more fairly distributes the credit/blame of each type of pitch. It isn’t perfect, but a step closer to the right way of looking at things. If you calculate pOPS for every pitch thrown this year you end up with .04 or a slightly higher value than the league average OPS (remember pOPS is basically a difference from league OPS). This isn’t too surprising since Pitch f/x wasn’t installed until late in the year in most stadiums and players hit better in the second half of the season.

Anyway, I plotted pOPS against regular fastball speed for the range 80 mph to 100 mph and here are the results.

Remember that .04 here is league average for all pitches. You can see some sort of tend downwards as the speed increases but it is a very small trend. .03 in pOPS seems like a very small deviation but I haven’t played with it enough to say for certain. This seems to imply that major league batters are good enough to hit a very fast fastballs. Maybe speed isn’t the first thing that teams should be looking for when evaluating a pitcher. In any case, this work is just in its infancy but hopefully more work along these lines are to come. Next week we will examine breaking pitches and look for league averages there.

Lastly, I’d like to post a correction to last week’s article on Tim Lincecum. Several people have pointed out that Lincecum actually throws a two-seam fastball not a four-seam fastball. Thanks to my readers who emailed or commented at Ballhype about this.

**References & Resources**

A big thanks to baseball-reference.com for help with the OPS numbers by count.

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