Help me run a better mile

Based on your current times, it seems like you have a lot of potential to improve your mile time. In terms of mile workouts, here are some suggestions:
Mile repeats: Run several repeats of 1 mile at a pace that's slightly faster than your goal mile pace, with a short recovery jog in between. For example, you could try running 4-6 mile repeats with 1-2 minutes of rest in between.
800m repeats: Run several repeats of 800m at a pace that's slightly faster than your goal mile pace, with a short recovery jog in between. For example, you could try running 6-8 800m repeats with 1-2 minutes of rest in between.
Fartlek runs: During a Fartlek run, you vary your pace throughout the run, alternating between periods of faster running and slower recovery running. For example, you could try running at a steady pace for 5 minutes, then sprinting for 30 seconds, then jogging for 1 minute, and repeating this pattern for the duration of your run.
Tempo runs: During a tempo run, you run at a steady pace that's slightly faster than your goal mile pace for a sustained period of time. For example, you could try running 20-30 minutes at a pace that's about 10-20 seconds faster than your goal mile pace.
As for 300s, they can be a great workout to engrain your goal mile pace in your legs. You could try running several repeats of 300m at your goal mile pace, with a short recovery jog in between. For example, you could try running 8-10 300m repeats at your goal mile pace with 1-2 minutes of rest in between. This can help your body get used to running at your goal pace and improve your ability to maintain that pace over the course of a mile.

Chat GPT is far worse than a human. Anyone who’s actually helpful?

Bump

An 8:30 3k is around 4:33/mile pace. I would agree with you that you have the aerobic capabilities/fitness to run a low 4:0x 1500m maybe even a 3:58-59. Here are some workouts that I recommend.
15-20x200@1500-Mile w/ 30-45sec rest with the last two near 800m pace. You should aim for 31-32s for the bulk of the workout and maybe 29-30s for the last two. This should be challenging but doable.
10-12x400@Mile Goal Pace w/ 90sec rest or if you want to suffer more do it with equal rest. You should aim for 62-64s for each rep.
And if you are lacking in the speed department I would recommend that you add a few strides after each easy run.
Something like run + 3x150m or run + 4-5x100m. The strides should be at mile effort or 800 effort. Occasionally you should do 4x60m or 4x40m to work on top end speed.
You could also swap out one of your workouts every other week with something like 10x100m starting at mile pace and working down to 400m pace.
And if you don’t already do hill strides I would recommend that you add those in once a week if possible.

With your 2:02 800, you don’t have the speed reserve to run under 4:10, maybe even 4:20.

Frankly you don’t have the aerobic strength to break 4:10 either, and you would do good to get under 4:20

If you want to get better at the mile you need to work on top end speed. All the best milers in the world (and even in NCAA) can break 50 for a 400. Jakob Ingebrigsten is a guy with “not great speed” and he could still run 50 flat as a teenager.

Based on your times I would think you could run 57 in a 400. If you want to run under 4:10 you will need at least 52-53 in the 400 and drop 15 seconds off your 3k

Work on top end speed development. Get in the weight room, do plyometrics, strides and hill sprints multiple times a week.

That’s more long term.

Right now, for the mile you should easily be able to hold 66-67 if you run even. I’m guessing you probably went something like 48, 68, 73, 66, because thats how most people try and race the mile. You don’t have the speed to go out much faster than 65. Try and hold even for three laps and then kick hard. That is physiologically the best way to run the 1500/mile

A 2:00 800, 4:30 mile, and 9:00 3000 are all roughly equivalent times, so improving your 400/800 ability is probably the key to running a faster mile. However, you'd probably have the most long-term success moving up to the 5k/10k considering how much stronger your 3k PR is.

He ran a 8:3x 3k, so I'd think a sub 4:20 mile should be easy

Seem to have good strength OP with the 3k.

I would hit some faster reps/do workout maybe you don't prioritize all the time. 8 x 200 @ 800 w./ 90s recovery. More reps in the 150-300m range with decent rest. Gotta get that 800 into the 1:50s. I think 4:30 is in line with 2:02. I wouldn't expect someone to have your 3k PB off of that. Keep it rolling.

You need a bigger aerobic base.

Try 3 months of 100 mpw at 8:30-9:30 with 100-120 hr.

Probably training like a 5k/10k athlete, but closer to 10k

Ended up running a converted 3:59 from the mile. Pacing was not exactly good and I ran the final 800 one second off my PR. But now I feel like I both have far better leg speed (I strides maybe 5x last year) and already better aerobic strength.

I'll break 4 next indoor

at least, that's the lofty, lofty goal. But I don't think it'll be unreasonable if I can run sub 24 in XC