What is a good shot?

A good shot is a shot that forces the keeper to save it. A shot that sails 2 inches over the bar is not a good shot because it had exactly 0% chance of going in. Again, if the keeper is forced to make a save, it was a good shot.

 

Thats actually a pretty good answer. I'm not sure if I can improve upon it at all. I do think it's weird that a shot off the cross bar doesn't count as a shot on goal, if only because can't a shot bounce off the inside of the cross bar and into the goal. Is it not counted as a SOG then but it's still a goal? Unfortunately it doesn't look like Peter Hirdt has returned this year or at least not yet and that'd be a heck of a question to pose to him. But I digress. The reason you haven't seen a lot of discussion beyond basically what galperin just said is that we're looking for things which can be objectively quantified, unfortunately a 'good shot vs. a bad shot' beyond a SOG vs just a Shot is about as objective as we can get anything else is just subjective.
However, if you want some Stats & Analysis Forum homework, I've noticed that in the game logs posted on mlsnet.com they've begun to indicate where a shot has missed, over, left side, right side. Not that those descriptions are very precise but it might be neat to know where shots are missed to more often or even more ambitiously who's missing shots to what side more frequently. This is the thread which orignially started this forum, it discussed a lot of the theories of objective analysis it might be of interest to you.
https://www.bigsoccer.com/forum/showthread.php?t=63798

 

It's definitely not just shots on goal, but it's not like shots on goal are irrelevant, either. Among MLS players with 50 or more shots, SOG/Shots has a quite strong .60 correlation with shot percentage. THat is, people who put more of their shots on goal are more likely to also put them in the net.

Although it's tempting to simply assume that a shot on goal is always better than a shot not on goal (or says a lot about shooting accuracy or something), that's not necessarily the case. Your examples aren't really fair, however; shots on goal are in general better than shots not on goal, I'd imagine because there's a lot more shots not on goal that are nowhere near scoring than there are Shots on goal that are automatic saves. This can't be applied universally, however. Stern John had a shots on goal percentage in the bottom third of MLS players with more than 50 shots, but is 9th (out of over 200) in goals/shot, and was the most prolific scorer on a per-minute basis in MLS history. There's clearly a lot of other factors at work here.

I hate to advertise my own threads, but me and beineke discussed this here. Can't say we reached any great conclusions though, or that it's even very clear.

 

Sorry, I made a mistake in my last reply. It shouldn't at all be surprising that sog% is strongly correlated with shot%, since goals are included in shots on goal. If you remove goals, you can get a ratio like (shots on goal missed)/(all misses), so the higher this is, the more of your missed shots you put on goal. This number, too, is correlated to shot % (r=.30), which implies that guys who tend to put their misses on goal also tend to put a better percentage of all shots on goal.

 

geeez and we had to tell him about a good and bad shot?
it is just like in basketball, golf or anything!