Tall and Fall Versus Drop and Drive Strategy in College Baseball Pitchers for Velocity and Elbow Valgus Torque

Abstract

Background:

Depending on anthropometrics and coaching style, pitchers are taught to pitch with a stride strategy that are traditionally classified as “tall and fall” or “drop and drive” for the purpose of maximizing pitch velocity.

Purpose/Hypothesis:

The purpose of this study was to determine the effects of stride strategy (tall and fall vs drop and drive) in college baseball pitching on pitch velocity and elbow valgus torque. It was hypothesized that pitch velocity and elbow valgus torque would increase as pitchers aligned more with the tall and fall technique.

Study Design:

Controlled laboratory study.

Methods:

Markerless motion capture data were recorded on 64 collegiate pitchers (height, 1.89 ± 0.06 m; weight, 93.06 ± 9.44 kg) during game play at the host institution during the 2023 season. Peak magnitudes of body center of mass (COM) vertical displacement were determined using a straight-line trajectory between peak knee height and lead foot contact and used as a continuous variable. Pitchers were required to throw ≥4 fastballs during their outing to be included in the analysis. Multilevel modeling was used to determine associations between peak magnitudes of positive and negative vertical displacement of COM on pitch velocity and elbow valgus torque. Every fastball throughout the season with biomechanics data for each pitcher was included in the multilevel model.

Results:

Fastball velocity was mean ± SD 90.68 ± 2.90 mph (40.54 ± 1.29 m/s). Mean maximal negative vertical COM displacement was −0.91 ± 0.47 inches (−0.023 ± 0.012 m), which occurred 18.1% ± 5.75% of the way between peak knee height and stride foot contact. Mean maximal positive vertical COM displacement was 1.73 ± 1.14 inches (0.044 ± 0.029 m), which occurred 65.7% ± 7.8% of the time from peak knee height to stride foot contact. Positive COM displacement (β = 0.54; P < .001) and timing of peak positive COM displacement (β = 1.82; P = .023) reduced interpitcher variance by 9.9% and improved the ability of our model to predict fastball velocity. Negative COM displacement improved the ability of our model to predict ball velocity (β = −0.45; P = .021). Vertical COM displacement did not influence elbow valgus torque.

Conclusion:

Increasing vertical COM displacement in either the positive or the negative direction resulted in increased fastball velocity but did not result in greater elbow valgus torque. This indicates that the stride method may be used for performance enhancement but is unlikely to influence ulnar collateral ligament injury risk in college baseball pitchers.

Clinical Relevance:

Clinicians should not use stride mechanics as an injury risk indicator or diagnostic factor in injury etiology for college baseball pitchers.

Keywords

push off pitch velocity elbow valgus torque

Baseball pitching has 2 commonly acknowledged lower extremity patterns: tall and fall (TF) and drop and drive (DD).^3,4 These 2 unique pitching styles are often associated with differing philosophies around how the pitcher strides down the mound. The TF style displays a higher posture and more extended drive-leg knee followed by a drop in the center of mass (COM) closer to stride foot contact (SFC). Maintaining a higher pelvis allows for a higher center of gravity during the stride phase, allowing for the benefit of gravity as the pitcher strides down the mound. This elevation of the pelvis, compared with the drive-leg knee, results in a more vertical trajectory.^29,31 The DD style is characterized by greater drive-leg knee flexion, where the pitcher lands in a front lunge position, with more lead-knee flexion.^8,29,31 Compared with TF, DD allows for a lower center of gravity as the pitcher strides forward, resulting in a longer and faster stride, increasing linear velocity of the COM toward home plate. Both the TF and the DD stride patterns aim to enhance pitching velocity.

The main factors contributing to a pitcher’s preferred movement pattern are thought to be anthropometric^26,34 and where the training occurred, specifically Asia versus North America.^11,13,25 Traditional thinking suggests that shorter pitchers tend to display pitching mechanics associated with the DD technique, enabling them to generate kinetic energy from pushing off the pitching rubber with the drive leg. In contrast, taller pitchers display characteristics of the TF technique, theoretically capitalizing on greater potential energy and longer lever arms to generate ball velocity.^3,4 In either method, pitchers take advantage of specific characteristics to optimize performed motions.³³ Given that both pitching styles produce elite pitchers, investigation is warranted into performance and injury risk implications of each movement strategy.

