As previously mentioned, there really isn’t anything better than getting your hands on new data. That new data smell, the excitement of telling someone that the singular of data is datum. I was really excited to see a follow up study (O’Connell, Hart & Boddy, 2016) to the Bauerfeind study that examined the influence of pitch velocity on arm stress (O’Connell & Boddy, 2016). After reading the article, there were some really surprising findings that I wanted to look into further. More specifically – the claim this study replicated the findings of Post et al (2015), and found a non-significant relationship between elbow valgus torque, and ball velocity.

The study can be found here:

https://www.drivelinebaseball.com/elbow-stress-motus-sleeve-velocity/

But, here are some of the key findings.

- A “very small” relationship between the stress metric, and pitch velocity of
*r*^{2}= 0.21 - “This contradicts a commonly believed hypothesis that when comparing pitchers across a population the ones who throw the hardest also experience the greatest stress. We are only looking at elbow stress, this may not hold up when looking at both elbow and shoulder stress. But this is a very interesting finding nonetheless!”

First of all, I wanted to look at simply the interpretation of these data. The *r*^{2} statistic infers how much of variable A can we infer from variable B. For example, if our *r*^{2} value is 0.5, that represents that variable B accounts for 50% of the variation in variable A. When studying human movement, Vincent and Weir (2012) proposed threshold values of r2 = 0.25 to 0.49 as low, 0.49 to 0.64 as moderate, and greater than 0.81 as strong. However, they included this caveat:

*“Values lower than (0.25), if they are statistically significant, can be useful for identifying nonchance relationships among variables, but they are probably not large enough to be useful in predicting individual scores. However, in conjunction with more than one predictor variable (multiple regression)… even individually modest predictors may be useful”*

*– Vincent & Weir, 2012, page 117.*

The values reported in their text are *r* values, but I have adjusted them to be *r*^{2} values.

So, let’s look at these results – a “very small” relationship, and “similar to the findings of Post et al., 2015”. Post et al (2015) found

*“very small r ^{2} values, indicated that very little of the variance in joint kinetics can be explained by ball velocity… the correlations between ball velocity and both elbow-valgus torque and shoulder external-rotation torque were not significant”*

The values reported by Post et al (2015) were an r^{2 }of 0.04, and p=0.053, or, 4% of elbow valgus torque could be explained by ball velocity, and this relationship was not statistically significant. This is where I have some concerns with the interpretations of the newest study from O’Connell and Boddy (2016). Their study reveals a statistically significant relationship between ball velocity and arm stress, in the low range of correlational strength (*r*^{2} = 0.21). Interpreting these results in their current form, these findings indicate that 21% of arm stress can be predicted using ball velocity alone. So, ignoring any differences in mechanics between pitchers, fatigued state, or pitcher body size, we already have a model that predicts 21% of our dependent variable. As someone who has spent a good amount of time wrestling with data, attempting to prove hypotheses about muscle fatigue, I would typically kill for a relationship with this strength! The findings of the O’Connell & Boddy study do not replicate those of Post et al., 2015 – they illustrate a link between arm stress and pitch velocity – and that is without moving on to some methodological concerns.

The beauty of blogging, and posting open source data to try and further science, is that you live in a state of constant, dynamic, peer review. In many ways, this is vastly superior to the traditional publication model, where studies are reviewed by academics, then go to sit on bookshelves and are never looked at again. When open data is published, it gives others a chance to chime in on the results.

Looking at the data that went in to calculating the r^{2} value of 0.21 between stress and velocity, a couple of things emerge. First of all, not all pitchers have the same contribution to the means. Two pitchers only threw 6 pitches, while one threw 19 pitches. If pitch velocity only indicates 21% of the variance in arm stress, there are clearly other factors at play. If we have an unequal number of pitches between our participants, we’re leaving room for error, by having someone with greater stress contributions from other variables swaying our correlation, one way, or the other. To try and accommodate for this, I removed the two pitchers from the analysis who only threw 6 pitches. I then took the average velocity, and stress, from the top 9 velocity throws from all other pitchers, and put them into the correlation with an n=15. The correlation between velocity and stress now goes up to *r*^{2} = 0.32, or 32% of the variance in arm stress is accounted for by ball speed. Including all of the pitches individually, and only using the top 9 pitches from each pitcher (an n=97), we end up with a correlation of *r*^{2 }= 0.37 between velocity and arm stress.

When your model can account for 37% of the variance between one variable and another, you are definitely on to something. This is statistically significant, and when visualized (Figure 1), it becomes quite clear that a relationship exists. In fact, this number appears to be nearly an exact replica of another study, where Hurd et al., (2012), found a relationship of *r*^{2} = 0.37 between pitch velocity and elbow adduction moment.

