Eric Cressey, of Cressey Performance, published a series of posts on his personal blog over the past two weeks that takes a fairly comprehensive look at the elbow. His series progresses through anatomy, pathology, and injury before discussing how to go about protecting pitchers.

The first three parts are factual in nature, heavy on scientific facts but without beating you over the head with mumbo-jumbo.

Part 4 of Cressey's series builds on the information from the first three. He uses a 4-category approach to make general suggestions for keeping a pitcher healthy. The last three categories are spot-on, but I have a few issues with his ideas about injurious pitching mechanics.

To kick it off, Cressey shows a photo of a 5' 7" pitcher and a 6' 7" pitcher standing side-by-side and says, "Anyone who thinks these two are going to throw a baseball with velocity and safety via the same mechanics is out of his mind."

This is a very interesting statement to me, since Cressey seems to be suggesting that "safe" mechanics for a tall pitcher are different from "safe" mechanics for a short pitcher. I may be out of my mind, but that's just plain wrong.

Now, in real life, dealing with two different pitchers, yes, safe mechanics for one pitcher aren't necessarily safe for another pitcher, but height has as much to do with it as a pitcher's choice in footwear. The basics of functional anatomy do not vary with a person's height.

Things that will cause variations in "safe" mechanics are long-term training and congenital joint laxity. Long-term training is a very general term that I am using here to refer to how the body has adapted over time to throwing a baseball. This encompasses principles involving conformational changes in the skeleton (i.e. humeral retroversion), increased bone density, changes in muscle contractile force, and changes in tensile strength of ligaments. Congenital joint laxity can be thought of as natural flexibility, and it varies from person to person.

Cressey might as well have included a photo of any two pitchers standing side-by-side.

Kinetically speaking, shorter people have shorter levers, so an equal amount of force applied at a given joint results in less torque for a shorter person than for a taller person. This, however, is unavoidable.

The safest mechanics for an individual will be the same no matter how tall or short that person is. There is no height at which certain mechanics become safe and others become unsafe.

Cressey then discusses two biomechanical studies that correlate horizontal shoulder adduction and external rotation, respectively, to elbow valgus stress. Neither study supports his proposition, but the points are well taken, if somewhat incomplete.

My chief complaint about studies like these is that they focus mainly on peak torque values instead of the loading rates of those torques (i.e. How much time did the joint tissues have to adapt to the stress?). This is a topic for another day, though.

He follows this up with a discussion about balancing health-risk with performance as it pertains to deception and pitch movement. This is an excellent point, but it's one that I think far too many young pitchers fail to understand. This is also a topic for another day.

Cressey has two more posts in this series, and if you aren't already a reader of his, I highly suggest you become one. Click here to visit Eric Cressey's blog.

Jeff Wilson has reported that Brandon McCarthy has been placed on the 7-day DL in Oklahoma City with a stress fracture of his right scapula. Unbelievable.

Seriously unbelievable. Bones get stronger after stress fractures. It's part of the healing process sometimes referred to as overcompensation (or supercompensation). Bones respond to stress and stress fractures by growing thicker, stronger, and more dense.

This is the third diagnosis of a stress fracture in McCarthy's shoulder. Having been through this twice before, McCarthy's shoulder blade should be plenty strong enough to withstand two months of pitching, but it apparently isn't.

Unbelievable.

What is believable, though? I see a couple of possible explanations.

The original stress fracture from 2007 simply may not be healed. If this is the case, the cause is likely dietary, but it could be that the injury has never been given sufficient time to heal. Stress fractures often become pain-free well before they are actually healed.

Another explanation is that the problem is not actually a stress fracture. Soft tissue is much more susceptible to re-injury than is bony tissue, and the location of McCarthy's injury is a confluence of soft tissue that literally encapsulates the glenohumeral joint.

The recommendations here are running short.

McCarthy attempted a mechanical overhaul, but it doesn't seem to have accomplished its chief goal despite leading to a sparking ground ball rate at Oklahoma City where McCarthy has been excellent.

