That could prove true for sure, and it sounds promising. But there is more to that discrepancy in goals against than just Larsson's impact. Remember that New Jersey has an all-world, top-five (or top-10 for sure) goaltender in Cory Schneider. Cam Talbot was strong in the second half and looked good at the worlds, but he's not on that level yet and the Oilers goals against reflect that (weaker goaltending) to a degree too.
Also, you have to take into account New Jersey's system and defensive structure. Mark Fayne also played top shutdown minutes there, with Greene, and was effective (not to mention an analytics darling). So as much as we all like Larsson (and I include myself in that all), we can't give him all the credit for New Jersey being 8th in goals against and we can't expect his addition to rocket Edmonton up those rankings either. If the Oilers crack the top 20 in that department in 2016-17, that would be a substantial improvement in my opinion.
In saying that, you could argue that New Jersey will feel Larsson's loss as much or more than Edmonton feels Hall's loss and I'd say that's fair. New Jersey's defence looks pretty awful now without Larsson whereas Edmonton's offence still looks potent with Lucic a slight downgrade on Hall.
Staying as healthy as possible throughout the lineup will obviously be a big key — as it is for every team — and that's unpredictable for better or worse.
I posted this before but it probably fits better with your comments:
There have been comparisons between Fayne with Greene and Larson with Greene as pairings. Here are some of the actual numbers. People can interpret them as they will.
Greene with Larsson 2014-2016:
TOI 1943
GF/60 1.64
GA/60 1.42
GF% 53.5%
CF% 45.5%
OZ% 34.1%
Top 8 forwards in TOI for: Zajac (32%) , Henrique (27%) , Palmieri (22%), Cammalleri (19%), Gionta (19%), Elias (16%), Tootoo (15%), Stempniak (13%)
Top 10 forwards in TOI against: Crosby, N. Foligno, Stepan, Atkinson, Pacioretty, Kreider, Ovechkin, J. Staal, Zuccarello, Giroux
GA /60 with Schneider 1.48
GA/60 with Kinkaid 1.82
Goals against for the Team 258 in 164 games = 1.57g/gm
Greene with Larsson 2015-2016:
TOI 1467
GF/60 1.57
GA/60 1.27
GF% 55.2%
CF% 44.1%
OZ% 31.8%
Top 6 forwards in TOI for: Palmieri (38%), Zajac (35%), Henrique (29%), Stempniak (23%), Kalinin (23%), Gionta (18%), Cammalieri (17%), Tootoo (14%)
Top 10 forwards in TOI against: Giroux, Zuccarello, Crosby, Stepan, Ovechkin, Nordstrom, Saad, Jenner, J. Staal, Atkinson
ES Goals against for the Team 133 in 82 games = 1.62 g/gm
GA /60 with Schneider 1.30
GA/60 with Kinkaid 1.62
Greene with Fayne 2012-2014
TOI 1085
GF/60 2.27
GA/60 2.10
GF% 51.9%
CF% 57.2%
OZ% 47.1%
Top 8 forwards in TOI for: Zajac(31%), Zubrus(27%), Henrique (24%), Jagr(23%), Bernier(23%), Elias(22%), Gionta(19%), Ryder (18%)
Top 10 forwards in TOI against: Giroux, E. Staal, Voracek, St. Louis Backstrom, Kessel, Bozak, B. Boyes, Crosby, JVR
GA/60 with Schneider 2.28
GA/60 with Brodeur 2.28
ES Goals against for the Team 210 in 130 games =1.62 g/gm
I won't say much other than the following observations: While the rate at which the team gave up ES goals against stayed relatively constant the Larsson/Greene pairing had far better results, particularly last year, in preventing ES goals against than the Greene/Fayne despite the fact that the former pairing seemed to have a much more defensively challenging assignment. This success is sometimes attributed to better goal tending but that does not seem to be the case. Greene aand Fayne played behind Broduer and Schneider. And if it was just Schneider having improved you would have expected a corresponding reduction in the GA when that pair was off the ice. But NJ GA/60 at ES when Larsson was not on the ice was about 2.4 or roughly double what it was. Moreover Larssons GA/60 with Kinkaid in net would have ranked 5th best behind only Stralman, Campbell, Doughty and Niskanen.
The Corsi difference is likely why the analytics crew loved Fayne. But it would be impossible for anyone who has seen both players to argue that Fayne is better either defensively or as a puck mover than Larsson. So it would seem clear that this difference is attributable to overall team play and the fact that as a pair Greene/ Larsson start in their own end far more often.
The Fayne/Greene pairing played against a relatively similar group of high quality players but the difference is that many of the top players they played against put up much better numbers against them than they did against Larsson/Greene. This is especially true for the 2015-2016 season.
I will also add this. Of the 124 defensemen that played 1000 minutes or more 5 vs 5 Larsson had the second lowest GA/60 behind only Stralman. Greene was 3rd. Amongst that group Larsson and Greene had the lowest OZFO% at 20.7% and 20.5% respectively. Stralman was 115th on that list 36.6%.
For DZFO% Larsson was first at 44.4% with Greene second. Stralman was 105th at 29.4%.
And of course while one might argue that Larsson had Greene to lean on Stralman had a guy who was not so bad either. So while none of this proves that he will have a similar impact in Edmonton, it is true that there is evidence to back up an more optimistic point of view.