From Derick Velazquez in January to Lance Lynn in November, there were 112 ulnar collateral ligament (UCL) injuries requiring reconstructive surgery — commonly called Tommy John Surgery (TJS) — in the 2015 season. Once a career-killer, UCL injuries have become a much more survivable injury over the last 30 years. And while more and more players are successfully returning from TJS, the procedure itself is a catastrophic event and requires a minimum of a year to recover.

That makes predicting UCL injuries a valuable and worthy endeavor. From the GM to the fantasy owner, being able to steer away from players with early warnings signs of UCL injuries can save a team’s season. The red flags for UCL injuries are not big, though, and many UCL injuries appear from nowhere. But using a large data set, culled from a variety of valuable resources, we can find the tiny red flags, the little baby red flags.

For the past seven months, I have been working with Tim Dierkes and his staff to develop a model to predict Tommy John surgery. The creation of this model required, quite literally, hundreds of thousands of lines of data and hundreds of man hours to combine and connect and test data from a variety of disparate sources. The project also took, as a sacrifice, one of my computer’s CPUs, which burned out shortly after completing some herculean computations. Fare thee well, i7.

[For further details on the process, results, and limitations of this study, please refer to Bradley’s MLBTR Podcast appearance and MLBTR Live Chat.]

The Results

The following is an attempt to quantify the risks that foreshadow potential UCL injuries. It is a combination of FanGraphs player data, Jeff Zimmerman’s DL data, PITCHf/x data, a bunch of hard work, and the keystone data: Jon Roegele’s TJS data, as stored on Zimmerman’s Heat Maps. We also checked our numbers against Baseballic.com, which houses arguably the most comprehensive injury data online.

And while most efforts at quantifying TJS risk have focused on recent appearances or recent pitches, our research takes a step further back and examines injury risks on an annual basis. It seeks to consider the problem from the GM’s view, and not the game manager’s.

The following names are sorted by greatest risk to least. For more details about the columns and the model that has created this data, continue reading after the embedded data.

Click Here for Interactive Tableau and Full Results

The results include three terms that help define where the players fit:

1. Prediction: My method of regressing the variables against pending TJS events resulted in a scale of 0 to 7, where 7 is the season before a player undergoes TJS. So our top player above, Brandon Morrow, ranks a 2.04 out of 7.00, meaning he is nowhere near a player about to absolutely have a shredded UCL. But it is certainly above average.
2. Risk: This is the player’s prediction, divided by the highest possible result, 7. Then, I then multiply the result by the degree of confidence I have in the model, which is the R^2 of .22. R^2 is the statistical tool for checking how much the model explains the variation in the data. It is unconventional to multiply the regression result against the R^2, but I wanted to firmly assert that this model can only explain — at most — 22% of the variation we find in the TJS population. I have additionally listed the results as whole numbers in an effort to limit the perception of precision that a decimal place conveys.
3. Risk+: This is merely a representation of how far above average or below average the player’s risk is. Here, 0% indicates a league-average risk; 100% is 2x the league average; 200% is 3x, and so on.

The Raw Numbers section includes the specific variables involved (explained in further detail in the “The Inputs” section). The Indexed Section includes the same data, but indexed (unless it is binary). That means the average is 100, twice the average is 200, and so on. This is the same as wRC+ or OPS+ or even Risk+, minus the % sign and with league average at 100 instead of 0%.

The Inputs

Over the preceding months, I have tested, prodded, and massaged many numbers. These were the factors that ultimately proved to have the strongest, most consistent relationships with impending TJS:

1. LHP = 1: MLB pitching staffs have been 28% left-handed since 2010. TJS victims are 25% left-handed. Throwing the ball with your right hand — unlike Tommy John, the original — is the first tiny red flag.
2. St. Dev. of Release Point: Previous studies (such as here and here) have attempted to connect release point variations with injuries. In the various models I created, release point had a consistent, while small, predictive power. I did not control for whether or not the pitcher appeared to have a deliberate difference in release points (as in, guys who pitch from multiple arm slots), but the infrequency of that trait does not seem to impact the variable.
3. Days Lost to Arm/Shoulder Injury in 2015: After many different permutations of what constitutes “an injury” or an “arm,” I landed on this unusual definition of an arm/shoulder: It’s everything from the wrist back, including the elbow, shoulder, and — why not — the collarbone. So it’s basically the principle upper-body actors of the throwing motion. No fingers, no legs. So if a player injured this arm/shoulder/collarbone area, the sum of their missed days has a decently-sized red flag planted on it. This is among the most important predictive factors for TJS — which makes intuitive sense. Previous injuries could be a forewarning of a bigger injury, or it could be a contributing factor in creating an UCL injury as pitchers compensate for a tweak or a partially-recovered injury.
4. Previous TJS?: This is a count of how many times the pitcher has gone under the knife. While only a small percentage of pitchers have Tommy John Surgery in their career, it strongly predicts a second surgery. Since 2010, there have been 10,000+ pitchers in the majors and minors combined. In that time, about 560 pitchers in the minors and majors have had TJS, and 57 were repeats. So the ratio of MLB and MiLB players to TJS victims is about 5%, but the repeat rate is over 10%. In other words, TJS begets more TJS.
5. Hard Pitches: This variable is the sum of four-seam fastballs (FA), two-seam fastballs (FT), and sinking fastballs (SI) as categorized by the default (MLBAM) PITCHf/x algorithm. Various attempts to include different pitch types and pitch counts all proved inferior to just a raw count of the hardest three pitches that the PITCHf/x database records.
6. ERA-: This is a park-, league-, and era-adjusted ERA, as reported by FanGraphs. This is the most puzzling part of the model, and the part I am least comfortable about, but a good ERA- (below 100) correlated weakly but negatively with good health. Possible bad data aside, the only theory I can muster to explain this is the idea that pitchers in the middle of good years are more likely to pitch on short rest or make emergency relief appearances in extra-inning games or key late-season games. The elite closer is more likely to pitch the three-consecutive-days marathon than the struggling middle reliever.

1. Age: Here is another iffy variable. Why do older guys without a previous TJS have fewer Tommy John Surgeries? Well, for one, there are fewer older pitchers than younger pitchers, but even after we control for that, we see fewer 38-year-olds going under the knife. The reason is probably that fewer late-career guys see a major UCL tear as worth trying to overcome, and instead call it a career. Few can forget the end of Ramon Ortiz‘s 2013 season, when the then-Blue Jays starter suffered what appeared to be an UCL injury and left the field in tears. Many assumed the 40-year-old righty would end his career then, but Ortiz was fortunate enough to avoid a UCL tear and managed to pitch in Mexico as recently as 2015. Had the 2014 injury been an UCL tear, Ortiz may have just ended his career then. There is also some survivor bias in here. Guys with truly durable UCLs are more likely to make it to their age-35 seasons (and beyond).

Here is a breakdown of the variable and coefficients involved:

It is important to remember that the coefficients here do not visibly represent the strength of each variable because they each use a different scales. For instance, the largest Previous TJS is 2, but the largest Hard Pitches number is 2,488. (That said, Previous TJS is a much more predictive variable.)

P-values, in short, are the probabilities that the given variable is actually meaningless. Traditionalist might bristle at some of the P-values involved there. I personally find the customary cut-off P-values of .10, .05, or .01 artificial and unnecessarily limiting. Others are welcome to disagree.

Why is Player X So High/Low?

So your favorite pitcher is Brandon Morrow, and you’re distressed to see him top the charts here. Let’s look at why:

• In 2015, Morrow missed 155 days after having debris removed from his shoulder. That’s 22x the league average among pitchers that completed at least 30 innings. No other pitcher on this list missed more days. (The average time missed was a little under 7 days.)
• And despite missing most of the year, he still managed to throw a large amount of fastballs because, as Brooks Baseball puts it, he “relied primarily on his Fourseam Fastball (95mph) and Slider (88mph)…” Morrow threw his fastball almost 60% of the time in 2015.
• Lastly, he is just barely on the wrong side of the average age of this group. While the age variable is still an odd one, it is important to keep in mind that TJS culls the herd in the early years. If Morrow were 36 and coming off an injured season of this magnitude, he would still probably be the most likely TJS candidate, but he’d get a few bonus points for proving his UCL could have lasted this long in the first place.

