how fast can you increase lactate threshhold? like if mine is around 8 minutes a mile for 5 miles, how fast can I get to doing 4:30 minutes a mile for 5 miles? I know it also depends on your training, but I also wonder if theres a limit on how fast you can increase it
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Lactate Threshold (LT) is very trainable, but the improvement you're asking about is hard to gauge. Realistically, you'll never get to 4:30/mile as your actual LT. That isn't because you're starting at 8:00 either, it's just insanely difficult to be at that level.
I have a guy on my team now that runs the 3k in just a shade over 8:00. He doesn't even tempo under 4:50 pace. 4:30 as a LT is simply a level of fitness that most people don't have the genetics for.
Now to scale things back, I am usually pretty happy to see our athletes get about 10 seconds faster per mile over the course of a 6 month season. We might see more, but usually won't see less. For our college runners that's an improvement of about 2-4% in 6 months.
For someone running 8:00/mile I'd at least want to see 15-20s drops per season assuming they are relatively new to running. For our girls that walk-on it's not uncommon to see them starting out at low-7's and by the next year being able to tempo 6:30.
In one study I recall cyclists LT improved 30% (as expressed as watts) from pre-season to peak. These were highly trained, mature cyclists and that was over roughly 8 months (pre-season to world championships).
After the season LT dropped (as one would expect with a drop in training).
Here is a paper (abstract) on time course in one group. A lot would depend on the type of training you are doing. Please note these were "physically active", not trained. They showed a 10% increased in power at LT over 6 weeks of training using 1 or 2 interval sessions per week.