Several days ago, it was reported by several local media outlets that Brandon McCarthy choked down 7,000 calories a day this off-season to add about 25 pounds to his slender frame. This weight gain has a lot of fans excited about the positive impact it could have on his 2009 season.
The expectation is that McCarthy will be stronger and more durable going into 2009 than he has ever been before, but while he may be stronger, he may not necessarily be any more durable.
At 7,000 calories a day, there is virtually no chance that all 25 pounds are added muscle, and even if it is all muscle, that isn't necessarily a good thing.
Since coming to the Rangers before the 2007 season, McCarthy has battled a stress fracture in his right scapula, a strained flexor tendon in his flexor-pronator mass, and a strained flexor tendon in his right middle finger.
McCarthy's injury trouble started with a stress fracture in his right scapula in July 2007. A stress fracture occurs when a bone "flexes" repeatedly - an action obviously not meant for bones. The injury indicates that the bone is being bent, stretched, or pulled by some unnatural movement, but it is not out of the question that natural movement can cause it as well.
Following his 2007 shoulder injury, McCarthy spent the off-season working hard to get stronger for 2008. Word had it that he was up about 15 to 20 pounds. Without a doubt, his focus was on staving off another shoulder injury.
The nature of a stress fracture indicates (but does not guarantee) that a mechanical flaw is responsible. The other two injuries are indicative of a lack of physical fitness.
When throwing a pitch, the arm and hand have to be strong enough to overcome the inertia created by the rest of the body. If the inertia is stronger than the bones and soft tissue, the unfit tissues tend to break down.
THE WEAK LINKS
Strains occur when muscles attempt to handle larger loads than what they are capable of handling.
McCarthy's body got stronger, and thanks to both his increased mass and increased strength, he was creating more intense loads for his elbow, wrist, hand, and fingers. His forearm was not ready for the increased load, and his forearm flexor tendon suffered a very serious strain.
Pitching with a compromised flexor tendon puts the ulnar collateral ligament at serious risk for strains and ruptures, and it's usually pretty painful.
After spending several months strengthening and conditioning his forearm, McCarthy finally returned to the mound. With a stronger forearm, the next injury occurred at the next weak link in the kinetic chain, the flexor tendon of his right middle finger.
DOING THE MATH
If you've followed what I've said so far, you can see how it's important for a pitcher to be strong from his toes to his finger tips.
A pitcher's arm must be strong enough and conditioned to handle the loads generated by the rest of his body, otherwise, even someone with anatomically perfect mechanics can suffer muscle strains, fatigue, tendinitis, or worse.
Richard Durrett of the Dallas Morning News wrote the following on January 20, 2008 during the Rangers pitching mini-camp:
McCarthy said he's worked hard to strengthen not only the area that has proved bothersome, but also the areas around that.
To me, this is far more encouraging than reading that he gained 25 pounds. Perhaps now, his arm is ready to take advantage of the leverage his 6' 7" frame is capable of generating. If it is, McCarthy is primed for a break out season.
It has become somewhat fashionable to blame Mark Connor for Eric Hurley's shoulder problems - a torn rotator cuff and frayed labrum. Without a full blown analysis of Hurley's arm action, though, it is also hard to say with certainty that his mechanics were responsible.
Given the nature of these injuries, though, Hurley's mechanics and hamstring are far more likely than Connor's teachings to be the cause of Hurley's shoulder injuries.
Like any soft tissue in the body, rotator cuff muscles and tendons are torn gradually over time as stress creates micro-tears that build up and compound. There are exceptions, of course, but most of them involve severe external trauma like violent collisions and power lifting.
In pitching, the rotator cuff contracts most powerfully during the deceleration phase as it tries to keep the humerus from twisting and flying out of socket. When the arm moves across the body, the head of the humerus becomes an obstacle to this contraction. This forces the muscles to contract "around a corner" which adds more tension to the muscle than it can create on its own.
