Olympics Math: 800 m Race

Alright guys, help me out here. I've been watching the 4 x 400 m relay, the 800 m race, and the other track races which require runners to start in assigned lanes and then merge to the inside lane after a certain distance. And I can't help but wonder why the runners quickly merge to the inside lane on that straight away rather than go straight for the curve. Wouldn't it make more sense for them to gradually make their way to the inside lane and time it so that they hit it just as they begin the next curve?Here's what I mean:If a runner is in lane eight as they make the curve, let's assume they're about 8 m from the inside lane. As they run down the straightaway most runners cut immediately to that inside lane and are there by about 50 m down the straightaway. I did the math, using Pythagorean's theorem, and it looks to me like timing the merge for the end of the straightaway would shave off .3 m. In an 800 m race, that adds up to about 5/100 of a second. That may not sound like much, and in an 800 m race it may not be significant, but races have been won by lesser fractions of a second.What do you think? Is my math sound? Are there other factors to consider?