I am a 800m/1500m runner who has been a relatively good kicker from distances of 200-400 meters out but I can't accelerate quickly, it is a gradual rise in pace to top speed. How can I train for that explosive change in pace that lagat and other great kickers have?
We did a workout in HS to train for accelerating quickly. It was 400 repeats with the first 300 easy and a rapid acceleration for the last 100m. Make sure you warm up well to avoid pulling a hamstring.
We did something like the above poster. After easy runs, we would sometimes do a few 300m repeats where we would run hard but controlled for the first 200m and then shift gears and sprint the last 100m. We might do 4-6 of these after a distance run once a week or so.
Reaction drills are another thing you can do. These should be 100m or so. Pick one guy to lead. The leader starts out running at race pace. Whenever the leader feels like it, he shifts gears and sprints to the line. Everybody else runs with the leader while he's running at race pace. When the leader shifts gears, everyone has to react and go with him. It's basically like reacting to a kick in a race. One guy goes and you try to beat him to the line. We'd do these in place of strides after a run occasionally.
Find a hill that is 100 to 150m long with a flat section of 50m at the top.
Run the hill at race pace and sprint the flat 50m at the top. Walk back down.
Start with 3-4 reps. Work up to 8-10reps.