Interesting article. Shot quality effects tend to be underestimated quite often in the stats community.
However, I do take issue with Birnbaum using raw Corsi (it looks like he's using raw Corsi because 44.1% was the Leafs' raw 5-on-5 Corsi last season) and comparing it with shooting percentage. High shooting percentages lead to more goals, which means the team is more frequently in the lead and score effects will come into play, lowering their Corsi. His conclusion is that Corsi is "too biased by situation and shot quality to be taken on its own". But this is something most analysts already know - and that's why stats like Score-Adjusted Fenwick, Corsi/Fenwick Tied, etc. exist - to limit score effects.
Against most teams, 3 quality shots. Against Toskala or Dubnyk, I'll take 20 easy shots.
But like the old cliché goes, good things happen when you throw the puck on net. If you could choose between 3 quality shots or 3 quality shots plus 17 easy shots, which one would you pick? Gaining control of the puck and putting it on goal is generally a good thing, even if it's not
everything. Even Carlyle recognizes this - in his post-game interview last night he said "we're going to get our butts kicked most nights if we play like this".
The year that Carlyle's Ducks won the Cup, we don't have Corsi or Fenwick stats available, but they did outshoot their opponents heavily. The other time they had a good playoff run (2009), they had a 50.1% Fenwick Close and 50.9% score-adjusted Fenwick. The one time the Ducks made the playoffs with a low Fenwick (2011), they needed a brilliant performance from Hiller, and were knocked out by Nashville in the first round with Hiller sidelined with vertigo. So generally, even with Carlyle the pattern is that good things happen when you outshoot your opponents in the long run.
Corsi and Fenwick measure the effectiveness of a team's skaters at even strength. It does not cover goaltending or special teams (and Corsi doesn't even consider shot blocking a skill). Also, shootouts are ignored.
The 2009-10 Leafs were dead last in the league in both PP and PK, and had Toskala/Gustavsson in net to boot. So the reason they could come in 29th when they had a high Corsi is because they were downright awful at all the aspects of the game not covered by Corsi.
It's fairly well known that having great goaltending can "cheat" Corsi - see 2010 Habs, 2011 Bruins, 2012 Predators.
Shots definitely come in different qualities, and most statistical analysts have identified that:
A) shot quality is higher when a team is on the power play, because there are more cross-ice passes and back-door plays that make life difficult for goalies.
B) teams take better-quality shots when they are ahead (because the other team is taking more chances) and lower-quality shots when they are behind (because the other team is retreating into a defensive shell).
Analysts generally have decided to consider special teams a completely separate aspect of the game (limiting Corsi and Fenwick to measurements of even-strength play) to account for A, and have developed formulas to take score situations into account to account for B (for an example see here:
http://www.broadstreethockey.com/2012/1/23/2722089/score-adjusted-fenwick).
But aside from those two relatively simple factors, shot quality is just considered too subjective to be factored into calculations.
So essentially, we're just going to have to live with an imperfect system. Current Fenwick stats still give a pretty good picture of what is going on for most teams, despite the imperfections. (For example, the Hawks and Bruins showed up near the top of most shot-based stats last season, and the Sharks are currently #1 in Fenwick).
It's just difficult to figure out how "good" a shot is without having game tape in front of you. The only thing you can really do is work with shot locations, and even that is pretty tedious. So for the most part, people just ignore shot quality and accept that the system isn't perfect.
In the case of the Leafs, the blog Pension Plan Puppets actually did a series of posts over the off-season which showed that the Leafs weren't particularly good at keeping shots out of prime scoring areas last season. So in other words, even accounting for shot location wouldn't change the fact that the Leafs were getting outplayed on a regular basis.