At this point, it looks like mechanics aren't McCarthy's real problem. If it isn't his mechanics, the culprit is one of the following: diet, strength/conditioning, and genetics.

Genetics, of course, can not be changed, but the other two can be addressed.

In addressing the diet, there are three things to watch for, and they all go hand-in-hand. The goal is improved bone density so the main focal points are calcium, vitamin D, and pH balance. I am not a dietician or a nutritionist, so I will stop short of making specific recommendations.

In addressing potential strength and conditioning issues that may be contributing to McCarthy's problems, a recently published DVD set contains just about everything anyone would ever need to know ranging from prehab and diagnosis to rehab and high performance.

You (and Brandon McCarthy) should check out Optimal Shoulder Performance.

[[Update: The evidence is apparently quite clear. This is, in fact, a scapular stress fracture. Someone who has seen recent video of McCarthy believes that McCarthy had fallen back into old mechanical habits.]]

In winning 87 games last season, the Texas Rangers drew an average attendance that was nearly what my model predicted for that win level -- predicted attendance: 27,958 per game; actual attendance: 27,641 per game.

For this year's model, there have been no tweaks to the methodology. I have simply added last year's data to the model. For details on my wins-attendance model, click here. It is based on the model presented by Vince Gennaro in his book Diamond Dollars: The Economics of Winning in Baseball.

Here's this year's model of Attendance versus Wins:

At 2009's level of 87 wins -- represented by the red dot -- my model predicts the Rangers to crack the 30,000 mark for average attendance at 30,593 per game. The model also predicts the Rangers to maintain last year's attendance level with as few as 73 wins -- represented by the yellow dot.

Regression Notes

The standard error is down from last year's 2,646 attendees per game to 2,602. The R-square and Adjusted R-Square values are nearly identical.

The growth factor variable is slightly more significant than last season, but still seems more significant to the calculations than its relatively low t Stat value (1.326) suggests. Removing it from the regression results in smaller R-Square values and a larger standard error.

Playoff Chances

Using a logistics regression for the past 12 seasons (since the Tampa Bay Rays franchise came into existence), I took a look at the odds of making the playoffs for a given win level. This is based on historical probability rather than a super complex mathematic system. For a more in-depth explanation of this process, click here.

Josh Hamilton predicted that the Rangers would win 96 games. Historically, 96 wins gives an American League West team a 94.54% chance of making the playoffs (94.50% across the entire American League).

Team president Nolan Ryan predicted 92 wins. Those four wins dramatically change the team's playoff chances. 92-win AL West teams can expect to make the playoffs 62.77% of the time, while a 92-win team from any AL division can expect to make it 68.44% of the time.

Various projection systems predict the Rangers to win between 81 and 87 games. This represents quite a wide range of playoff chances -- AL West: < 0.50% to 8.39%; AL overall: 0.73% to 14.02%.

After about the half-way point in a season, the results from such a logistics regression become fairly meaningless for that season. At that point, the division and wild-card races are taking firm shape, and a daily look at the standings tells a much more complete story.

[Note: When properly applied during the off-season (or at the trade deadline), though, playoff probability added can be used to more accurately estimate a player's true dollar value to an organization. This was to be explained in Part III of my Texas Rangers win-curve series, but I stopped at Part II. I may take another crack at finishing that series this year.]

For a long time, I've been frustrated by spin movement (Magnus effect) charts because they don't genuinely show how much a pitch actually moves. These charts perfectly demonstrate how the spin of the ball changes its path, but they don't show how velocity adds a vertical element to the pitch's movement.

Take this chart for example. These are the pitches thrown by Texas Rangers LHP Derek Holland during September and October of last season.

Even though they are much slower pitches, Holland's change ups are located in the exact same place on the graph as his fastballs. If his fastball and change up start with the same trajectory, the change up will always cross the plate lower than the fastball. I wanted to capture this on a chart, so I put gravity back into the equation.

Using Gameday's physics data (initial position, initial velocity, acceleration), I calculated how long each pitch was in the air. Keep in mind, though, that PITCHf/x starts at 50 from the plate and ends just in front. The mapped data covers only about 48 1/2 feet.