So, what about the other variables that the Motus sleeve spits out? I can’t tell you with 100% certainty what arm slot, or shoulder rotation means from these data, but I included ball speed, arm speed, arm slot, and shoulder rotation, in a multiple linear regression model to predict Stress. Once again, I used the top 9 velocity pitches from 15 pitchers to do this analysis.

To put all of the variables on the same scale, I converted them all into z-scores – this will give us standardized coefficients that we can compare against one another in our regression output.

In summary, this model produced an *r*^{2} value of 0.55, with Arm Slot and Shoulder Rotation not being the weakest predictors of arm stress, and arm speed having a negative relationship with arm stress (Figure 2).

SUMMARY OUTPUT | ||||||||

Regression Statistics | ||||||||

Multiple R | 0.74 | |||||||

R Square | 0.55 | |||||||

Adjusted R Square | 0.53 | |||||||

Standard Error | 0.67 | |||||||

Observations | 97 | |||||||

ANOVA | ||||||||

df | SS | MS | F | Sig. F | ||||

Regression | 4 | 49.78 | 12.44 | 28.06 | 0.00 | |||

Residual | 92 | 40.80 | 0.44 | |||||

Total | 96 | 90.58 | ||||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |

Intercept | 0.01 | 0.07 | 0.17 | 0.86 | -0.13 | 0.15 | -0.13 | 0.15 |

MPHz | 0.83 | 0.09 | 9.77 | 0.00 | 0.66 | 1.00 | 0.66 | 1.00 |

ArmSpeedz | -0.47 | 0.08 | -5.90 | 0.00 | -0.62 | -0.31 | -0.62 | -0.31 |

ArmSlotz | 0.16 | 0.08 | 1.97 | 0.05 | 0.00 | 0.32 | 0.00 | 0.32 |

ShoulderRotationz | 0.11 | 0.05 | 2.10 | 0.04 | 0.01 | 0.22 | 0.01 | 0.22 |

It is quite clear that there are other variables not being measured that will help produce a better model of arm stress, but from the main predictor of arm stress right now remains ball velocity. These data collected using the Motus Sleeve, on one of the more advanced populations of pitchers that have been researched, echoes many of the findings that Hurd et al., (2012) produced in a lab setting. It is important to understand how statistics are interpreted, and what assumptions go in to calculating results.

This study goes deeper into understanding the stress on the arm during pitching (as this is tracked from actual bullpen sessions, and not flat ground throws like in the Bauerfeind study). Other studies that have examined the risk of UCL injury in youth pitchers, have identified fatigue, stature, and cumulative pitch effects as risk factors for injury (Chalmers et al., 2015).

**Conclusion**

In summary, pitch velocity shows a significant relationship with arm stress, using the Motus Sleeve. If you throw harder, chances are, you will have higher levels of stress on your UCL. It is important to properly condition and be strong, so you can withstand these stresses. There are many other factors that go in to determining just how much stress is on the UCL, but these must be further studied by hard working groups like Driveline, and researchers in other facilities.

Here are the data I used for the analyses above.

**References**

Chalmers, P. N., Sgroi, T., Riff, A. J., Lesniak, M., Sayegh, E. T., Verma, N. N., … & Romeo, A. A. (2015). Correlates with history of injury in youth and adolescent pitchers. *Arthroscopy: The Journal of Arthroscopic & Related Surgery*, *31*(7), 1349-1357.

Hurd, W. J., Jazayeri, R., Mohr, K., Limpisvasti, O., ElAttrache, N. S., & Kaufman, K. R. (2012). Pitch velocity is a predictor of medial elbow distraction forces in the uninjured high school–aged baseball pitcher. *Sports Health: A Multidisciplinary Approach*, *4*(5), 415-418.

O’Connell, M., Hart, S., & Boddy, K. (2016). Elbow Stress, Motus Sleeve, and Velocity. Retrieved from https://www.drivelinebaseball.com/elbow-stress-motus-sleeve-velocity/, November 4, 2016.

O’Connell, M., & Boddy, K. (2016). Can You Reduce Pitching Elbow Stress Using a Sleeve? Retrieved from https://www.drivelinebaseball.com/can-reduce-pitching-elbow-stress-using-sleeve/, November 4, 2016.

Post, E. G., Laudner, K. G., McLoda, T. A., Wong, R., & Meister, K. (2015). Correlation of shoulder and elbow kinetics with ball velocity in collegiate baseball pitchers. *Journal of athletic training*, *50*(6), 629-633.

Sonne, M.W. (2016). UCL Stress and Velocity Increases. Retrieved from http://www.mikesonne.ca/baseball/ucl-stress-and-velocity-increases/, on November 4, 2016.

Vincent, W., & Weir, J. (1999). *Statistics in kinesiology*. Human Kinetics. Champagne, Illinois.

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