## Hitting as a Multi-Objective Optimization Problem

You may not know this, but my background is in engineering. (I have a B.S. and M.S. in electrical engineering from Oklahoma State University if I may brag a little.) I’m naturally an analytical person, which when combined with my love of baseball has led me down this path of hitting mechanics. I view hitting mechanics – as well as personal training- as simply problem solving. There are objectives we are trying to accomplish, problems in the way, and we have to come to a method of achieving the goal. The more objectives and variables involved, the more challenging the problem becomes.

Take for example the challenge of designing an automobile. We will limit our discussion to having the objectives of minimizing cost, maximizing fuel efficiency, and maximizing top speed. You don’t have to be an expert car designer to see that a single solution is not possible. We simply cannot optimize all the objectives without impacting the others. For example, increasing the top speed of the car more than likely hurts fuel economy. These objectives are conflicting. There is not a solution that optimizes each objective at the same time. Essentially, there is no one

However, there does exist a set of solutions that are considered Pareto optimal. Say we build Car A such that it costs $10,000 and achieves a top speed of 100 mph with fuel economy of 35 mpg. We build the car such that more optimization of either the top speed or fuel economy would impact each other or the cost of the car. Thus, we would consider this a Pareto optimal design. However, if we build Car B in a way that it costs $11,000 and achieves a top speed of 95 mph and fuel economy of 33 mph, we would call this a non-Pareto optimal design – we know we can optimize two objectives without adding cost. But we could also build Car C for $12,000 and achieves a top speed of 110 mph and a fuel economy of 33 mpg. Again, we can’t improve any metric without impacting another one. This is also a Pareto optimal design. There exists a whole suite of possible solutions that fit this category, the Pareto frontier.

Deciding which one is the preferred design requires subjective analysis. Do we think people will pay extra for the top speed? Is the more fuel efficient car ugly? So on. Now when we think about hitting, we see a similar issue. We have objectives: bat speed, swing time, barrel path, hand path, ability to adjust to pitch locations/speeds, and more. We also would like hitting to be such that we do not require enormous amounts of strength to perform the swing (analogy to cost). Just like we saw with the car design, we cannot come up with a single way to hit that optimizes each of the objectives. We could go all slow-pitch softball style to maximize bat speed, but this hurts many other objectives. We can just stand there and play pepper to optimize adjustability, but then we have no power. We can’t optimize each variable without requiring Superman strength. Essentially, there is no one optimal way to hit.

But, thanks to our dear friend Vilfredo Pareto, we know there exists a set of solutions that are at least efficient, in that we can find a method such that we can’t improve one thing without hurting another. The fact that there are many methods to successfully hit shouldn’t come as a surprise. Hitters come in all shapes and sizes and we saw that yes, they do actually swing the bat differently from each other. For example, both Michael Brantley and J.D. Martinez have posted the same offensive production this year at wRC+ 141. They have done it with different swings, approach, and athleticism.

So what does all this mean? Let’s hit some key points.

Take for example the challenge of designing an automobile. We will limit our discussion to having the objectives of minimizing cost, maximizing fuel efficiency, and maximizing top speed. You don’t have to be an expert car designer to see that a single solution is not possible. We simply cannot optimize all the objectives without impacting the others. For example, increasing the top speed of the car more than likely hurts fuel economy. These objectives are conflicting. There is not a solution that optimizes each objective at the same time. Essentially, there is no one

*optimal*solution.However, there does exist a set of solutions that are considered Pareto optimal. Say we build Car A such that it costs $10,000 and achieves a top speed of 100 mph with fuel economy of 35 mpg. We build the car such that more optimization of either the top speed or fuel economy would impact each other or the cost of the car. Thus, we would consider this a Pareto optimal design. However, if we build Car B in a way that it costs $11,000 and achieves a top speed of 95 mph and fuel economy of 33 mph, we would call this a non-Pareto optimal design – we know we can optimize two objectives without adding cost. But we could also build Car C for $12,000 and achieves a top speed of 110 mph and a fuel economy of 33 mpg. Again, we can’t improve any metric without impacting another one. This is also a Pareto optimal design. There exists a whole suite of possible solutions that fit this category, the Pareto frontier.

Deciding which one is the preferred design requires subjective analysis. Do we think people will pay extra for the top speed? Is the more fuel efficient car ugly? So on. Now when we think about hitting, we see a similar issue. We have objectives: bat speed, swing time, barrel path, hand path, ability to adjust to pitch locations/speeds, and more. We also would like hitting to be such that we do not require enormous amounts of strength to perform the swing (analogy to cost). Just like we saw with the car design, we cannot come up with a single way to hit that optimizes each of the objectives. We could go all slow-pitch softball style to maximize bat speed, but this hurts many other objectives. We can just stand there and play pepper to optimize adjustability, but then we have no power. We can’t optimize each variable without requiring Superman strength. Essentially, there is no one optimal way to hit.

But, thanks to our dear friend Vilfredo Pareto, we know there exists a set of solutions that are at least efficient, in that we can find a method such that we can’t improve one thing without hurting another. The fact that there are many methods to successfully hit shouldn’t come as a surprise. Hitters come in all shapes and sizes and we saw that yes, they do actually swing the bat differently from each other. For example, both Michael Brantley and J.D. Martinez have posted the same offensive production this year at wRC+ 141. They have done it with different swings, approach, and athleticism.

So what does all this mean? Let’s hit some key points.

**1. N=1.**Each player has a Pareto optimal solution for hitting, and each player’s solution is different. The optimal solution is going to be based on tons of things from your build to your approach. If this wasn’t true every successful hitter would swing the same way, and that simply isn’t true. Just because something worked for someone else does not mean it will work for you. Josh Donaldson exploded after adding a leg kick and bat tip? That’s lovely. Ken Griffey Jr. is going into the Hall of Fame never doing either. There is no one optimal way for everyone to swing the bat. It is not possible. As instructors there needs to be less of teaching “our way” and individualizing hitting to the hitter. They are the ones who get at-bats.**At a certain point, trying to optimize one thing WILL impact others. Case in point is Donaldson. In 2014 he went huge with his barrel tip for added power. Power went up, but contact went down. In 2015 Donaldson calmed the bat tip and has gotten back the contact. 2014 probably wasn’t a Pareto optimal design. Haha. Understand the pros AND cons of swing changes. Once the swing reaches a certain level, there are no freebies. Changing one thing will impact another. Coaches, try to understand WHY a hitter does certain things before just saying “that’s wrong” and setting off with your favorite drill to fix it.**

2. Understand the interplay between variables in hitting.2. Understand the interplay between variables in hitting.

**3. This goes for issues beyond the swing.**Sure, working on your swing can and will help your hitting. For each hitter, there exists a point where optimizing the swing is no longer the long pole in the tent. (More than likely, you probably aren’t there however.) Regardless, at a certain point we have to consider making the other objectives in hitting important. We turn to Donaldson once again. In working with his swing, he realizes that to do one thing you have to give up another. So he adjusts his approach to only look for certain pitches. At some point we have to taper off the worrying about what the scap is doing in the swing and start trying to beat the pitcher. Part of this is knowing your strengths and weaknesses.**4. Athleticism is always in style.**With the car design, we could optimize several objectives further if we had a bigger budget. Similar analogy with hitting. With a better movement base, we won’t have to “sell out” so much for power or contact, we can optimize both a little further without giving up something else. I would argue the point of diminishing returns for working on athleticism is much further out than the point for swing mechanics for the vast majority of individuals. Get to work!**5. Make sure you ask your coach if his/her methods are Pareto optimal.**You know, just for the look on the instructor’s face.