With the flight time for each pitch, I calculated the drop caused by [sea-level] gravity. After converting this number from feet to inches, I added the vertical spin movement. Here's how it turned out:

Success. The change ups now appear below his fastballs. The chart reflects not only gravity's effect on a pitch, but it also helps separate pitches by velocity, making identification a little bit easier.

This chart does not replace virtualizations by any stretch of the imagination, but I think it does show how different two pitches can be from each other even when spin movement alone can't show it. Taking this a step further could lead to a "hitter's decision" chart that would represent how different the pitches look at a certain time or distance from the plate.

The gravity charts are now available for all pitchers in TexasLeaguers.com's PITCHf/x Database.

[[Update: On April 24, 2010, the Spin Movement w/Gravity charts were updated to reflect gravity's effect from y = 40 to y = 1.417. This change was made based on the information that can be found at Alan Nathan's PITCHf/x site: MLB Extended Gameday Pitch Logs: A Tutorial]]

If you're a betting man, you should know that the odds are good that this won't be my last article featuring the mechanics and health of the Texas Rangers starting pitcher Brandon McCarthy.

As my favorite subject, his mechanics have spent a lot of time on my computer monitor playing forward and backward, in slow motion, and in still shots. As a result, I have a small tendency to see a little bit of McCarthy in just about every pitcher. Every once in a while I run into a pitcher whose mechanics have a lot in common with him.

Meet University of Texas at Dallas junior Marvin Prestridge.

In light of recent mechanical changes, Prestridge doesn't look much like McCarthy does these days [Edit: this may not actually be true since I haven't seen high-speed video of McCarthy's new mechanics], but when I pulled up the video I shot of McCarthy last spring, the similarities were striking. The angles aren't quite the same, so you may have to use a little imagination in places.

They don't look too similar at the top of their leg kicks, but they appear to have a similar degree of reverse rotation (turning their backs to the plate). McCarthy is more compact, and Prestridge lifts his knee much higher.

At hand-break, their mechanics are starting to run together. McCarthy sits a little lower on his back leg. Prestridge breaks his hands much closer to his body.

Before foot plant, this is the frame where their elbows stop moving upward and backward (toward 1B), and their arms begin external rotation. You can clearly see McCarthy's inverted W and that Prestridge's arm is below shoulder level with an extended elbow. Both pitchers have their arms well behind their shoulders.

I much prefer Prestridge's method of picking up the baseball to McCarthy's method from last spring. As a part of the changes he has made to his mechanics over the past 9 months or so, McCarthy's current pick-up features a full arm swing that positions his pitching arm much like Prestridge's arm.

By the time they hit foot plant, there's only one evident difference between the two: Prestridge is pulling his glove arm back toward second base. McCarthy's glove arm is essentially dead weight, while Prestridge's arm helps create additional rotational force through his shoulders.

Again, the only difference is the glove arm action and position, though it appears that Prestridge has a greater degree of trunk tilt toward 1B.

At this point, the pitchers are literally inches away from letting go of the baseball. Prestridge is able to reach a little more toward vertical, thanks to his 1B-side trunk tilt.

After release, the pitching arm continues internal rotation while the body tries to keep the arm from flying out of socket. This frame attempts to capture the moment where internal rotation stops.

What's clear in this frame is that McCarthy's arm continued to fly forward, winding up closer to his head than to his chest. Prestridge's arm, on the other hand, is still essentially at shoulder level. This is the most significant difference between the two deliveries.

With McCarthy's arm positioned like this, the head of his humerus is placed in an anatomically questionable position while his rotator cuff applies extreme compressive force at the glenohumeral joint, driving the humerus awkwardly into the scapula.

Prestridge's arm is in a more natural position at this point, and as a result, I do not view his mechanics as risky despite their on-the-surface similarity to McCarthy's old, problematic mechanics.

[Edit: For reference, here's a link to the video I shot of McCarthy at spring training in 2009.]