The story is set: Andersen was really bad, then worse, then terrible, until he won the Leafs Game Five in a feat of heroics. Just count the shots and the goals that went in past him, adjust for the goals scored by the Leafs — because every story about every goalie is all about team offence at its heart — and you have the proof. He was broken, and now he’s not.

Are we sure about that?

In the preview before Game One, I kept it brief:

I think most people think Tuukka Rask is the better goalie, and they are not really correct there. He’s been functioning this season at just about the Expected Save Percentage. It’s easier to be Rask than it is to be Frederik Andersen, and it’s Andersen who has made the more meaningful contribution to his team.

And before I talk about playoff Andersen, it’s a good idea to dig into that a little.

I’m going to start with a visualization Cole Anderson posted before the playoffs began:

He said this in the tweet that accompanied that:

Rask vs Andersen game performances this year  Rask slightly better overall, Andersen fewer awful games. almost exact same % of games with positive goal prevention. simulate this series 100 times & goaltending likely won’t significantly favor either team (but simulate it once..)

For more depth on his thoughts on goalie analysis and playoff performance, this article is excellent, and explains a little how he made the density curves above.

The density curve shows you the probability of the goalie achieving the result along the horizontal axis via how high the mountain is at that point. This is based on this season’s regular season results. Anderson uses his own expected goals model and plots the goalie’s saves over expected. For most goalies who play regularly, the graph forms a neat shape like these, and most of the time, the goalie performs in the area closest to his average, the peak of the mountain. Every goalie has some tails that stretch off either in the bad end or the good end.

Anderson’s conclusion here is that Rask and Andersen are very close to equal in regular-season performance. But that on any given game, you don’t know where on their curve their performance will land. This is how sample size works. One game can be anything.

One thing to consider in comparing regular season results to playoffs is that in the regular season coaches start the backup or pull the starter based as much on performance of the skaters or rest for that backup as they do the starter’s performance. Andersen played all the time, as you know. Rask gave way to Anton Khudobin a lot more.

In the context of the NHL this season, Rask and Andersen were better than average, but not in the top tier in goalies. That top tier for me starts with Corey Crawford, and then includes John Gibson, Pekka Rinne, Marc-Andre Fleury, Sergei Bobrovsky, and a couple of goalies who played only about half their team’s games, but were nonetheless spectacular.

Now let’s see where Andersen’s and Rask’s performances in the first three games landed on their curves:

Before you look at the top two goalies, look at how much variation many of the goalies have had. Connor Hellebuyck, whose team dominated the first round, laid down a stinker in Game Three. So did Pekka Rinne. Fleury and Jonathan Quick were both equally consistently good, and only one of them won any games at all.

Okay, now onto the goalies who count. Rask has three games all within his normal range, but Game Three is in a fairly low probability area. Probability isn’t a light switch. Just because it’s somewhat unlikely doesn’t mean it won’t happen.

But what about really unlikely? Well, ask Frederik Andersen, because while Game Two is so far out in the weeds, it’s his worst game ever, he did produce that anomaly. This is part of looking at past history and judging a probability of it repeating.  Rare things happen.

Anderson talks about “black swan” games in the article linked above:

Just because something isn’t in the data doesn’t mean it can’t happen. In game 2 against Boston, Frederik Andersen was pulled 12 minutes into the game, posting a save% 40% below expected, which he hadn’t done during the season. Part of this is artificial, he likely would have worked himself back into something less extreme by finishing the game. However, other games during the regular season where Andersen or any other goalie was pulled, would functionally look the same, whether it was -40% or -20%. A loss is quite likely. We’re more interested in: how often do they shit the bed?

The curious thing about Rask and Andersen is that Rask has done harm to the bed sheets more often, albeit by a small margin.

Game One and Three are both within Andersen’s normal range and at about the same probability of happening, even though one is good and one is bad.

Okay, now I’m going to switch to Corsica’s similar Expected Goals model and look at actual numbers for all five games of Save Percentage over Expected Save Percentage. This is all-situations, as are Anderson’s values.

Save Percentage above Expected Save Percentage

NameFrederik AndersenTuukka Rask
Game One-4.605.40
Game Two-49.800.40
Game Three2.00-3.00
Game Four-6.005.00
Game Five2.20-18.80

So, just like in the graph up above, we can see that the results for both goalies moved around a lot, but always within what they’d done in the past with that one exception. Rask in Game Five was well within his historical performance, and the chances of that game happening were around as unlikely as Andersen’s even worse Game Two.  Andersen’s Game Five was a touch better than Game Three, and Rask had two good games, better than Andersen, but he also had one where he was a null factor at nearly average goalie performance. Rask also has one poor game at below expected, just not a disaster.

One of the things many people like to do is find patterns in the variations of results all players and teams produce. You can average out whatever stat you like, plot it on a line graph and use action verbs to make claims about a team soaring up or crashing down. Alternatively, you can pick some arbitrary end points for your player, take the average of that period and ta-da, you have defined their true nature, and you should expect their future results to conform to that average.

Expectation that a single future result will land at the average of past results is a sin committed by everyone. It’s built in to the nature of Expected Goals models, and it’s up to us as interpreters of measurements to remember that many futures are possible, even probable, and that performance at the average — consistency, in other words — really isn’t a thing in hockey.

The reality is that all player and team results bounce all over the place, up and down, the averages move around over time, and usually, that movement cannot be explained.  No matter how many stories get made up about rest, confidence, injuries, or how often someone psychoanalyzes body language, none of that is provable. All those things factor in, but imagining you can see the causal factor (and there always seems to be just one) in a result where a range of possible outcomes is normal is no different from seeing shapes in a starry sky. Humans are good at it, and it’s how we make up the stories we tell ourselves to make sense of the world.

You can point to specific things you saw Andersen do. I’ve got a list: the poke checks in the first couple of games, failure to track pucks in traffic, positional choices, etc. But trust me (because I’ve done this before) if all you do is note what you’ve noticed, or worse, analyze the goals against and ignore all the rest of his activity, you know as much as Jon Snow about the reasons for Andersen’s results. As at any other time he’s been worse than we’ve wanted him to be, he’s not broken.

None of that helps how it feels to watch Andersen shit the bed in true black swan fashion, but you shouldn’t expect him to keep doing it, and he didn’t.  Unfortunately, don’t expect Rask to repeat Game Five in Game Six.

So what to expect from Andersen in Game Six? Something in the range of his past highest probability results. Or not. But more likely something good than bad. The future isn’t just a foreign country, it’s a dangerous and terrifying one and the maps not very reliable. That’s why we watch the games.

One other thing Cole Anderson knows about is goaltending under that name: