Because Force x Velocity equals power. If your sport requires power production then yes.
Its dependent on sport. In the case of sprinting, all of the best sprinters lift heavy.
Do you have any reads that all the best sprinters lift heavy? As far as I've heard it's very mixed, most do S&C, few do a lot of heavy lifting and few do no lifting at all.
How do you move faster then? Let’s say you’re a sprinter. How do you sprint faster? Why is lifting going to help you run faster?
So why lift to improve athletic performance at all?
There's a few things to unpack here.
It is always a good idea to incorperate a specific and block periodized strength program for any athlete. There's a few distinct advantages, and this is without including heavy lifting necessarily. You can target weak points, you can work on muscles and tissue that are not addressed during your sport and most importantly, you can strengthen relevant tissue and prevent injuries. Add to that, you can increase power production, strength at specific lenghts and work on biomechanics that will transfer to your sport at the same time.
How much time someone needs to spend on "strength training" (we are using an umbrella term for now that covers maximal eccentric and concentric strength, isometric strength and explosive strength) depends on the person. If someone has very good running technique but are injury prone or need relative strength in accordance to their mass, then working in the gym more might benefit. If someone is very strong in certain positions but have poor running technique, then they should forgo the gym a bit and work on the track a lot more.
In regards to maximum strength in the compounds like squat, benchpress and deadlift specificly, there's a few drawbacks.
1. There are diminishing returns. You reach a point where time spent is not worth it.
2. Recovery can suffer.
3. Hypertrophy can occur and lower relative strength to weight.
4. Max strength increase at slow velocities and isometric strength does not necessarily transfer to sprinting speeds. Stronger (as in absolute strength) is not always faster.
However, there are still benefits and they are very much worth improving if managed sensibly. Improving maximum strength and isometric strength can improve performance, tissue strength (prevent injuries), biomechanics and more.
Now, you asked first of all how someone trains to be faster. The most important part in my opinion is actually working on the running drills, careful planning of runs and running mechanics. Sprinting itself will also improve your speed. That can be covered at another time. In regards to how doing S&C and "lifting" can help, there's a few things to consider.
Moving something very fast requires motor efficiency and muscle co-ordination (which is basicly something you can train by doing countless of repetitions), less antagonist muscle activity at certain times, high neural drive and rate of force development (can somewhat be trained by lifting something heavy with intent, increasing max strength or lifting something light-moderately heavy at a high velocity), tendon stiffness (is improved by lifting and weight bearing exercise), the stretch shortening cycle/SSC (which is improved at very high speeds of tendon elongation and contraction as in sprinting itself, various jumps and doing track drills), rate coding as in the speed and sequencing of your nervous systems signalling to the muscles (mostly trained at high velocities with low-moderate loads), contractive velocity (high velocity at low-moderate loads), fiber types and
mental acuity and motivation.
Lifting heavy increase neural drive and motor unit recruitment in muscles, working at high velocities with low-moderate weights will increase rate coding and contractive velocity and working on balancing muscles, iso-eccentric strength and alignment can improve tissue and some performance parameters and reduce injuries. Another thing to add to this is that in order to be more sport-specific and have a greater transfer to the field, it's adviced to choose exercises that works at specific muscles lenghts, ranges of motion and directions of power. A few examples for sprinting would be:
1. Exercises that overcomes inertia and produces powerful horizontal force vectors against resistance - as this is what happens during the acceleration phase
2. Exercises that forcefully extends the hip at short ranges of motion - as this is what happens during pushoff in upright running
3. Exercises that strenghten the hamstrings eccentricly - as the hamstring store very large amounts of eccentric energy during the late part of the swing phase - this also helps with injury prevention like fiber tears.
4. Exercises that creates powerful hip flexion in large ranges of motion - as this is what happens during the leg lift
5. Exercises that improve ground reactionary forces and the SSC, ie. less ground contact - as this generally increase force and improves time
6. Exercises that incorperates triple extension - extension of the hips, knee and ankle, which is the basics of the kinetic pushoff of the lower body during sprinting.
7. Exercises that uses a split stance - more transferable to sprinting
8. Exercises that stabilises the core, improves core strength and upper body strength - as core stability during dynamic movements frees up the extremities and upper body push/pull strength also helps with running form and force, using the crossed anatomy slings which is a part of energy creation during walking and running.
So that would be the gist of it. Without going into too much detail, exercise suggestions for the following could be:
1. Sled drags, prowler pulls - vertical shins and torso, about 20-X+% of BW depending on the goal and block.
2. Squat jumps, trapbar jumps, hip thrusters, kettlebell swings at medium loads (30-50% of 1RM) with high velocity and effort - Squat and DL/trapbar DL variations at heavy loads (70-90% 1RM).
3. Nordic hamstring curls, glute ham raises, leg curls, romanian deadlifts, single leg deadlift variations at moderate to heavy load
focusing on a controlled eccentric part
4. Band resisted march variations, drills
5. Besides the obvious fact that sprinting and sprinting/track drills work this a lot, then hurdles, depth jumps, bounding and so forth can be incorperated into a S&C program.
6. Power cleans - at light to heavy loads at high velocity or intent depending on skill and block, also improves force production. Mid-thigh pulls with the same programming. Counter movement jumps, split stance jumps, skips.
7. Bulgarian split squats moderate to heavy loads - can add a stepup here and torso lean to work on single leg force during the acceleration part of sprinting. Partial ROM Jefferson Deadlifts at medium loads with high velocity for power (30-50%) and heavy loads for max strength (70-90%). Stepups, other split stance variations at moderate to heavy loads.
8. Various isometric and dynamic core exercises scaling up with moving extremities. Besides, the compound lifts like squat and DL obviously helps. Various bilateral and unilateral upper body push/pull exercises.
That would be the gist of it.