Regarding injury risk, the only current research analyzing stride strategy on elbow kinetics was a conference abstract that suggests greater elbow valgus torque was produced by the TF technique.⁹ However, it remains uncertain if the impact of ball velocity was included in this factor influencing elbow valgus torque. Additionally, a limitation of the Cheltin abstract data was the use of the Motus sleeve (Motus Global), which has not been deemed reliable for measuring elbow valgus torque.^5,12,17 Other studies have indicated that those using the TF technique are more prone to experiencing injury to the ulnar collateral ligament.^3,4 However, confounding variables such as anthropometrics and ball velocity were not accounted for, which may have influenced the results.^3,4 Furthermore, the most recent research suggests a discrepancy in the categorization of pitching strategy. Beaudry et al^3,4 classified pitching strategies based on the angle of lead knee flexion and the position of the pelvis in relation to the front knee at stride SFC. In contrast, Chen et al⁸ used the 2-dimensional analysis of pelvic trajectory.

Both research groups faced challenges of establishing a clear cutoff point in a continuous variable to categorize pitching styles.^3,4,8 This issue was highlighted by the Chen et al group,⁸ which created a “mixed” group, and Beaudry and colleagues required an additional classifier for those in midranges of lead knee flexion at SFC.⁸ Although historical qualitative categories create useful jargon for communicating among coaches and in informal settings (ie, the initialisms TF or DD), discretizing continuous variables distorts the relationship between the variables of interest.^10,23,30 Considering the various classification schemes, the dichotomization of groups for analysis, and the influence of lower extremity mechanics leading up to SFC,¹⁴ it is necessary to further investigate the effect of pitching style (spectrum of TF vs DD) on performance and injury risk. On the basis of the findings of Beaudry and colleagues⁴, we hypothesized that as college pitchers became more oriented with the TF strategy, defined by a higher COM, interpitcher velocity and elbow valgus torque would increase. Further, we hypothesized that the later in the pitch cycle (closer to SFC) the maximal displacement value occurred, the higher the ball velocity and elbow valgus torque would be.

Methods

This research study received institutional review board exempt approval from the university. In-game, markerless motion capture data were collected at a National Collegiate Athletics Association Division I Southeastern Conference collegiate baseball stadium on 64 pitchers (height, 1.89 ± 0.06 m; weight, 93.06 ± 9.44 kg; right-hand dominant, n = 42) playing for 7 different teams during the 2023 season. Data were collected if they pitched in a game at the host institution. Pitchers were included in the analysis if they threw ≥4 four-seam fastballs in their respective outings where motion capture data were available. Every pitch of the season at the home institution, for both home and visiting pitchers, was captured, and all fastballs thrown throughout the season for each pitcher were used, providing the pitcher threw ≥4 fastballs during the season. The 4-fastball cutoffs were selected to include opposing pitchers who may have only pitched 1 inning at the host institution. Pitchers were excluded if they threw in an underhand/submarine manner, as data from these pitchers would not generalize to most of the applicable population.²

The stadium used for collection hosts an 8-camera, markerless motion capture system (KinaTrax, Inc) to collect pitching data. The cameras are permanently mounted around the playing field and digitally calibrated before each game. Kinematic and temporal data, including event detection, were processed using proprietary algorithms (KinaTrax Computer Vision Model: Human Pitching Algorithm, Version 6.3.9) and paired with pitch performance data gathered using ball-tracking technology (Game Tracking, Version 3; TrackMan). Pitch location was visually inspected by the lead author (K.G.) to ensure they were within 12cm of the strike zone and could qualitatively be called a “competitive pitch.” We did not want to draw a hard cutoff at the strike zone border, as pitchers purposefully throw pitches out of the strike zone and useful data can be gathered from pitches very close to the plate. All motion cameras captured images at 300 Hz for full resolution. Computed musculoskeletal metrics, consistent with International Society of Biomechanics recommendations,^37,38 were filtered using a second-order, low-pass variable filter with the trunk and pelvis at 10 Hz, legs at 6 Hz, and arms at 20 Hz, as set by the proprietary software. Variables of interest extracted were maximal elbow valgus torque (external reference), COM vertical global position, and COM anteroposterior (from pitcher to catcher) global position. Ball velocity was calculated at the point of release. All units are presented in their native form to better transfer to other users of the same software platform. However, we have included SI unit conversions where necessary for fastball velocity and inches.

