We missed out by a tiny distance on our first choice school. The criteria is described as follows:
"Distances are calculated in a straight line from the address you provide to the nearest school gate."
Is there any room for error with this method? Will the LA show me which gate they used?
"address" also seems vague - is it the centre of our house, or the centre of our plot of land, or the closest point of our plot of land, or the middle of the part on the road, or, or.. 
I'm fairly sure I'm not going to find anything by going down this route, but I don't want to leave any stone unturned just in case for my own peace of mind. We have plenty of (hopefully) good evidence for an appeal as mentioned on other threads.