I am pleased to see the likes of R.A. Dickey, Mark Buehrle, and Bartolo Colon at the bottom of the list. They are older pitchers with incredibly steady release points and no recent injury history (Dickey, of course, doesn’t have a UCL in the first place, though obviously the statistical algorithm in question doesn’t take such factors into consideration. We left his name in the results regardless of that fact, for those wondering why, as a means of illustrating the type of pitcher likely to rank low on the list). Of course, these guys, at their age, are perhaps even more likely to be ineffective and retire mid-season than they are to suffer a catastrophic injury, but that is neither here nor there.

Free agent Tim Lincecum also makes the list, and in a very positive way with a risk that is 51% below the league average. While any GM or fantasy owner looking into a Lincecum 2016 season will no doubt be aware of his injury history, it is a great sign for the two-time Cy Young winner hoping to move forward in his likely-post-Giants career. The strongest contributing factors to Lincecum’s risk, however, are his inconsistent release point and the fact he makes a living off mixing up four generally slower pitches. While he has not shown great effectiveness in the past four seasons, avoiding TJS could buy him enough time to find a rhythm with his greatly decreased velocity.

Young Marlins ace Jose Fernandez only missed 35 days due to a biceps issue — if we don’t count the 97 days he missed recovering from TJS in 2015 — but that previous elbow operation combined with his young age suggests he is at greater risk of a second TJS heading into 2016. Again, we need a caveat here to remind us that age, while a predictor of TJS, may not be a good predictor of UCL tears.

Mark Buehrle, Bartolo Colon, and Eric Stults all have negative risk rates. Does that mean they are growing additional ulnar collateral ligaments? Yes. Almost certainly.

Rejected Variables

There are a few variables not included that might seem intuitive or necessary to include, but ultimately did not make the cut:

1. Velocities: Early versions of this model included pitch velocities, but it became apparent after later revisions that pitch velocities — at least given the present variables — was serving as a poor proxy for the number of hard pitches thrown. It follows that guys with fast fastballs throw those fastballs frequently. Take, for instance, freshly Rockie’d reliever Jake McGee, who has a scintillating fastball and rumors of maybe another pitch. Throwing hard may not actually lead to elbow injuries, but throwing a LOT of hard pitches might.
2. Other Pitch Frequencies: Throwing breaking stuff did not seem to have a meaningful relationship with TJS events — at least above and beyond the relationship with hard pitch totals. That does not mean sliders might not result in shoulder injuries or knuckleballers don’t have more fingernail issues, but in the given sample, with the given scope of our investigation, breaking and off-speed pitches did not create meaningful relationships.
3. Altitude of Home Park: Despite the considerable effort it took to match up each player’s home park with their park’s altitude, this attribute appears to have no effect on TJS. One might suspect that environmental issues impact the prevalence of certain injuries, but we can cross off altitude for now.
4. Non-Arm Injuries: I figured leg injuries — given how important legs are in delivering a pitch — or general injuries might have a connection to TJS if in no other way than causing inconsistency in the pitcher’s delivery or release. But once we add in the arm/shoulder injury days into the calculation — along with previous TJ operations — the value of other injuries goes away.
5. Injuries in Previous Seasons: Despite connecting players up with five years of injury history, the unstable relationships (i.e. high P-values) also came with negative coefficient — suggesting an injury in 2013 makes you stronger against a possible UCL injury in 2015. That makes no sense.

Room for Improvement

Without comprehensive dumps from the PITCHf/x data at Brooks Baseball or the Baseballic.com injury database, and without good information on late-career UCL injuries that result in retirement instead of TJS, and without medical records from these players themselves, we will always be playing catch-up with our prediction models. If I am a team considering one of the players listed above, I would defer to medical and pitching experts opinions following a thorough medical examination.

But from our perspective, from the data available in the public sphere, these are the best, strongest tiny red flags I could find. And I hope and expect they will push this field forward. If you’d like to discuss my Tommy John research further, check back at MLBTR at 7:30pm central time, as I’ll be doing a live chat.

A special thanks to Jon Proulx who helped do some very boring data work with me!