Only thing that annoys me with EN goals is when a player makes a bonehead play by causing an icing trying to shoot for the EN and misses. This, when your team is up by only one goal, with plenty of time left on the clock for the other team to even things up.
I think this way of thinking is becoming obsolete.
I have a hunch that the benefit of shooting for the ENG with an NHL caliber shooter outweighs the cost of missing and being called for icing. I've noticed (especially this year) that it's becoming less taboo to go for the ENG even if you haven't gained the red line. AV seems to have encouraged several of the Rangers to just shoot for the empty net regardless of location on the ice (which is different from when he first arrived). I can recall one or two of Grabner's goals that would have been icings had they missed.
Just spitballing - say a player hits the empty net (guaranteeing the win) 40% of the time on attempts from beyond center ice, we could determine the odds of giving up a goal after an icing on the same play. Obviously the times it backfires truly stand out and are memorable (hence the "tisk-tisk" approach from broadcasters towards players who try it), but I'd be willing to wager that it happens infrequently and the risk is minimal -
especially compared to the risk of a defender trying to reach the red line before going for the ENG, turning the puck over, and allowing the opposing team to enter your zone quickly with possession anyway.
I imagine the best way to look at it is by aggregating all offensive zone face-offs at 6 vs. 5 and determining how many of them end up with the losing team scoring a game-tying goal (without the puck leaving the zone and forcing a regroup by the losing team). My hunch (without any factual evidence) would be the odds of this kind of goal - one directly off an offensive zone face-off that ends up in a game tying goal in a 6 vs. 5 situation - is probably
around 5%.
Let's say that the Rangers win ~45 games in regulation every year and have 25 one goal leads to protect in a 6 vs. 5 situation (perhaps a high estimate). Let's assume that they average one opportunity in each of these 25 games to shoot for an empty net goal from beyond the red line. With a conversion rate of 40%, this guarantees the Rangers 10 wins automatically. The risk of giving up a game tying goal off the offensive zone draw would lead to 1-2 game tying goals per season in this situation. Of course, this still almost always guarantee them a point with a chance in OT to play for the second point anyhow. This also doesn't account for problems caused when a player cannot reach center ice to shoot/dump-in and turns the puck over leading to a rush by the trailing team.
In an absolute worst case scenario, shooting for the empty net can cost you four points in the regular season - and this would only happen if you ice the puck, give up the tying goal AND the game-losing goal in regulation in the two games per season where the losing team converts off of the ensuing draw to tie the game. This -4 point effect would also require we assume that the losing team would have lost all 10 games where the ENG occurred. This scenario probably has never happened.
More likely, the Rangers would lose one or two points in the games they choke, but the 10 ENG's probably prevent a few instances where the game would have been tied/lost had the ENG not been scored. In most scenarios, I would venture a guess that shooting for the ENG from anywhere is the best way to go.