A frayed labrum is an early stage SLAP (superior labrum from anterior to posterior) lesion. Later stage SLAP lesions are commonly referred to simply as "torn labrums". The lesions are caused by the compressive force and friction created when the long head of the biceps brachii contracts and pulls directly on the glenoid labrum in an unnatural manner.
Certain arm actions, most notably transverse hyperabduction of the shoulder (scap-loading), can position the head of the humerus as an obstacle to the contraction of the biceps creating extra tension on the labrum where the long head of the biceps attaches.
Since part of the long head of the biceps merges with the labrum, SLAP lesions can sometimes be misdiagnosed as biceps tendinitis. This is was the reported initial diagnosis for Hurley's shoulder injury on July 30, just three days after his final start of 2008. On August 1, the Rangers reported that it was, in fact, shoulder soreness.
ATTACK OF THE HAMSTRING
Hurley was cruising along fairly well before he injured the hamstring of his left leg - his landing leg.
The hamstring of the landing leg experiences an eccentric contraction as the upper body moves forward over the waist. A negative change in the muscle's flexibility can decrease the amount of trunk flexion and/or shoulder rotation that occurs during a pitch. Since the body is less engaged in the deceleration of the arm, the shoulder handles more of the load than it would with normal hamstring flexibility.
Limited trunk flexion or shoulder rotation can cause the throwing shoulder's forward movement to stop early, even though the arm tries to continue moving toward the plate. The force of this action slings the arm across the body and moves the head of the humerus into the path of the muscular contraction as described above.
Hamstrings are notoriously slow-healing muscles, and flexibility can be compromised for a long period even after the muscle is fully functional.
Hamstring injuries will not always lead to shoulder injuries, but they represent a huge risk factor for someone already dealing with a weakened shoulder.
WAS HURLEY'S SHOULDER ALREADY WEAKENED?
The answer to this question simply has to be, "Yes."
In 234 minor league innings over the last two seasons, Hurley worked primarily with Rick Adair, Terry Clark, and Andy Hawkins - one of whom has one of the greatest mustaches in baseball. All three coaches are extremely well regarded; none of them is Mark Connor.
Mark Connor was Hurley's primary pitching coach for about 32 innings, all in 2009. (Hurley had a 7.1-inning rehab start in Frisco near the end of that 32-inning span.) 32 innings is simply not enough to tear the healthy rotator cuff of a professional pitcher - someone whose rotator cuff should be exceptionally strong and well conditioned.
Barring severe external trauma, his shoulder must have been compromised before reaching the Majors and long before he hurt his hamstring.
Hurley likely began damaging his shoulder well before his injuries became apparent. One can argue about the inevitability of a major tear, but excluding an external traumatic event, Hurley's mechanics are the most likely cause of the injuries.
When his hamstring started giving him trouble, his body compensated for that injury, effectively placing more (too much) stress on a rotator cuff that was, in all likelihood, already damaged.
Rotator cuffs simply don't tear suddenly enough to blame Connor for the injury.
Why Hurley was allowed to start that last game (and remain in it for as long as he was) is a different matter entirely.
Fans respond to winning, but different fan bases respond differently. Fan response is most easily measured by a team's revenue stream, the largest factor of which is home attendance - essentially a measurement of demand. It follows that if one can understand the relationship between wins and attendance, then one can reasonably predict revenue at different win levels.
When plotted on a wins versus revenue graph, the function that predicts these points is called a win-curve. (NOTE: The win-curve is actually disjoint. Since modern-era Major League Baseball games do not end in ties, there are no fractional wins. The line itself serves strictly as an illustration because win totals will always be integers.)
The concepts discussed here are elaborated on in far greater detail in Vince Gennaro's Diamond Dollars - a book that I highly recommend if you find that this article sparks your interest (check the Offline Reading list). Mr. Gennaro developed win-curves for all 30 teams as a part of his research into these relationships. Using 37 years of historical data, I attempted to build my own for the Texas Rangers.
