Just looking at the save/shots x 100% ignores context of the type of saves the goalie had to make. Is a goalie who stops 20 of 25 super high-danger scoring chances getting outplayed by one who makes 40 relatively routine saves? That's obviously not the full story here, as Jake flubbed at least 1 easy one and Hellboy made an outstanding save or two. But Jake did make some outstanding saves, had little chance on a few goals while we did put a ton of rubber right into Hellebuyck's chest. To put this in more context, even though we almost doubled their shot out put, High Danger chances were dead-even and we had far less 5v5. We missed fired on a lot of those high danger chances too, and the Jets did not.
I wanted to piggyback off this for a quick tangent without commenting on this game specifically.
Hypothetical scenario (loosely based off Blues team performance in recent years), if you're giving up 8 good scoring chances against and 21 low danger scoring chances on average as a team, would you rather have the goalie with a .850 HDSC SV% and a .915 LDSC SV%, or the one with a .800 HDSC SV% and a .940 LDSC SV%?
Even though the former is > 6% better at stopping high danger shots and only < 3% worse at stopping low danger shots than the second goalie, the latter goalie's GAA is still going to be better (2.86 GAA vs 2.99 GAA) because the shot type disparity disproportionately emphasizes the value of stopping "routine" shots.
We've seen this firsthand in recent years with the Blues, as goalies like Elliott and Hutton have (often handily) outperformed Allen behind the same team, in spite of Allen fairly consistently having a higher HDSC SV%.
With that in mind, I think the value of making "routine" saves is too often minimized. Your fundamentals still have to be on point, or you are going to leak (a lot) more goals than you should.
If, for example, you're deeper in your net, you're inevitably going to give up more goals to late deflections and screens than a goalie who more aggressively presses that initial angle. It may look like it's "not the goalie's fault," but it most certainly can be a direct byproduct of things completely under his control, and other goalies would make those saves simply because they're far enough out on their angle (and square enough) that there's zero net exposed, rendering any puck bounces directly in front of them moot.
Theoretically the goalie that stays deeper will have other advantages as compensation, such as an advantage on any potential rebound (having to travel less distance to recover or re-position on a new angle) as a trade-off benefit, but the "value" of those advantages depends on many different things (like how good the goalie's rebound control is, how good the defense is at contesting/clearing rebounds, etc.). Do the advantages there make up for the initial disadvantages? It just depends. For Allen's particular case, I think the historical evidence pretty strongly suggests that it doesn't.
Anyway, all I really want to see from Allen is some evidence that his past struggles with "routine" saves are behind him. I didn't see anything that I considered to be a particularly encouraging sign in that first game, but it's just one game. We'll see how it goes.