Defining TF Versus DD

Custom MATLAB (Mathworks) algorithms extracted variables from time-series kinematic data. The author group collectively decided the vernacular of “tall and fall versus drop and drive” was better represented by drive-leg activity during the stride phase than the lead knee position at SFC. Therefore, we chose a method more similar to that of Chen and colleagues,⁸ who tracked the center of the pelvis in the plane from the pitcher to catcher and compared it with a straight line (the mean path). We tracked the COM from peak knee height to SFC, and that path was compared with a straight line drawn from the COM at peak height to the COM at SFC (Figure 1).¹⁶ However, unlike previous work, rather than discretizing into categorical groups,^10,23,30 we took the maximal positive and maximal negative vertical displacement between the path of the COM and the straight-line trajectory and used that as a continuous independent variable. The terminology of “maximal positive and maximal negative displacement” rather than “maximal and minimal displacement” is used in this article because both directions have meaning in representing the spectrum of TF to DD, whereas the terminology of maximum and minimum may result in reader confusion regarding interpretation of less displacement. Generally speaking, positive COM displacement would be associated with the TF strategy, and negative displacement would be associated with the DD strategy. We then calculated the percentage of time between peak knee height (0%) and SFC (100%), where both the positive and the negative maximal displacement occurred.

Statistical Analysis

Four separate multilevel models were run using positive and negative COM displacement to predict ball velocity as our performance metric and elbow valgus torque as our injury risk metric.^1,36 Separate models were used for positive and negative displacement because the mechanism for power generation was different between TF and DD pitching types.^31,34 Therefore, a pitcher benefiting from a lower negative displacement may not benefit from a greater positive displacement and vice versa. For our models predicting velocity, we built progressively more complex models, beginning by adding in our covariate model, including height and mass.²⁰ We then added a level 1 explanatory variable of the pitcher’s COM displacement and maximal displacement timing, while allowing random intercepts to vary across individual pitchers. Next, we allowed the slopes of height and mass to vary across each pitcher. Last, we added a cross-level interaction between COM displacement and height to determine if the pitcher’s height influences the relationship between COM displacement and fastball velocity.

For our models predicting elbow valgus torque, we began with a covariate model including height and mass to account for the linear variance of anthropometrics with intercepts varying across each pitcher.²⁰ We then added our level 1 explanatory variables of vertical displacement of the pitcher’s COM and timing of maximal displacement. That left us with no remaining level 2 explanatory variables because both mass and height resided in the covariate model. Next, we allowed the slopes of height and mass to vary across pitchers, as anthropometric variables heavily influenced within-pitcher torque variance.^6,20 Last, we allowed height to interact with vertical displacement of the pitcher’s COM to determine if pitcher height influenced the relationship between COM displacement and elbow valgus torque. All statistical analysis was performed in R Studio (Version 3.6.1; RStudio Inc).

Results

Mean fastball velocity was 90.68 ± 2.90 mph (40.54 ± 1.30 m/s). Average intra-pitcher velocity standard deviation was 1.09 mph (0.049 m/s). Mean maximal negative vertical COM displacement (DD strategy) was −0.91 ± 0.47 inches (−0.023 ± 0.012 m), which occurred 18.1% ± 5.75% of the way between peak knee height and SFC. Mean maximal positive vertical COM displacement (TF strategy) was 1.73 ± 1.14 inches (0.044 ± 0.029 m), which occurred 65.7% ± 7.8% of the time from peak knee height to SFC. All descriptive values are reported as within-pitcher means rather than the grand mean of all trials.

Level 2 covariates of height (β = 7.75; P = .10) and weight (β = 0.014; P = .73) did not improve the model predicting ball velocity. Negative COM displacement improved the ability of our model to predict ball velocity (β = −0.45; P = .021), where each inch (0.0254 m) of vertical displacement beneath the COM straight-line trajectory (more DD) resulted in a 0.45 mph (0.20 m/s) increase in fastball velocity. The timing at which the peak negative displacement occurred did not influence ball velocity (β = −1.55; P = .36). Allowing height and mass slopes to vary across pitchers did reduce interpitcher variance by 78.7% (7.70 to 1.65), but resulted in an unstable model and did not improve the predictability of ball velocity (Table 1). Therefore, we did not proceed to add cross-level interactions into this model. In total, 52 pitches were not included in this analysis because maximal negative COM displacement occurred just before SFC, rather than during the stride when the “drop” in DD is considered.