This is Part I: Wins vs. Attendance.
PREPARING THE DATA
Each team's win-curve is different. The trick to building an accurate win-curve is identifying trends in the relevant market. In Mr. Gennaro's model, he used a 50-50 weighted average of the previous year's wins and the current year's wins, and he compared that to a per-game average of the current year's home attendance.
He accounted for a "new franchise halo", overall industry growth, new stadium effects, and work stoppages. Due to the small sample size, these effects were identified and generalized for Major League Baseball as a whole, rather than for individual teams.
Based on the assumption that each market behaves differently, it is unreasonable to assume these effects will be the same from market to market, but they do represent a reasonable approximation.
In my attempts to recreate Mr. Gennaro's work, I struggled to capture these effects. Without doing similar studies for the other 29 teams, I tried to find other ways to account for these other attendance factors.
As Gennaro surely did, I played with several different values for my wins variable. Each was represented as a winning percentage to help adjust for seasons of different lengths. Here is the list of my various definitions for wins:
Gennaro's average of previous wins and current wins
Separate variables for previous wins and current wins
Average wins of the three most recent seasons
Separate variables for the wins of the three most recent seasons
For each definition of wins, I tried different weights. In nearly every model, the only significant variable from the group was current wins, though the previous wins variable was significant in a few. In the final model, I chose current winning percentage as my wins variable.
"New Franchise Halo"
This effect was minimal at best with the Rangers. In their first two years, 1972 and 1973, the Rangers averaged fewer than 4,000 fans per home game. Early on, the Rangers weren't very good, but after several years in Arlington, attendance climbed to well above 15,000 fans per game. This is counter to the typical new franchise halo, where a team sees an early boom that tapers off after a few seasons.
The Metroplex area has only had one Major League Baseball franchise, so there is only one from which to develop a model, leaving too few samples to effectively quantify the "new franchise halo" for Dallas/Fort Worth.
To measure industry growth, a simple counting variable was added - a value of 0 in 1972, up to 36 in 2008. Effectively, this functioned the same as a "Years in Area" variable. In the final model, this variable is not significant - p = 0.255 (approx.) - but its inclusion in the model resulted in a smaller standard error and better R-square and Adjusted R-square values than when it was excluded.
New Stadium Effect / Work Stoppages
The Rangers are a unique franchise in this aspect. In 1994, the year they opened the only new stadium in their history, the MLBPA went on strike and the World Series was canceled. The strike continued into 1995, dramatically reducing and effectively negating the new stadium effect that was experienced prior to the strike. As a result, in every regression that was run, 1994 was a positive outlier and 1995 was a negative outlier.
Until 2008, these two seasons were the only outliers in every single model tested.
In 1996, the Rangers began the winningest period in the franchise's history, and in each of the models I ran, the results suggested that this winning period was responsible for the high attendance experienced during that period rather than the new stadium. The coincidence is somewhat striking, and in actuality, it was probably a combination of the two that resulted in the high attendance averages.
I added a value for stadium age (in years) to try and capture the new stadium effect, but even after figuring in Arlington Stadium's prior existence as Turnpike Stadium (making it 7 years old in 1972), the variable failed to be significant.
I tried several other variables to help build a better statistical model. Though none turned out to be significant, the following variables were included at some point during testing:
Years since playoff appearance
Made playoffs (1 or 0)
I also tried to include TMR's Fan Cost Index, but I was only able to find data for the 18 most recent of the 37 seasons. The lack of sample data for this variable resulted in its exclusion from the tested models.
THE FINAL MODEL
When narrowing my model down to the most relevant sample data, I greatly simplified my thinking. Instead of trying to identify individual factors that affect attendance, I realized that, historically, all of this information already existed as a single variable: attendance. It is definitely not the perfect solution, but last season's attendance is the most significant indicator of attendance for the current season.
