People really expect too much from an easy out. They have a very limited use because they are just too damn hard and are for the most part too small. Guide lines I use for an easy out and I have been dealing with this stuff for 30 years as a machinsit by trade.
1. if you broke the bolt while comming out you cant just drill a hole and use an easy out, you surly will just break it. you have to do something different. Like heat it up red hot let it cool by flodding with PB Blaster do this a couple of times and get back down to cold before inserting the easy out. 50/50 probability
2. always drill through the bolt to the space under it this gives you a chance to get lubricant under and behind the bolt as you heat it up. as you heat it up it gives the trapped metal a place to go.
3. The best application for using an easy out is if you over tightened the bolt and snapped it. the bolt is realy only stuck by dirty and streched or galled threads. drill through the bolt add lubricant and go to town. 98% probability
4. If you broke the bolt because it bottomed and you snapped it you wont get it out without drastic measures like heat and you must drill through the bolt to relieve some of the end load. 50/50% probability
5. Always use a tap handle and not a wrench or cresent wrench to turn the easyout.
6. Do not use too large an easy out because if you do as it wedges up tight it will expand the bolt and lock it up even tighter. This also applies to drilling the hole off center.
7. Center punch the bolt and drill it on center with a small bit like 5/32" it is far easier to control the wander and if you miss a little with a small bit it is still just a little miss, miss a little with a larger bit and your way off. As Mel Gipson once said "aim small miss small".
For most this is too much work and unnecassary until they break an easy out in an engine block or something else much more expensive. Take your time do it right the first time and know when to quit and seek other options. remember Easyouts dont twist, if it feels like its twisting stop its going to break start drilling and tapping it is far easier to do this now than after you break an easyout in a bolt. The urge to give a little more twist will always break the easy out.
As for those advocating punching out an easy out without backside access try it some time. for the easy out to break up there must be a place for the metal to go and there isnt any You will wear it well and still punching for a long time to come. If you must, try a pnumatic hammer. You would be far better to slap the part really hard on an anvil or something like the head of a sledge hammer to use inertia and shock to break the taper lock on the easy out. but any kind of miss resulting in striking the easy out or around the hole will distort the metal and pean everything in place.