Table 1

Negative COM Displacement Model Summaries^a

	Intercept	Covariate	Fixed Predictors	Random Slopes
Intercept	90.78^b (0.36)	77.30^b (8.22)	74.84^b (8.27)	74.95^b (8.11)
Height, m		6.32 (4.69)	7.68 (4.71)	7.05 (4.63)
Mass, kg		0.02 (0.04)	0.01 (0.04)	0.02 (0.04)
Negative COM displacement			−0.45^c (0.20)	−0.30^d (0.11)
COM displacement peak timing, %			−1.55 (1.68)
AIC	7410.76	7411.98	7407.75	7414.39
Log-likelihood	−3702.38	−3700.99	−3696.88	−3696.19
Pitches, n	2116	2116	2116	2116
Pitchers, n	64	64	64	64
Interpitcher variance	8.00	7.71	7.70	1.65
Intrapitcher variance	1.69	1.69	1.68	1.68

A fixed predictor model best represented our data, and those estimates are presented. Independent variables are presented as beta estimates and (standard errors). Negative COM displacement is maximal negative vertical displacement of the COM during the pitch in inches. COM displacement peak timing percentage is the percentage of time between peak knee height and stride foot contact when the maximal negative COM displacement occurs. AIC, Akaike information criterion; COM, center of mass.

Indicates P < .001.

Indicates P < .05.

Indicates P < .01.

Adding level 2 covariates of height (β = 9.06; P = .050) and mass (β = 0.013; P = .74) improved the overall model (ΔAkaike information criterion [AIC], –1.18) predicting ball velocity, with height being the driving contribution. Positive COM displacement (β = 0.54; P < .001) and timing of peak positive COM displacement (β = 1.82; P = .023) reduced interpitcher variance by 9.9% and improved the ability of our model to predict ball velocity. Allowing random slopes for height and mass resulted in an additional 76.7% (7.02 to 1.63) reduction in interpitcher variance, but the model had unstable convergence and an increased AIC of 5.46 over the level 2 explanatory model (Table 2). Therefore, we did not proceed to add a cross-level interaction to this model.

Table 2

Positive COM Displacement Model Summaries^a

	Intercept	Covariate	Fixed Predictors	Random Slopes
Intercept	90.70^b (0.36)	72.41^b (8.04)	69.16^b (7.82)	67.98^b (7.50)
Height, m		9.06^c (4.60)	10.13^c (4.48)	9.92^c (4.28)
Mass, kg		0.01 (0.04)	0.00 (0.04)	0.02 (0.04)
Positive COM displacement			0.54^b (0.10)	0.56^b (0.10)
COM displacement peak timing, %			1.82^c (0.80)	1.92^c (0.80)
AIC	7588.56	7587.39	7556.42	7561.88
Log-likelihood	−3791.28	−3788.69	−3771.21	−3768.94
Pitches, n	2168	2168	2168	2168
Pitchers, n	65	65	65	65
Interpitcher Variance	8.16	7.79	7.02	1.63
Intrapitcher Variance	1.69	1.68	1.66	1.66

A fixed predictor model best represented our data, and those estimates are presented. Independent variables are presented as beta estimates and (standard errors). COM displacement is maximal vertical displacement of the COM during the pitch in inches. COM displacement peak timing percentage is the percentage of time between peak knee height and stride foot contact when the maximal COM displacement occurs. AIC, Akaike information criterion; COM, center of mass.

Indicates P < .05.

Indicates P < .001.

In predicting peak elbow valgus torque, covariate height (β = 72.45; P = .09) and mass (β = 1.30; P < .001) were significant predictors of elbow valgus torque in a model with random intercepts across pitchers, accounting for a 50.88% variance reduction. Neither peak negative COM displacement (β = −0.39; P = .60) nor the timing of when that occurred (β = −2.68; P = .68) helped improve the model. Similarly, neither the peak positive COM displacement (β = 0.14; P = .82) nor the timing of when that occurred (β = 1.38; P = .80) helped improve the model.

