Pitchers and Injuries: The Biomechanics of Baseball

December 13, 2007

Note: The formatting is a bit bollocksed in this post, sorry. Haven’t been able to fix it

If you spend any time at all reading about baseball players, you’ll have seen comments like this regarding certain pitchers:

“[player z] has a very violent delivery, putting too much torque on his elbow, and is therefore a huge injury concern.”

How do the experts in the field come to these conclusions? How much weight should we give to their opinions? These are important questions, and to answer them we’ll have to go right back to the beginning.

The first question we should ask ourselves is this one: What is the goal of a pitcher’s delivery, in the purely physical sense?

The answer’s fairly straightforward – to impart angular (spin) and linear acceleration to a baseball using just the pitcher’s body to do so. The amount of linear force imparted to a ball will manifest itself as the velocity of a pitch, while the angular acceleration more or less controls the spin. We won’t get into the physics of a ball in flight here, rather we’re concerned with a very different problem.

How does a pitcher apply this acceleration?

In essence, what a pitcher does is store up energy in his body, and then release it all at once. The first part is pretty easy to understand, albeit with some gross simplifications along the way…

Muscle systems are more or less paired springs for the purposes of an analysis like this. When you compress a spring, it stores the energy you use in pressing on it as potential energy (the exact amount is determined by what’s called a strain energy function, but as this gets absurdly complicated for biological tissue, we’re going to gloss over that one here), and then releases it as soon as it’s free to do so. If you think of the upper body of a pitcher as a series of springs, you can see that the the windup is accomplishing more or less the same thing. Note that this has very little to do with the leg kick, as that’s exploiting a different type of potential energy: gravity.

So that’s actually pretty straightforward, and really not where pitchers get hurt. Rather, injury occurs in the process of transferring all of that stored up energy to a baseball. Limbs twist, the body gyrates, and the elbow and shoulder are having to hold the whole arm together through what is really a very violent motion. So it is reasonable to say that the more energy which a pitcher has to transmit to get results, the more likely he is to be hurt?

No, it’s not, and doing so is actually quite lazy. Remember, the best pitchers are the ones putting as much acceleration on the ball as possible, so in terms of pitching performance, maximising torque and such around the joints is a good thing. What we have to do is look at some anatomy. I’m going to specifically examine the elbow here, since it’s far less complicated than the shoulder, but the same principles will generalise to other joints as well.

(source: Gray’s Anatomy)

The elbow is theoretically a biological hinge, but it doesn’t really work the same way your door hinges do. The joint allows for two kinds of motion: flexion/extension, or basic hinging, which everybody is familiar with, and pronation/suppination, which is the rotation of the forearm relative to the upper arm. Three major ligaments provide structural integrity to the joint as it performs these movements. The Ulnar Collateral ligament (UCL) is undoubtedly the best known to baseball fans, due to its place as the ligament rebuilt in Tommy John surgery, but the other two are decidedly less familiar – the Radial Collateral and the Annular. The reason these are less familiar to us is because they’re rarely what goes wrong in an elbow (this is unsurprising if you actually look at where the annular is and what it does).

Anyway, the point of this brief digression into anatomy is to show that far from being a simple hinge, the elbow is actually a fairly complicated system, with each movement stressing many different elements of the joint. None of these ligaments works in torsion, either – they’re designed to generally take tensile stresses (i.e. pulling). In addition, elbow failure will occur when any ligament in the elbow begins to fail, as even if a minor one begins failure, it will put incrementally more stress on the major ones, leading to their eventual yield as well. In essence, what a pitcher ideally does is tailor his motion to take advantage of the capacity of every element in his elbow.

Still, no problem, right? We have models of the elbow that will turn the relative movements of the upper and lower arm into stresses  inside the elbow, right? Uh… Not so much. Same goes for the shoulder, but the main problem here is that we don’t even know the general engineering properties of many of these  ligaments, which causes problems when looking at how to distribute forces in a computer model. Honestly, it probably wouldn’t help much if it did, because of the actual failure mechanism involved. Yep, it’s time for another anatomical tangent.

In order to accommodate the tensile stresses they have to take, cartilaginous bodies are reinforced by fibres running in the same direction as the primary loading they received (this is loosely analogous to rebar in reinforced concrete). These collagen fibrils greatly strengthen the material matrix they lie in, but can themselves fail. And they do, one by one, with each failure causing their neighbours to take on additional stress until they fail as well, which is how tears propagate.

Of course, we don’t really care about the material’s true yield strength, because a pitcher isn’t just throwing a single time and then calling at a career. Hell, a starting pitcher might throw 50,000 pitches over 15 years. What we have instead is cyclic loading, which leads to fatigue failure (or the biological analogue, at any rate).

The danger stress for cyclic loading is, without exception, significantly lower than for a time deal, but here we again run into the problem of lack of research. About all we know is that ligaments can indeed suffer fatigue failure (which will be made manifest as a slow, growing tear), and that they suffer it significantly faster if the stresses that said ligament takes are out of plane with its fibril reinforcements (this is fairly intuitive, and is probably why throwing hard breaking balls is bad for most pitchers). Apart from that, it’s all a bit up in the air.

What doesn’t help is that all pitchers aren’t created equal, in both pure ability and their bodies’ capacity to take punishment. Biological parameters are one of the few things that actually turn up as a true bell curve, and so we’ll have fragile guys, average guys, and indestructible guys in the pool of pitching talent (NB: for the most part, the really breakable pitchers will never get as far as the majors before blowing out their arms). Mark Prior was said to have perfect mechanics until his arm exploded repeatedly, but that doesn’t actually mean the people who said so were wrong. Pitching is an exceptionally violent activity, and a ‘perfect delivery’ will not reduce stress to zero or anywhere close to it, it will merely minimise the damage done while throwing a baseball at 90+ mph, or with obscene spin, and Mark Prior could have been doomed from the start.

So. We don’t know how much stress goes into each element which might fail, we don’t know how much it would take them to fail in the first place, and even if we did we wouldn’t know where a specific pitcher might fall on the bell curve of ligament toughness anyway. Oh dear.

How do we tell if a pitcher is going to get hurt then?

Well, we wait for them to start hurting, and if it’s bad enough, they put them through an MRI and look for tears. If they find them, it’s rehab/surgery time. Otherwise, it’s back to the grind until they actually break.

No educated guesses?

Well, yeah, you can make some, and this is really all the experts are doing, unless they’re holding back key information from academia at large. Watching for guys with painful looking deliveries is a start. Fransisco Rodriguez instantly jumps to mind. Liriano is another example, and he’s one of the few guys I’m comfortable with predicting future injury problems before if he keeps throwing the same way he does (after all, he’s already busted his UCL once). Honestly, if you start watching closely enough, your guess is as good as anyone else’s. It will take a lot of research and work before anybody’s really qualified to look at a pitcher throwing, stick the numbers in a computer, and give him [x%] chance of damaging [ligament y] in the next 10,000 pitches. I can’t wait for it to happen, though.

Man, that was a lot of writing, and I didn’t even touch on some of the subjects I’d have liked to, like development and the injury nexus. I think I’ll leave it at that, anyway. Feedback is more than welcome.

Graham MacAree is currently working on a Masters degree in Biostructural Engineering at Cambridge University in the UK, specialising in structural failure of cartilagenous material