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]]
The Texas Rangers won 87 games in 2009, and the 2009 attendance numbers for Major League Baseball were compiled by Maury Brown in early October.
The model I prepared says that 87 wins should be worth an average attendance of 27,958. According to the data gathered and prepared for the Brown article, the average attendance of Texas Rangers home games in 2009 was 27,641. A difference of only 317 attendees per game translates to an overshot of only +1.15%.
As much as I would like to pat myself on the back for this, I have to acknowledge the extreme amount of luck involved with the startling accuracy of my prediction.
My model came with a sizable standard error attached to it: 2,646 attendees per game. You don't need to be a statistician to recognize how large that is or the uncertainty that it projects. I addressed this briefly in the comments of the original article:
The line in the graph marks the raw estimate based on the information provided by the model. At any given point on the line, the standard error says that the attendance level could be 2,646 higher or lower than the line.
With the reason for the 2008 drop off in question, it is probably unreasonable to expect that attendance will simply rebound to the 2006 or 2007 level. For this reason, I expect that actual attendance will fall somewhere below the line but within 2,646 attendees per game.
The luck of this season will definitely narrow the standard error of the 2010 model. Look for the 2010 model some time in February as the new season approaches.
Kenny Rogers (2001). Hank Blalock (2007). John Rheinecker (2008). Matt Harrison (2009). Jarrod Saltalamacchia (2009). These are the five major leaguers from the Texas Rangers who have been diagnosed with thoracic outlet syndrome in recent history.
Aaron Cook (2004). Kip Wells (2006). Jeremy Bonderman (2008). Noah Lowry (2009). These are the four major leaguers from all other teams who have been diagnosed with thoracic outlet syndrome in recent history. [Note: There may be more, but there aren't many. This is all I could find.]
Texas Rangers 5, Everyone Else 4. The Texas Rangers also had a minor leaguer diagnosed with thoracic outlet syndrome - pitcher John Hudgins (2005).
The definition of an epidemic, according to Wikipedia, is "when new cases of a certain disease, in a given human population, and during a given period, substantially exceed what is 'expected,' based on recent experience."
Recent experience tells us that roughly 10 players have been diagnosed with TOS in the past 9 years. More than half of those players belong(ed) to a very specific population: the Texas Rangers.
Thoracic outlet syndrome (TOS) is fairly common in overhead athletes like swimmers and baseball players. The overhead movement of the arm changes the orientation of the clavicle (collar bone) in such a manner that it may compress the brachial plexus (the nerve bundle the leads into the arm from the neck) and/or the subclavian artery and vein against the first rib.
The compression usually leads to numbness or pain in the affected arm, but it can also lead to blood clots like it did with Aaron Cook in 2004.
Undiagnosed TOS can have very serious health implications. In Cook's case, a clot broke away from the compression site in his shoulder and traveled to his lungs resulting in a pulmonary embolism.
Diagnosis is clearly very important when it comes to TOS. The Texas Rangers, however, have experienced quite a large number of TOS cases in recent years. Here's a brief look at a few reasons why this may be the case.
Access to expert opinion
Dr. Gregory Pearl, of Texas Vascular Associates, is a well-respected vascular surgeon who happens to live in the Metroplex. Dr. Pearl was involved with the TOS cases for Rogers, Blalock, Harrison, and Saltalamacchia - and likely Hudgins and Rheinecker as well. This relationship history and his proximity to the ballclub makes it far easier for Texas Rangers to be diagnosed with TOS.
Kenny Rogers provided the club with a first-hand example of what TOS can do to a pitcher's performance. When Rogers returned with an extra 4-5 mph on his fastball, Dr. Pearl was probably put on speed dial.
Pitchers are a high risk group for TOS compared to position players because of the quantity and intensity of their throws but also because of the way they turn their heads toward the plate. With the previous image in mind, take a look at Matt Harrison.
When the head and neck turn away from the compression site, the brachial plexus and subclavian blood vessels are pulled into the narrowing gap between the rib and clavicle.
For low intensity throws where the head doesn't turn, TOS is less of a concern.
Of particular note are position players Hank Blalock and Jarrod Saltamacchia, each of whom had TOS in his throwing shoulder. To discount their mechanics entirely would be foolish, but I found no reports of TOS diagnosis in any other position player. This suggests, perhaps incorrectly, that something behind the scenes has made a significant contribution.
Weight lifting can produce stress far in excess of what an intense throw can produce, but it's practically impossible to properly perform any exercise and cause thoracic outlet compression at the same time. When bad form enters the equation, though, all bets are off.