Based on the models I ran, none was able to predict the huge drop off experienced in 2008. Something that I think might be responsible is the price of gasoline and the increased reliance on gas-guzzling vehicles. Not only did families have less disposable income to spend on baseball games, but the trip to the games became more expensive. Without an effective public transportation solution as an alternative means to get to the ballpark, the mostly commuter fan-base spent their money elsewhere.
After including the previous year's attendance in my models, its significance was immediately apparent, but two other variables remained viable: current winning percentage and growth factor (the counting variable discussed above). Logically, this makes sense.
With this three-variable model, three seasons stood out as dramatic outliers: 1994 (new stadium), 1995 (strike), and 2008 (transportation cost).
It is statistically questionable to eliminate outliers, but in this case, I think it makes sense. I understand that this brings the study as a whole into question, but I'm going to run with it anyway.
In 2009, the Rangers will not be moving into a new stadium; there is no labor conflict on the horizon; and for now, the price of gasoline has returned to a reasonable level.
Because another spike in gasoline prices is possible, 2008 was not removed from the data set. 1972, 1981, and 1995 were all removed because of work stoppages, and 1994 was removed because of the new stadium. (The years that followed still used accurate previous year attendance, so the effects of these events were carried forward to future years even though the immediate effects were not a part of the model.)
The final model included data from 1973 through 2008, skipping over 1981, 1994, and 1995. The dependent variable, of course, was current season average home attendance. The independent variables were the previous season's average home attendance, the current season's winning percentage, and the growth factor described above.
The model says that for 2009, Texas Rangers home attendance can be estimated within 2,646 attendees per game using a chosen win level, the 2008 attendance per game (24,021), and the growth factor (37).
The graph below represents the relationship between wins and attendance for 2009.
The yellow dot marks the 2008 average home attendance, and the red dot marks last season's win total. According to the model, the Rangers should see an increase in attendance over last season for as few as 69 wins.
I think the transportation cost will be a huge factor going into the 2009 season, since the most viable method of getting to the ballpark is to drive.
RELEVANT STATISTICS NOTES
For the final model, the R-square value is 0.904, the adjusted R-square is 0.894, with a standard error of 2,646.
The independent variables have the following p-values: previous attendance average < 0.000002, winning percentage < 0.0008, and growth factor < 0.255.
As discussed above, the removal of the growth factor variable resulted in smaller R-square values and a higher standard error, so it was left in the final model.
IN PART II
In Part II, I will tackle the topic of post-season probability at different win levels. Combined with this article, it will be possible to start turning these numbers into dollars.
"Delayed internal rotation" is the term I use to describe the arm action in which internal rotation does not occur until after the elbow is mostly extended. In some instances, depending on the path of the elbow in space, this delay allows the triceps brachii to actively contribute to the throw. It remains to be seen whether this is beneficial to velocity or health when compared to intertial forearm acceleration which is believed to be more common.
In either case, given sufficient external rotation, delaying internal rotation allows elbow extension to occur in the plane established by the path of the humerus -- a sign of system efficiency, two segments working together -- and in the direction of the throw -- a sign of segment efficiency.
ARM ACTION - EFFICIENT SEQUENCING
As the humerus is accelerated, it generally moves in an arc. This arc establishes a plane of motion along with momentum (and therefore intertia) of the forearm and ball.
The distal end of the humerus (near the elbow) reaches peak forward velocity shortly after the humerus is perpendicular to the line between second base and home plate. At this point, from a laid back forearm position, two actions continue the acceleration of the forearm: elbow extension and internal rotation. Sequencing matters.
When internal rotation occurs prior to elbow extension, whether intentional or not, the forearm moves from the laid back position into a more upright position, changing the plane in which elbow extension occurs.
As internal rotation pulls the forearm further out of a laid back position, the further toward the target the humerus must be for elbow extension to be efficient. While that increases segment efficiency, it decreases system efficiency as the forward velocity of the humerus is sacrificed to achieve this.
