The home team wins game seven 80% of the time. When the visiting team wins game seven they got lucky.
... No. That's simply not a good statistic.
First, the 80% is an overstatement, it's more like 76%, which would be 3-1 odds. Second, the home win percentage is much more like 60-65% when we look at all games.
Now why the difference for game seven? A game seven team (outside of the finals) has the better seed, meaning they did better in the regular season, which usually means they are the better team. So what you are observing is really a correlation between the better seeded team being a better team than anything else.
Only the Heat clearly weren't the best team in the East. They weren't even the second best (that would be the Bucks). The discrepancy is from how the Celtics started horribly, then were brought together a little before halfway through the season.
And this isn't that unusual anymore. With stars resting, etc, teams care less about their regular season record, only that they make it to the playoffs, which we can see happen in the last couple of years.
If we look at just 2016 onwards, the road record becomes 11/24 by my count (hand counted from
this list, could have miscounted).
Or, just look at the series: Only two games were won at home! One by both teams!
So no, that's a bad statistic.
On top of this, the discounting of gambling markets is just a bad idea. A gambling market is the most reliable predictor of outcomes we know of, as it works somewhat similar to a normal market (with a lot of transaction tax).
Celtics got lucky alright. Jimmy Butler was a missed three pointer away from sending the Heat to the NBA Finals.
Only he's shit at 3's. He had
at best a 40% chance to make that. That doesn't even guarantee a win, so no, while scary, it wasn't just luck.