Discussion

Our data show that taller and heavier pitchers both throw harder and experience greater elbow valgus torque. After accounting for anthropometrics, the results of this study indicate that greater vertical displacement of the COM is advantageous for increased fastball velocity, regardless of whether a pitcher displays throwing patterns associated with TF or DD. Each inch (0.0254 m) of COM displacement below the straight-line trajectory of the COM (more DD) from peak knee height to SFC resulted in a 0.45 mph (0.20 m/s) increase in fastball velocity. Each inch (0.0254 m) of COM displacement above the straight-line trajectory of the COM (more TF) resulted in a 0.54 mph (0.24 m/s) increase in fastball velocity. Given the higher mean and variability in positive vertical displacement of the COM during the pitch, we have weak evidence to suggest there is greater room for performance enhancement the more a pitcher approaches the TF method of pitching. This finding is likely due to maintaining gravitational potential energy for longer during the stride, resulting in a greater rate of energy transfer later in the pitch,³⁵ which should be analyzed with future research. Although approaching more extreme ends of both TF and DD methods resulted in increased fastball velocity, it did not result in greater elbow valgus torque. Resultant increased velocity without concomitant increased elbow valgus torque is somewhat contradictory to current literature^20,24,32; however, the conflict is likely because of the low in-game velocity variability and relatively homogeneous study population. Therefore, drive-leg movement strategies may be employed to increase fastball velocity without increasing elbow valgus torque in college baseball pitchers. However, for both TF and DD strategies, the addition of the COM vertical displacement variable reduced between-pitcher variance more than within pitcher variance (Tables 1 and 2). This reduction in between-pitcher variance likely indicates that an individual pitcher does not sustain substantial benefits by making subtle changes in COM vertical displacement on a pitch-to-pitch basis without a conscious effort to substantially change pitching mechanics. The discrepancy between intra- and interpitcher variance reduction is intriguing, as for both positive and negative displacement there is a large amount of intrapitcher variance in COM displacement from pitcher to pitcher (Figures 2 and 3). However, this interpretation is limited by the in-game nature of this study, where intrapitcher fastball velocity variability was relatively low.

Interestingly, even though the timing of when the maximal positive COM displacement occurred positively influenced ball velocity and negative displacement timing did not, no linear relationship existed between the magnitude of positive COM displacement and when that peak occurred (Figure 4). Conversely, there was a very strong relationship between the magnitude of negative COM displacement and when it occurred (Figure 5), where larger COM displacements required more time to achieve (the “drop” in DD). This relationship between negative COM displacement and when it occurred potentially indicates a moderation or mediation effect that was not explored in the scope of this study. However, the early timing of maximal vertical displacement pairs nicely with recent data by Chen et al,⁷ discovering that ground-reaction forces (GRFs) remained lower earlier in the pitch in TF pitchers. If a pitcher remained tall early in the delivery, he would not experience greater GRF until closer to SFC when he pushed through the drive leg. Similarly, the findings of Chen et al⁷ of increased GRF earlier in DD pitchers could indicate that once a pitcher with greater COM drop reached his low point (Figure 5), he increased his horizontal GRF to push toward the plate.⁷

A fundamental difference between this study and previous work in this area was our lack of categorization of pitchers into their subgroups. This means that every pitcher’s maximal positive and negative COM displacements were included in our models, so it is difficult to determine the “better” strategy. However, as Chen et al⁸ pointed out, the 2 stride strategies differ in acceleration timing. The DD strategy accelerates the body toward the plate sooner than the TF strategy. Further, their mixed group exhibited traits similar to the DD group but were delayed temporally. Therefore, contrasting these pitching styles as opposing techniques may not be necessary. It stands to reason that if every pitcher has a maximal positive and negative COM displacement, both of which are associated with increased ball velocity, pitchers could train to “coil” in a more flexed position as they stride down the mound before accelerating and landing with a more extended front knee.³¹ This strategy aligns with our data showing that negative COM displacement occurs earlier in the stride phase and that peak positive COM displacement occurs approximately 60% to 65% of the way through the stride (Figures 4 and 5). However, even though this strategy may potentially improve velocity, we cannot speculate the effect it may have on command (eg, keeping the ball low in the strike zone).