When the elbow extends prior to internal rotation, the extension accelerates the forearm more directly toward the target and in concert with the forearm's momentum established by the path of the humerus. In this sequence, elbow extension can maximally contribute to pitch velocity and is a strong link in the kinetic chain.
As elbow extension decelerates, pronation, wrist flexion, and internal rotation work together to powerfully finish the pitch directly toward home plate.
A HALL OF FAME EXAMPLE
Take a look at Nolan Ryan's arm action in the following 4-frame image.
In the first frame, you can clearly see that external rotation has taken place with the forearm trailing the elbow.
In the second frame, Ryan has finished accelerating his elbow, and elbow extension has begun. His forearm is still trailing his elbow in a laid back position.
In the last two frames frames, Ryan's elbow extension is decelerating and nearly complete, internal rotation has begun, rotating his forearm toward the plate. As the pitch is released, pronation occurs, and internal rotation continues through the deceleration phase.
DR. MIKE MARSHALL AND ELBOW PATH
Dr. Marshall has something to say about elbow paths that have a large lateral component. From an email he sent me:
When, after 'traditional' baseball pitchers take the baseball laterally behind their body, they drive their pitching arm back to the pitching arm side of their body, they generate forces toward the pitching arm side of their body that 'slings' their pitching forearm laterally away from their body.
This can be fairly easy to see with the naked eye by looking for a lateral component to the elbow's path. For example, if a left-handed pitcher brings his arm toward third base (or a right-handed pitcher brings his arm toward first base), he must drive his elbow laterally to the other side of his body before he can accelerate toward the plate.
Much of this article assumes a traditional delivery in which the humerus moves in an arc as the shoulders rotate. Depending on exactly how the pitcher moves, this arc can be pronounced or nearly non-existent. A pronounced arc is the result of a greater lateral component in the arm path and creates more centripetal force on the forearm.
Dr. Marshall believes those two effects to be inefficient and injurious because he believes:
the triceps can generate elbow extension force that exceeds the centripetal force of a traditional delivery, and
the lack of an effectual triceps contraction prevents the brachialis from properly decelerating elbow extension.
Frankly, I'm not sure either belief stands up to scrutiny, but I'm also far less qualified than Dr. Marshall in such matters. (It's also entirely possible that I've misunderstood or misstated his beliefs. You can investigate this for yourself at his website.)
IN A FEW PARAGRAPHS
A cursory analysis of primary arm action movements suggests that arm actions are generally more efficient when internal rotation is delayed until after arm extension. This means that less energy is wasted on movement that doesn't directly contribute to pitch velocity.
My conclusion: delayed internal rotation has positive performance implications.
This information, coupled with my previous conclusions regarding UCL health, leads me to believe that there are both performance and health benefits to delayed internal rotation.
[Updated January 2020 to reflect evolution of thought in the 11+ years since the post was originally published.]
Throwing a baseball is not nearly as simple as it seems at first glance. Different parts of the arm and body accelerate and decelerate at different times and different speeds. Analysis of the order and timing of these movements can theoretically help estimate a pitcher's injury risk and isolate areas of inefficiency.
In the throwing motion, the rotation of the shoulders and the drive forward allow the arm to exceed forces that it can generate on its own. Arm action translates these forces into a throw and then must powerfully slam on the brakes in fractions of a second.
In part because the arm is tasked with handling forces beyond what it alone can generate -- engineers might call this a design flaw -- a number of injuries can result from repetitive throwing. The most well known of these injuries is a tear of the elbow's ulnar collateral ligament (UCL).
Significant tearing of the UCL is often the result of an accumulation of micro-tears caused by repetitive near-limit stress, but it can also result from a single catastrophic event - almost never one "bad" pitch.
Valgus force is responsible for the tensile stress that causes these tears. In the elbow, valgus force is measured by its rotational translation: valgus torque. This force "pushes" the forearm and hand laterally, stressing the medial stabilizers of the elbow joint.
