Running for intermediates
Evidence: strong
Once you can run comfortably for half an hour several times a week, the next gains come from more consistent volume, a long run, a small amount of structured faster running, and strength work, in that order of priority.
The intermediate stage begins once the beginner goal is met: running comfortably for around 30 minutes, several times a week, without undue soreness or injury. The instinct now is to start running hard. The evidence says otherwise: the biggest remaining gains still come from doing more easy running, consistently, with only a small amount of faster work added.
Build volume before intensity
More weekly volume, almost all easy, remains the strongest lever on performance (training volume versus intensity). Add running days and gradually lengthen runs before worrying about speed. The constraint is still your slow-adapting tendons and bones (physiological adaptations), so raise volume in small steps and hold them.
Add a long run
Extend one run each week into a long run, building endurance and the durability that lets you hold pace when tired. Keep it easy and grow it gradually.
Introduce a little structure
The order to add faster running
Start with strides, a few relaxed 15-to-20-second accelerations on easy days, to reintroduce leg speed safely. Then add one weekly quality session, beginning with the gentlest forms: a fartlek or a threshold run, before progressing to harder intervals. One, or at most two, harder sessions a week is plenty; keep everything else easy. See types of training for the menu.
Start strength training
This is the stage to add strength work, two short sessions a week. It is the best-evidenced way to reduce injury and it improves economy, and as volume rises the injury-prevention benefit matters more.
Prepare for a goal race
A first 5 km, 10 km or half-marathon gives training a focus. Train mostly as above, then add a few weeks of slightly more race-specific work and a short taper before the day. Learn to pace from effort, not just the watch, and rehearse any fuelling for longer events.
Watch for doing too much
As training grows, so does the risk of overtraining and injury. Protect sleep, keep easy days genuinely easy, and treat persistent fatigue or niggles as a signal to back off. Consistency over months and years, not any single hard block, is what turns an intermediate into a strong runner. When you want to go further, the named training philosophies are the next thing to explore.