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I went from scraping in under 2 hours to a 1h38 still weighing 95kg (2015)
Tempo runs at goal race pace, interval track sessions long runs and slow mileage to recover on days in between and you will get better.
Edit: check out the paunch but still smiling at mile 12 https://i.imgur.com/wBY3HXN.jpg
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The biggest improvement in my running times I ever made was when I switched to a vegan diet. I went from 6:00/km to 5:00/km over a period of a couple of months without significantly changing my training. Slow compared to some in here but still a big improvement. Almost certainly a large proportion of the minute that I lost was due to weight loss but I did feel a hell of a lot fitter as well. I also smashed a bunch of PBs on my bike.
It was sort of annoying actually, because I had been running for a few years at that point, and like I said I had never seen such an improvement. Made the training seem like a waste of time - why bother actually running when changing my diet has a bigger impact (and probably getting more sleep, drinking more water - I should try those too).
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I just did my first half too - Paris semi, last Sunday. Made it in 2h17 which was much better than anything I'd done in training (about 2h30) so I was quite pleased with myself. I also agree that all the years substance abuse haven't helped much.... Thing I'm most scared of though is the full marathon I've got coming up next month, as I wrote about here: https://www.lfgss.com/conversations/313991
So, I've still got a few weeks to go until April 8th, but my furthest distance so far is 15.5 miles (and I was intermittent walking the last mile or so), so I figure anywhere under 10h I will be happy.
My current dilemma is whether to keep on building the mileage up to 20m over the next two weekends, or whether to focus on interval training instead. I've had mixed advice...
The grand total of....wait for it...1 min 35 sec. HUGE!