The UCL connects the medial epicondyle of the humerus to the coronoid process and olecranon of the ulna, and valgus torque increases the separation between these bony structures. Increased tensile stress on the medial soft tissues in the elbow is the result of these bony structures being pulled apart. This tensile stress, caused by valgus force, is appropriately called valgus stress.
The flexor-pronator mass also anchors the forearm, wrist, and hand to the medial epicondyle. This collection of muscles is comprised of the pronator teres and the wrist and finger flexors. Contraction of the pronator teres causes pronation -- medial rotation of the forearm and wrist. Contraction of the wrist and finger flexors creates wrist and finger flexion, respectively (and hopefully obviously).
When these muscles contract, varus torque is generated. The varus torque contribution from these contractions varies from pitcher to pitcher and even from arm to arm based on the strength of the muscle group, the magnitude of the contractions, and the pitcher's arm action. A strong enough contraction will hold the ulna firmly against the humerus effectively minimizing (potentially even eliminating!) valgus stress in the UCL.
Between 30° and 120° of elbow flexion, the UCL is the primary stabilizer against valgus force.1 Outside of this range, bony structures and other soft tissues take larger roles in stabilization.
Morrey and An showed that, at 90° of flexion, up to 55% of the stabilizing force is contributed by the UCL.5
A study by Fleisig, Andrews et al. estimated the average peak valgus torque to be 64 Nm (Newton-meters), with a normal range between 52 and 76 Nm.4 Building from the Morrey and An study, 55% of this is roughly 35 Nm, with a normal range between 28 and 42 Nm in UCL stress.
This number is in line with the study by Dillman et al. that showed an average failure load of 32 Nm.3 This indicates that pitching frequently results in stress that is far in excess of the observed failure load of the UCL.
These widely cited studies, however, were performed on cadavers and do not measure the varus torque contribution of contracted flexor-pronator muscles. If a pitcher's arm actually relied primarily on the UCL for valgus stabilization, UCL tears would be routine, expected, and basically unavoidable for every single pitch!
In another cadaveric study, Park and Ahmad measured the valgus correction of individual muscles in the flexor-pronator mass. The muscles were electrically stimulated, and their valgus correction angles were measured. Park and Ahmad concluded that the flexor carpi ulnaris and the flexor digitorum superficialis were the primary and secondary stabilizers, respectively.
Somewhat surprisingly, their tests also showed the pronator teres to provide the least dynamic stability.6 This may or may not be true for throwing athletes since they presumably have stronger pronator teres muscles than an "average" cadaver.
Arm wrestling is an example of a non-pitching activity that creates extreme valgus force. Arms are typically positioned at approximately 90° of elbow flexion, and the force is applied in far greater magnitude over a much longer period of time than in pitching. Arm wrestlers have immensely strong forearm flexors which prevent most of this force from stressing the UCL.
Based on a cursory review of media regarding arm wrestling injuries, arm wrestling seems to result in far more injuries to bony structures (avulsion fractures of the medial epicondyle) than to soft tissues (UCL tears), but I found no study that provides concrete evidence.
Those previous two paragraphs are a long-winded way of saying that it can't be valgus torque alone that leads to UCL injuries.
IN THE DELIVERY
Valgus force can be created a number of ways in the delivery including but not limited to:
The equation for calculating torque (t = F*r) tells us that, assuming equal force (F), valgus torque is greatest when the elbow is flexed to 90° because that maximizes the distance (r) from the axis of rotation (humerus). Additionally, the Morrey and An study discussed above also showed that the UCL handles its largest relative valgus load when the elbow is flexed to 90°.
This paints a very alarming picture of 90° of elbow flexion, but would you be surprised to learn that, due to the ridiculously large number of factors involved, there's nothing magical about it? One arm action might hit its peak valgus torque at 75° of flexion. Another might hit its peak at 100° of flexion. And those peaks might not even represent the greatest load on the UCL during the throw!
