## 3 Results & Discussion
The trade-off is that even though Bat Profile D is least likely to crack, it is also the second most likely to break into multiple pieces. That high probability may be why it is perceived to have poor durability, as noted in previous observations. Overall, Bat Profile C shows to be the least durable profile. Recall from Figure 7 that Profile C has significant durability differences among the wood SoGs, which indicates that SoG is more influential to this profile's durability than to the other profiles. Bat Profile B is a good profile in that it has the lowest mean MPF%. Bat Profile A could also be a good profile as it has a relatively high NF% value, and it also has a relatively low MPF% probability. Utilizing the information from the contour plots in the Supplementary Material, Bat Profile A was also found to have some of the highest  
Figure 7: Probability analysis results of each bat profile by SoG. maximum threshold velocities regarding SPF and MPF among the modeled profiles. The reasonably good correlation of the finite element results with proprietary data implies that the modeling approach can be used to study the relative durabilities of bat profiles. All of the data shown in Table 2 are from finite element simulations of the bat/ball impact where the centerline of the baseball and the centerline of the bat were collinear. Intuitively, these types of collisions would be the \"worst case\" test of bat durability; however, such centerline-to-centerline impacts are rare occurrences in MLB games. It is much more common to see a glancing impact, which results in either a ball hit on the ground (ground ball) or a ball hit high into the air (fly ball/pop-up). The degree of severity of the ground ball or the fly ball depends on how far apart the centerlines of the baseball and bat are at impact. To understand how off-center impacts effect bat durability, finite element models were analyzed where the centerline of the baseball was incrementally translated by factors that were 1/3 of the bat radius at the 2.0 in (5.1 cm) and the 14.0 in (35.6 cm) locations. An illustration of the off-center impact locations is shown in Figure 8. It was based on the finite element model outcomes which state that overall, baseball bat durability generally increased as the baseball impact on the bat moved further away from the centerline of the bat at both locations. Using the information related to off-centerline impacts and how they affect bat durability, allows for a full characterization of baseball bat durability. As the centerline impact resulted in the least durable bats, the baseball bat collisions that are most likely to result in MPFs are the same centerline collisions that are shared in Table 2. Thus, the information shown in Table 2 is a high estimate of how likely the bat is to break for a given impact speed and location scenario. Fully characterizing the baseball bat durability of one unique bat profile to include the effects of glancing impacts would lead to the creation and analysis of 12,420 finite element models (1 profile \(\times\) 4 off-center locations \(\times\) 15 impact locations \(\times\) 23 impact velocities \(\times\) 9 SoG), which can open the door for future studies.