Watching the Superbowl, I was struck by how big and strong and fast these guys are. It reminded me of the crucial importance of specificity in training.
If you want to be powerful and quick for 10-20 seconds at a time, then lift that way. Lift heavy and explosively for 10-20 seconds, then rest before the next round.
If you want to be more like a distance runner, with the endurance to sustain long bouts of low-level output, make your weight training routine reflect that by lifting long sets (18 or more reps) with little rest in between. Aim to target the muscles that fatigue and cause your form to break down in running. This will help you build that endurance.
In theory it's really quite simple. You can target your strength accordingly by working certain muscles and adjusting the weight and reps to reflect power, speed or endurance.
Have fun, make sure your progressions make sense, and knock your workout out of the park!