With 90° representing the position of theoretical maximum valgus torque, however, it is helpful to look at the parts of the delivery that generally involve that level of elbow flexion.
In many different styles of delivery, the pitching elbow is commonly flexed near 90° starting late in the cocking phase and into the early part of acceleration phase. In fact, in a 1992 study by Conway, Jobe et al., 85% of their subjects experienced their greatest pain during the acceleration phase.2
Generally speaking, the late cocking phase is when active external rotation has ended and passive (inertial) external rotation sets the arm in the fully cocked position at or near maximum external rotation. At this point in a typical delivery, the muscles that cross the elbow are generally not doing much to stabilize the elbow, leaving the UCL to deal with a significant portion of the valgus torque generated by the inertia of passive external rotation that turns the forearm over, laying it back behind the elbow.
When it happens after the pitching shoulder starts moving forward, this is called "late forearm turnover". Dr. Mike Marshall originally coined the term "late pitching forearm turnover", and this action occurs in nearly every non-Marshall-approved arm action.
The later in the delivery that active external rotation begins, the later and more violently the late cocking phase will start, leaving less time to get the arm into position for the acceleration phase.
If it occurs late enough -- usually with intent via inverted arm positions -- there's a visible violence to it that can resemble a bounce. This is called "reverse forearm bounce", and it's another term from Dr. Marshall, originally "reverse pitching forearm bounce".
Such a delay also practically guarantees that the upper arm is already being accelerated by the body as the forearm lays back. If the forearm is "outside" of the flexed elbow -- in other words, if the elbow is flexed between 30° and 90° -- when this happens, there is an additional distraction at the elbow due to the centripetal force of the upper arm moving through space.
REDUCING VALGUS STRESS IN THE UCL
To a large extent, pitchers reduce UCL tension with a varus torque contribution from the flexor-pronator mass. Though it isn't entirely clear which of the muscles of the flexor-pronator mass provide the best support, it should be safe to conclude that stronger contractions of this muscle group will result in larger varus torque contributions. As the varus torque contribution of this muscle group increases, valgus stress in the UCL decreases.
Conclusion #1: functional strengthening and conditioning of the flexor-pronator mass is beneficial to the health of the ulnar collateral ligament.
The best way to reduce UCL injury risk, though, is to create as little valgus torque as possible. Going back to the equation for torque -- torque (t) = force (F) * radius (r) -- there are two variables that we can manipulate to effect torque.
Since force is equal to mass (m) times acceleration (a) and mass will be constant since we're talking about a regulation baseball and not planning to chop off any of our fingers, the only way to manipulate force is to reduce acceleration. This is counterintuitive since we're trying to throw the ball pretty hard. Stay with me.
Our other variable is the radius. When calculating torque, the radius is the distance of the force variable from the axis of rotation. In this case, the axis of rotation is the humerus.
With the elbow flexed near 90°, the mass of the forearm, hand, and ball cannot be moved any further from the axis of rotation, so the radius's greatest possible value is when the elbow is flexed near 90°. With the elbow fully extended, the mass of the forearm, hand, and ball cannot be moved any closer to the axis of rotation, so the radius's smallest possible value is when the elbow is fully extended.
Near to full extension gets bonus UCL protection as the joint orientation alters the relative contributions of the joint stabilizers. At less than 20° of elbow flexion, the bony structures in the elbow provide primary stabilization1, dramatically reducing the relative stress in the UCL.
Original Conclusion #2: extending the arm as much as possible prior to external rotation and prior to internal rotation is beneficial to the health of the ulnar collateral ligament.
While this conclusion makes sense from a logical standpoint, at the very least, it is incomplete, overly simple, and too idealistic.
