What are the odds?

In game 5 of the Western Conference Finals, the Los Angeles Kings were 14.4 seconds away from elimination. They trailed the Blackhawks 2-3 in a score or go home situation. They scored. (They eventually went home anyways in OT, but that's not the point.)

What are the odds that they would score a goal at that point?

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Method #1

With that little time, the Kings pretty much had to win the faceoff cleanly. Clean wins don't happen every time, and a tie-up would waste valuable seconds. I'll be conservative and say a clean win for the Kings would happen 40% of the time.

Even with the puck, they had to get a shot to the net. In a situation like this where the Blackhawks know they need to shoot quick and should be ready to block anything, that's not easy. I'd say once they have the puck, getting a shot on net might happen 60% of the time.

Now is the tricky part. Getting it in the net. In the regular season the Kings scored 2.73 goals on 29.8 shots for a season shooting average of 9%.

So Method #1 says that when the play started, the Kings had a (.4*.6*.09 = .022) 2.2% chance of scoring. Even that seems high, no?

Method #2

The Kings averaged 2.73 goals in 60 minutes over an entire season. The time remaining (14.4 seconds) constitutes .004 of a single game. Ergo, I could expect the Kings to score .01092 goals in that amount of time. Which I think is the same thing as saying they would score a goal in 1.1% of the scenarios with 14.4 seconds left.

Analysis

If so far, Method #2 seems more plausible, how did Method #1 double it? Well using estimates I pulled out of my ass, I gave them a (.4*.6) 24% of getting a shot on net. But using their shots per game average, over an entire season they only got a shot on net every 120.8 seconds. Which would mean that their chances of getting a shot on goal in the final 14.4 seconds was really only 11.9%. But that leads us back to the same 1.1% chance of scoring.

But these numbers are based on season averages covering all instances of play, and the moment in question was a offensive zone faceoff, with a 6 of 5 to boot. So it would make sense that their chances of scoring in that stretch were higher than over the typical 14.4 second stretch in the season.

Conclusion

I think 1.1% to 2.2% is a reasonable range. For my final answer, I'll err more on the side of the season averages and say the Kings had a 1.5% chance of scoring when the puck was dropped.