Dynamic exercises may contribute an intertial element in a manner similar to that of throwing a baseball. Even these, when performed properly, aren't likely to be significant contributors. As with weight lifting, if they are not performed correctly, they become a risk for TOS and a number of other potential problems.
If training is to blame, it's likely a series of exercises rather than a single one that results in thoracic outlet compression.
Blind, stinking luck
Not to be overlooked is random chance. It is entirely possible that the Texas Rangers have simply been unlucky. It is possible that each affected player was genetically at risk for TOS and would have been diagnosed no matter what team he was playing for. It may be nothing more than luck that has brought these players to Arlington.
So which is it?
In truth, it's most likely a combination of these factors. Given the current state of exercise science, training methods are probably the least likely to blame.
Throwing mechanics and luck combined with having a "resident" expert have likely been equally responsible for the Rangers' having lapped the rest of Major Leage baseball in thoracic outlet syndrome diagnoses.
[Historical TOS Note: David Cone and J.R. Richard, both pitchers, were also known/beleived to have suffered from thoracic outlet syndrome, but both diagnoses were well before the "Dr. Pearl era."]
Yesterday, for the second time in his 3-season stint with the Texas Rangers, Brandon McCarthy was diagnosed with a stress fracture of the scapula. With consideration to the number of muscles that move and stress the scapula when throwing a baseball, it's amazing how rarely scapular stress fractures are diagnosed in pitchers.
In 1987, Texas Rangers pitcher Edwin Correa was diagnosed with a stress fracture in his scapula. Correa never again pitched in the Major Leagues.
In 2003, Kurt Ainsworth, then pitching for the San Francisco Giants, was also diagnosed with a stress fracture in his scapula. Ainsworth recovered but pitched in only 7 more games in the Majors, all in 2004.
The most detailed information that I can find on this type of injury is what I know from McCarthy's previous stress fracture and what I learned from reading "Scapular Stress Fracture in a Professional Baseball Player," a study published in the American Journal of Sports Medicine in February 2007.
The study takes a look at the injuries suffered by an unidentified right-handed Major League Baseball starting pitcher. This pitcher's mechanics were apparently a mess. Prior to his scapular stress fracture, the pitcher had been through Tommy John (ulnar collateral ligament replacement) surgery and a "transient episode of subacromial bursitis" in his shoulder. In the three years that followed his recovery from the stress fracture, this pitcher had surgery on both his elbow and shoulder, though neither was directly related to his scapula injury.
Pitcher X's stress fracture was located on the lower outside edge of the scapula bone, called the lateral border. The doctors who authored the study concluded based on the fracture's location that the likely cause of Pitcher X's stress fracture was "repetitive stress in the area of the teres minor attachment."
Repeated stress on muscles and bones causes them to grow stronger and more resilient over time. When the growth can't keep up with the stress, stress fractures occur in bones and tendonitis occurs in muscles. In the case of Pitcher X, his teres minor grew stronger at a faster rate than his scapula. Eventually, the stress fracture developed.
The teres minor attaches the lateral border of the scapula to the outside edge of the back of the humerus (see the diagram). It is one of the muscles of the rotator cuff, and its primary function is external rotation. The teres minor is stretched by internal rotation when the back of the humerus turns away from the scapula. It is also stretched as the humerus moves away from the scapula.
In the delivery, the rotator cuff contracts most powerfully during the follow-through as it tries to stop the arm from twisting and flying out of socket. The faster the humerus is moving away from the scapula and the greater the rate of internal rotation, the more powerful the contraction must be to maintain joint stability.
Brandon McCarthy's follow-through is a little unique in this regard. I missed it when I reviewed his mechanics last month because I wasn't looking for it. Of course, maybe I'm just seeing what I want to see. Here's the clip I used for my original analysis:
Notice that, after release, McCarthy's arm continues to move away from his scapula and towards his head. Even at 210 frames per second, it only lasts for a few frames, so look closely. You might even see his shoulder blade "hump up" a little around this time.
This high-intensity eccentric contraction stresses the teres minor muscle more than the other rotator cuff muscles because its scapular attachment is the furthest from the joint.
A reasonable outlook
Rangers general manager Jon Daniels has reportedly said that McCarthy will not pick up a baseball for several weeks. That might be a bit of an exaggeration, depending of course on the severity of the stress fracture. McCarthy himself said the pain has been there for a while and that he feels like he did in 2007.
McCarthy suffered and recovered from an injury similar to this one back in August/September 2007. I can not say how similar because I do not know the exact location and severity of either his 2007 or his 2009 stress fracture. McCarthy recovered from the 2007 injury fairly quickly and missed only a month of Major League action.
Rest is the only way to recover from a stress fracture. While the bone heals and gets stronger, the offending muscle atrophies and weakens - killing two birds with one stone. Often times, the pain will subside long before the bone fully heals, sometimes months after diagnosis. It might be that McCarthy's original stress fracture never healed.
I believe the Rangers are more or less "on the lookout" for injuries like this with McCarthy, so I feel that this injury is probably an early-stage stress fracture. They will probably keep him from throwing until scans no longer show signs of the fracture. Hopefully, this is no longer than 3 or 4 weeks.
Last month, I said that if McCarthy could stay healthy and have success with his mechanics, there was no reason to change them. I now believe there's sufficient reason to start that process. McCarthy and the Rangers need to give serious consideration to making major changes in his delivery.
[I suspect that Pitcher X is Darren Dreifort, though the article was written by doctors in Baltimore.]
In limited action in 2008, Nelson Cruz finally started hitting Major League pitching to the tune of .330/.421/.609. Given the small sample size, people openly questioned whether he had actually turned the corner.
Through Friday, April 17, 2009, Cruz was off to a .282/.356/.718 start, more or less a continuation of his 2008 success. Using PITCHf/x data through the first 10 games of 2009 and some stats from Nelson Cruz's FanGraphs profile, here's a little plate discipline analysis to see if it supports his impressive start.
The black boxes in these charts are approximations of the actual strike zone. Based on average PITCHf/x data for Cruz's at-bats, the bottom of Cruz's strike zone is about 1.6 feet from the ground, and the top of his strike zone is about 3.4 feet from the ground. The left and right edges of the zone are approximated at 1 foot to either side of the plate based on half the plate's width (8.5 inches) plus some wiggle room for pitches that scrape the black (3.5 inches). (NOTE: All location graphs are from the catcher's perspective.)
The first chart shows us what Cruz has been swinging at by location and by pitch type.
Based on this chart, Cruz has mostly been swinging at strikes. According to his O-Swing% at FanGraphs, only 20.2% of these pitches are outside of the strike zone. That is the lowest of his career. Since his 2006 Rangers debut, his O-Swing% has dropped every season - 29.4% in 2006, 26.5% in 2007, and 23.1% in 2008.
Notice that Cruz hasn't swung at many pitches near the bottom or near the outside edge of the zone. This has helped Cruz lay off of breaking pitches away. Through 10 games, Cruz had not swung at a single pitch off the outside edge of the plate.
The second chart shows us what Cruz hasn't been swinging at by location and by pitch type.
This chart fills in the obvious holes from his swings chart. There are a lot of pitches in the zone low and away that Cruz has not swung at. According to his Z-Swing%, Cruz has swung at 78.5% of pitches in the zone. Based on that stat, the chart doesn't exactly match up. It appears that he's been taking pitches in the zone more often than 21.5% of the time. This could be the result of the PITCHf/x strike zone not matching up with the zone being called by the umpires.
Without getting in too terribly deep, here's a quick look at the righty-lefty split broken down by location and pitch result. The small sample against lefties in the first 10 games doesn't give us much to look at, but the righties scatter plot is interesting.
The PITCHf/x strike zones for Cruz appears to be pretty accurate. Keep in mind that some of the strikes outside of the zone were swung at.
Let's look at Cruz's Z-Swing% again. My rough count based on my unofficial strike zone suggests a 61:23 ratio or a 72.6% Z-Swing%, which would still be a career high for him. From 2006 through 2008, Cruz's Z-Swing was very steadily between 70% and 71%.
This year, he's swinging at strikes more often, but he's also swinging at fewer pitches overall - 46.8% in 2009 versus 50.8% in 2006, 49.6% in 2007, and 47.1% in 2008.
April 19, 2009 Update: Cruz has reached base safely in all 12 games this season on 13 hits and 7 walks against only 10 strike outs. He is now hitting .289/.377/.667.
The numbers and charts say he's being more selective than ever. This can only be good news for Cruz, the Texas Rangers, and their fans. I believe that Nelson Cruz has finally arrived.
Some other observations:
Very few pitches have been thrown low and in to Cruz. I wonder if his AAA scouting report says to stay away from that quadrant.
Righties stand a good chance of getting Cruz to put the ball in play by throwing him up and in.
Cruz's first-pitch strike percentages by year: 62.3% in 2006, 63.4% in 2007, 52.6% in 2008, 51.0% in 2009. It's a small sample size and might not mean anything anyway, but it is interesting.
One step further, Cruz is seeing fewer strikes than ever: 52.5% in 2006, 52.4% in 2007, 50.2% in 2008, and 45.7% in 2009. Combined with the stat above, I'm pretty sure this means something.
One concern: what happens when opposing pitchers start hammering that outside corner?