**PITTSBURGH** – On Christmas Eve of last year, The Hardball Times released an article by Dr. Alan Nathan entitled, “Optimizing The Swing Part Duex: Paying Homage To Teddy Ballgame”.

The piece was a follow-up by Dr. Nathan to a previous Hardball Times story, “Optimizing The Swing” where he looked at determining whether a curveball can be hit farther than a fastball, assuming both are hit optimally.

Through his research, Dr. Nathan discovered the idea *“that an optimally hit curveball travels farther than an optimally hit fastball is not confirmed by my own analysis. In fact, the fastball beats the curveball, but only by a little bit. My takeaway from this analysis is that the distances are comparable.”*

In “Optimizing The Swing Part Duex”, Dr. Nathan focused on maximum on-base probability as opposed to focusing on maximum distance – in his words he attempted to “…connect the batted ball characteristics with the probability of actual outcomes.”

With that in mind, we are going to take a look at Dr. Nathan’s research and analysis and see just how it can apply to SwingTracker and the various SwingTracker metrics.

Let’s start by taking a look at approach angle (or as Dr. Nathan refers to it, attack angle), while also tying in trigger to impact – i.e. ‘timing’

According to Dr. Nathan, *“the level swing is one where the attack angle coincides with the descent angle of the ball, which in our case is 6 degrees. That angle is very close to the optimum angle for high BABIP. The home run swing is one where the attack angle maximizes the probability of hitting a home run, which we have just found to be 24 degrees.”*

In the side-by-side swing comparison at the top of this post, we can discern with the naked eye that both of those particular swings do not have an approach angle of 24 degrees. We can see the swing is, perhaps, what one would describe as ‘level’.

But how level are each of the swings?

The naked eye can’t quantify if the approach angle is slightly positive, slightly negative, or perhaps, perfectly level (but SwingTracker can, of course).

Before we reveal the answer to that, let’s allow Dr. Nathan to tell us just how much approach angle affects the swing from a timing and error perspective**¹**.

“Let’s suppose that the batter swings at some attack angle, with the goal of having some desired offset at the front plane of home plate. If the batter is going for a line drive single, that offset might be about 0.5 inches; if he is going for a home run, it will be around one inch. Now suppose that the batter is a little late with the swing (say, a bit over three milliseconds late), so that the contact occurs four inches behind the front plane of home plate. If the attack angle is level, the actual offset will be identical to the desired offset. Such a swing is therefore very forgiving for small errors in timing.”

With the help of Dr. Nathan, we have now established that the type of swing we see in the swing comparison video will be forgiving due to the fact it has a more level approach angle. Before moving on, let’s see how forgiving the swing would be if it had a much more positive approach angle.

“Things are very different if the batter has a home run swing. Over those four inches, the ball will be about 0.4 inches lower and the bat will be about 1.8 inches lower. The net effect is that the offset will be larger than the desired offset by 1.4 inches. Likewise if the swing were too early by the same four inches, the offset would be smaller than desired by 1.4 inches. Think about that for a minute: 1.4 inches is about half the diameter of a baseball. It is huge! For example, if you are aiming for one inch and are late by three milliseconds, your offset will be 2.4 inches, which gives you a on-base probability of close to zero. Indeed, if the offset is larger as 2.7 inches (the sum of the ball and bat radii), the bat will miss the ball altogether.”

With this information in hand, we can now see why hitting a baseball, much less a major league level pitch, is so difficult. Your margin for error involves tenths of an inch and milliseconds, while trying to hit a moving object that is 2.86 – 2.94 inches in diameter and traveling at a speed of anywhere from 80 to 95 mph.

Those numbers, however, are specific to a ‘home run swing’ with an approach angle of +24 degrees, not the swings below, which we can see each have a negative approach angle: -6.4 degrees and -0.8 degrees. Furthermore, we can see all the SwingTracker metrics, including the ones that are pertinent to this discussion: Max Bat Speed and Trigger To Impact.

So what to make of this data?

Let’s start by looking at this heat map below of StatCast data from Dr. Nathan’s article.

We can see the exit speed on the y-axis and the vertical launch angle (not to be confused with approach angle) on the x-axis.

While the batter in our videos is not MLB caliber, this can give us a look into a few things:

- In terms of approach angle, we can assume since the batter in our videos is hitting off a tee and has a negative approach angle, the ball will most likely result in a ground ball or line drive. This means the launch angle will most likely be between -10 and +10 degrees.
- Using the formula | v
_{b}= e_{a}v_{p}+ (1 + e_{a})v_{s}| a perfectly struck ball with a max bat speed of 53.2 or 52.3 will produce an exit velocity of roughly 64 mph. - Given these numbers: -10 and +10 degree launch angle, along with a 64 mph exit velocity, we see that falls in the bottom left corner of the plot. If the batter in our video happened to get miraculously signed by an MLB club, we could predict with our data he would have a batting average in the .090 to .200 range
**²**.

Before wrapping up, let’s take a look at how Dr. Nathan compares a level swing to a home run swing in terms of offset – which goes back to timing.

According to Dr. Nathan:

“Let’s suppose that the batter swings at some attack angle, with the goal of having some desired offset at the front plane of home plate. If the batter is going for a line drive single, that offset might be about 0.5 inches; if he is going for a home run, it will be around one inch. Now suppose that the batter is a little late with the swing (say, a bit over three milliseconds late), so that the contact occurs four inches behind the front plane of home plate. If the attack angle is level, the actual offset will be identical to the desired offset. Such a swing is therefore very forgiving for small errors in timing.

However things are very different if the batter has a home run swing. Over those four inches, the ball will be about 0.4 inches lower and the bat will be about 1.8 inches lower. The net effect is that the offset will be larger than the desired offset by 1.4 inches. Likewise if the swing were too early by the same four inches, the offset would be smaller than desired by 1.4 inches. Think about that for a minute: 1.4 inches is about half the diameter of a baseball. It is huge! For example, if you are aiming for one inch and are late by three milliseconds, your offset will be 2.4 inches, which gives you a on-base probability of close to zero. Indeed, if the offset is larger as 2.7 inches (the sum of the ball and bat radii), the bat will miss the ball altogether.”

This is under the assumption that contact is always taking place at the front edge of home plate simultaneously. But what if contact occurred later (three milliseconds later, as noted in the examples above), or in our case a whopping 16 milliseconds later – 189 m/sec as compared to 205 m/sec.

First, while the batter in our video is hitting off a tee and does not have to worry about such issues, he would have an extreme offset from one swing to the other (assuming he could make contact).

If he received the same exact pitch two times in a row, and was able to make contact with his swing that had a trigger to impact number of 205 m/sec, it would likely be at best a foul ball, compared to his first swing with a trigger to impact of 189 m/sec.

Considering one beat of a hummingbird’s wings takes 20 m/sec (which is impossible to discern with the human eye), we can see once again just how small the margin for error is (and why a swing training tool like SwingTracker can pay huge dividends in terms of figuring out and quantifying the smallest changes and differences in the swing).

**Footnotes:**

1. For the purposes of Dr. Nathan’s article, he considered only a fastball, with a speed at contact of 86 mph, a backspin of 2000 rpm, a descent angle of 6 degrees, a fixed bat speed of 70 mph and the assumption that the contact always takes place at the front edge of home plate, meaning that the bat and ball both arrive at that location simultaneously.

2. There are a few points in the data plot that have a +.300 BA, but those are most likely well-placed bunts or balls hit so poorly they become very difficult to field and turn into hits.

**#DKBaseball**