Shoulder Hump:

The hump is where a mass of muscles attach to the bear's backbone and give the bear additional strength and power.

P.Atrox : Absent

U.Arctos : Present

Edge : U.Arctos

Scapula Shape Index:

It's scapula width/forelimb length ratio.Higher score indicates greater muscle attachement on the shoulder joint as well as greater ability to make certain movements like full-functional upper extremity movement including protraction,retraction,elevation,depression,upward rotation,and downward rotation all else being equal.

P.Atrox : 21%

U.Arctos : 26%

Edge : U.Arctos

Scapula Length Index:

Scapula length divided by forelimb length. Higher score Indicates greater speed of movement via relative proportions of components of the proximal forelimb and exertion of greater force.

P.Atrox : 30%

U.Arctos : 30%

Edge : Draw 

API:

Acromion process length/Forelimb length.Higher score in this ratio increases attachment for the deltoid muscle.

P.Atrox : 2%

U.Arctos : 6%

Edge : U.Arctos

SMI:

Deltopectoral crest length divided by humerus length. Higher score Displays greater mechanical advantage of deltoid and pectoral muscles at the shoulder joint.

P.Atrox : 62%

U.Arctos : 72%

Edge : U.Arctos

HRI:

It is humerus mediolateral diameter at mid-shaft/humerus length.Robust forelimb bones protect the animal from violent stresses during grappling.

P.Atrox : 10%

U.Arctos : 11%

Edge : U.Arctos 

HRI2:

It is humerus anteroposterior diameter at mid-shaft/humerus length. Robust forelimb bones protect the animal from violent stresses during grappling.

P.Atrox : 16%

U.Arctos : 12%

Edge : P.Atrox

HKX:

A better score signifies relatively greater cortical thickness of the humerus.  

P.Atrox : exact value unknown 

U.Arctos : exact value unknown 

Edge : U.Arctos

HKY:

A better score signifies relatively greater cortical thickness of the humerus. 

P.Atrox : exact value unknown 

U.Arctos : exact value unknown 

Edge : U.Arctos

HCMI:
It is Humeral circumference/articular length Often-used variable in analyses of bone strengths in locomotion.The higher the ratio is, the thicker the Humeral bone is.
P.Atrox : 29%
U.Arctos : 34%
Edge : U.Arctos

HEI:

The HEI index measures the relative size of wrist stabilizing muscles and well as several grasping muscles in area which facilitate prey grasping. These muscles also likely help stability, pushing, and agility when legs are on ground.

P.Atrox : 27%

U.Arctos : 30%

Edge : U.Arctos

HTI:

It's Humeral trochlear length/Humeral length. Higher score increases muscle attachement on

the elbow joint and allows for more ulnohumeral flexion and extension.

P.Atrox : 20%

U.Arctos : 21%

Edge : U.Arctos

Brachial Index:

This measures radius length/humerus length. Lower scores in this ratio indicate greater

forelimb muscle mechanical advantage and results in stronger muscles all else being equal.

P.Atrox : 94%

U.Arctos : 86%

Edge : U.Arctos

Brachial Index 2:

This measures ulna length/humerus length. Lower scores in this ratio indicate greater forelimb

muscle mechanical advantage and results in stronger muscles all else being equal.

P.Atrox : 113%

U.Arctos : 96%

Edge : U.Arctos

Forelimb Proportion Index:

Length of proximal forelimb relative to length of distal forelimb ((Scapula length + Humerus length)/(Radius length + Metacarpal length)). Higher score Indicates greater degree of

morphological specialization for producing large out-forces in the forelimb.

P.Atrox : 132%

U.Arctos : 154%

Edge : U.Arctos

RRI:

This measures radius mediolateral diameter at midshaft divided by radius length. As mentioned above for humerus robusticity, a robust radius resists stresses on bones during fights and increases resistance to bites to the forelimb.

P.Atrox : 11%

U.Arctos : 11%

Edge : Draw 

RRI2:

This measures radius anteroposterior diameter at midshaft divided by radius length. As mentioned above for humerus robusticity, a robust radius resists stresses on bones during fights and increases resistance to bites to the forelimb.

P.Atrox : 7%

U.Arctos : 6%

Edge : P.Atrox

OLI:

Olecranon process length divided by functional length of the ulna. Higher score Indicates greater relative mechanical advantage of the triceps brachii and dorsoepitrochlearis muscles used in elbow extension.

P.Atrox : 16%

U.Arctos : 19%

Edge : U.Arctos

URI:

It is ulna mediolateral diameter at mid-shaft/humerus length. As mentioned above for humerus

and radius robusticity, Robust forelimb bones protect the animal from violent stresses during

grappling.

P.Atrox : 6%

U.Arctos : 6%

Edge : Draw 

URI2:

This measures ulna anteroposterior diameter at midshaft divided by ulna length. As mentioned above for humerus and radius robusticity, a robust ulna resists stresses on bones during fights and increases resistance to bites to the forelimb.

P.Atrox : 10%

U.Arctos : 10%

Edge : Draw 

MANUS:

Manus digit 3 proximal phalanx length divided by metacarpal 3 length.Higher score Indicates greater relative proportions of proximal and distal elements of the manus and size of the palmar surface.

P.Atrox : 49%

U.Arctos: 55%

Edge : U.Arctos

Foot Posture:

All else being equal, species that are able to adopt plantigrade foot posture, such as bears,badgers, wolverines, many rodents, spider monkeys, and great apes, should be able to apply substantially greater free moments to the ground than species that are restricted to digitigrade or unguligrade foot posture. Relative to digitigrade foot posture, plantigrade posture improves performance in lateral striking, lateral pushing, downward striking,forward pushing and rearward pulling.

P.Atrox : Digitigrade

U.Arctos : Plantigrade

Edge : U.Arctos

CLAW:

Manus digit three terminal phalanx length divided by pes digit three terminal phalanx. Higher score is to be expected in species whose claws are more capable of breaking soil.

P.Atrox : 98%

U.Arctos : 136%

Edge : U.Arctos

Studies Used For The Above Comparison:

 

https://www.jstor.org/stable/23735739 

 

https://www.researchgate.net/publication/230843015_Postcranial_morphology_and_the_locomotor_habits_of_living_and_extinct_carnivores

 

 

https://www.researchgate.net/publication/20806549_Differential_scaling_of_the_long_bones_in_the_terrestrial_carnivora_and_other_mammals

 

 

https://www.researchgate.net/publication/247494638_Ecomorphology_of_the_giant_short-faced_bears_Agriotherium_and_Arctodus 

 

https://www.researchgate.net/publication/281544339_Panthera_atrox_body_proportions_size_sexual_dimorphism_and_behavior_of_the_cursorial_lion_of_the_North_American_plains 

 

 

 https://www.researchgate.net/publication/229600388_Locomotor_behaviour_in_Plio-Pleistocene_sabre-tooth_cats_A_biomechanical_analysis 

 

https://pubmed.ncbi.nlm.nih.gov/28202470/#:~:text=In%20contrast%20to%20most%20other,force%20couples)%20to%20the%20ground

 

https://www.researchgate.net/publication/229063824_A_universal_scaling_relationship_between_body_mass_and_proximal_limb_bone_dimesions_in_quadrupedal_terrestrial_tetrapods 

 

 

As can be seen, most ratios point out to the Brown Bear having proportionally stronger shoulders, thicker Humeri,larger epicondyles,trochleas,olecrana, shorter forelimbs, longer proximal forelimbs, greater Manus Proportions, better Foot Posture and deadlier claws while the American Lion simply had more robust radii. Overall the Brown Bear was a stronger,more robust and better grappler than a similarly sized Atrox.Therefore, the Latter needs to significantly outweigh the Ursid to gain a considerable chance which would not be the case if we talked about Kodiak Bears and Coastal Grizzlies as some weight data suggest average weights of 352 and 334 kg respectively :

https://www.researchgate.net/publication/284678859_Brown_bear?enrichId=rgreq-628f82fba68bbb24aea0ecde0d73da52-XXX&enrichSource=Y292ZXJQYWdlOzI4NDY3ODg1OTtBUzo0NjkwODAyNTI2NTM1NjhAMTQ4ODg0ODg1NTY5NA%3D%3D&el=1_x_2&_esc=publicationCoverPdf 

https://www.semanticscholar.org/paper/What-size-were-Arctodus-simus-and-Ursus-spelaeus-Christiansen/14c1ecaa29bb88d8930fa543279937074628c946 

https://www.jstor.org/stable/3872615 

The American Lion on the other hand merely weighed around 260 kg :

 

https://www.researchgate.net/publication/249022988_Craniomandibular_Morphology_and_Phylogenetic_Affinities_of_Panthera_atrox_Implications_for_the_Evolution_and_Paleobiology_of_the_Lion_Lineage

Taking the weight difference into account, it appears that Panthera Atrox wouldn't do much against a Coastal Grizzly or Kodiak Bear in a fight !