To the best of our knowledge, our study is the first full article to analyze the influence of stride strategy on elbow valgus torque. Beaudry et al⁴ determined that TF pitchers more often sustained injuries to their ulnar collateral ligaments. In a subsequent conference abstract, they found greater elbow valgus torque in TF pitchers in a college sample using an inertial measurement unit fitted sleeve.⁹ Our present study did not support these findings in a sample of 64 elite college pitchers. These differences are likely due to analytic methods. We did not average across pitches for analysis, we used markerless motion capture, and our data were collected in games, all differing from previous work.^3,4,8

Limitations

This study provides key insight into biomechanical aspects of foundational pitching strategies, but it should be interpreted with several limitations. First, it is impossible to validate in-game markerless motion capture to markered. To date, this particular system has only been validated in gait²⁸ and 1 article in press on baseball pitching.²¹ Only 1 published study has validated a different markerless system in baseball pitching.¹⁹ This was performed in a laboratory setting to compare with a laboratory-based marker system. However, there is no reason to believe the data derived from this markerless motion capture system are inferior to markered data, given markered data struggles with fast longitudinal rotation movements.^15,22 As previously mentioned, the lack of groups resulted in a maximum and a minimum from the same variable used for separate analyses. However, as the work of Chen et al⁸ points out, the existence of TF, DD, and mixed pitching strategies indicates that the positive COM displacement peak likely does not have much influence on the negative COM displacement peak. In our data, positive and negative peak COM displacement only accounted for 20% of the variance in each other, including an artificial barrier at due to the crossing of 0, which would result in positive displacement being registered as negative displacement and vice versa. However, it should be acknowledged that we could not manipulate pitchers to exclusively elucidate the effects of positive versus negative COM displacement without the other occurring in the same pitch. Next, all fastballs were thrown with game effort. This resulted in relatively low intrapitcher fastball variance (SD, 1.09 mph, or 0.049 m/s) compared with interpitcher fastball variance (SD, 2.90 mph, or 1.30 m/s). Therefore, there was less intrapitcher variance to explain, leading to a lower level 1 variance reduction in models. We also reached statistical significance with a sample of 64 pitchers throwing 2168 pitches; however, when plotting relationships, there was clearly interpitcher variance in the relationships, and a strong, qualitative pattern did not visually emerge (Figures 2 and 3). This finding resulted in convergence issues with more complex models, meaning the organized least squares optimization process had a wide range of beta estimates that produced nearly as strong a model. Therefore, these findings should be verified on a separate data set to determine their replicability, and we rate the relationship as weak until further investigation is completed. On the validity of the measurements, we did not normalize our COM deviation measurement to pitcher height. However, straight-line COM trajectories for taller pitchers had steeper slopes and COM displacement did not meet the criteria for normalization with height.²⁰ We could have determined the intra-individual influence of height using a random slope for height, but the model did not converge, meaning we did not reach a precise answer. Therefore, we left COM displacement in its raw inches unit, but we believe the influence of varying pitcher height is minimal because of the standard deviation of pitcher height being only 3% of the mean. Another perceived limitation could be that we did not include any injury information or control for previous throwing arm injury. However, published literature has not found differences in elbow valgus torque or throwing velocity after ulnar lateral ligament reconstruction^18,27; therefore, we do not believe this affected our findings. Last, we opted for a multilevel model approach, which includes the strengths of accounting for the nested data structure and allows random slopes of anthropometric variables; however, it required us to collapse time-series data to a singular maximal displacement value. Statistical parametric mapping would have alleviated this problem, but in setting delimitations, we favored the strengths of the multilevel over analyzing the entire time series.

Conclusion

The notion of TF versus DD pitching strategies can be quantified using vertical COM displacement from a straight-line trajectory of COM at peak knee height to COM at SFC. Greater peak displacement in either direction increased fastball velocity but did not increase elbow valgus torque. Therefore, we have weak evidence to suggest baseball pitchers may use movement strategies from both traditional pitching styles to increase fastball velocity. Stride strategy did not affect elbow valgus torque, therefore coaches and clinicians should not use stride strategy as an injury risk determinant.

Footnotes

Submitted February 3, 2024; accepted July 22, 2024.

The authors declared that they have no conflicts of interest in the authorship and publication of this contribution. AOSSM checks author disclosures against the Open Payments Database (OPD). AOSSM has not conducted an independent investigation on the OPD and disclaims any liability or responsibility relating thereto.

ORCID iD

Gretchen D. Oliver

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