First of all, it fails to consider transitional improvements such as moving to 60° from 90° instead of all the way to 0°, but more importantly, it fails to consider two crucial factors: (1) a reduction in radius could also be achieved by increasing elbow flexion to 120° from 90°, and (2) when the elbow is moving in an arc around the body, an elbow extended to less than 90° of flexion can result in additional valgus torque independent of that created by internal and external rotation as well as a centripetal joint distraction force.
To understand Factor #2, think about the torque equation but realize that the axis of rotation in this case is the thoracic spine. (This is somewhat simplistic since we're focusing on torque at the elbow and not torque at the spine, but it will do for now.) With that in mind, it can be shown that the increased elbow flexion that reduces valgus torque in Factor #1 also reduces the valgus torque described in Factor #2 because it moves the forearm, hand, and ball closer to the spine.
With that, two new conclusions have replaced the original second conclusion.
New Conclusion #2: avoiding 90° of elbow flexion during external and internal rotation is beneficial to the health of the ulnar collateral ligament.
New Conclusion #3: flexing the elbow beyond 90° while the elbow is moving in an arc around the body is beneficial to the health of the ulnar collateral ligament.
Now, if you're trying to get your elbow flexed "inside" of 90° for thoracic rotation, it doesn't make particularly obvious sense to be "outside" of 90° during external rotation. You may not be surprised to find out that Dr. Marshall developed a "pendulum swing" for nearly this precise purpose.
Dr. Marshall's pendulum swing is a full-extension arm action that externally rotates the upper arm, engages the muscles of the flexor-pronator mass, and turns the forearm over early to prevent both late formearm turnover and reverse forearm bounce. He instructs pitchers to pendulum swing their arms to driveline height -- "slightly above the top of the head" -- and allow the forearm to trail behind the elbow. [NOTE: Dr. Marshall's delivery aims to eliminate the arc of the elbow in space during thoracic rotation, so he makes no specific recommendation for elbow flexion with respect to that movement.]
A simpler and more compact arm action that satisfies both new conclusions is the elbow spiral -- described here on the Driveline Baseball blog. The elbow spiral action picks up and turns over the forearm with the elbow flexed "inside" of 90°, setting the pitcher up to fairly easily stay "inside" of 90° during thoracic rotation.
The last implication from these new conclusions is a concept of delayed internal rotation which proposes that internal rotation is not initiated until after elbow extension. This concept may or may not hold water, but here are three photos that appear to indicate the sequence occurs in some deliveries.
IN ONE PARAGRAPH
Valgus torque in the pitching elbow is of great concern when it comes understanding ulnar collateral ligament injuries. External and internal rotation when the elbow is flexed near 90° has the potential to create near-limit stress in the UCL and lead to structural damage. To limit this stress and help protect the UCL from injury, I draw the following conclusions:
Improve functional strength and conditioning of the flexor-pronator mass.
Avoid elbow flexion near 90° during external and internal rotation of the upper arm.
Avoid elbow flexion "outside" of (less than) 90° during thoracic rotation.
Cain EL Jr, Duga JR, Wolf RS, Andrews JR. Elbow injuries in throwing athletes: a current concepts review. Am J Sports Med. 2003; 31(4):621-635.
Conway JE, Jobe FW, Glousman RE, et al. Medial instability of the elbow in throwing athletes. Treatment by repair or reconstruction of the ulnar collateral ligament. J Bone Joint Surg. 1992; 74A:67-83.
Dillman C, Smutz P, Werner S, et al. Valgus extension overload in baseball pitching [abstract]. Med Sci Sports Exer. 1991; 23:S135.
Fleisig GS, Andrews JR, Dillman CJ, Escamilla RF. Kinetics of baseball pitching with implications about injury mechanisms. Am J Sports Med. 1995; 23:233-9.
Morrey BF, An KN. Articular and ligamentous contributions to the stability of the elbow joint. Am J Sports Med. 1983; 11:315-9.
Park MC, Ahmad CS. Dynamic contributions of the flexor-pronator mass to elbow valgus stability. J Bone Joint Surg Am. 2004; 86-A(10):2268-74.