You can't quanitfy luck outside of running averages or running simulations, at which point you'd need to know how the game system actually works in the code or have a very high sample size from the game*. Since no game is ever going to have actually random results as one might expect them unless it enforces the percentages we see over x amount of rolls, it is entirely plausible that my estimations are more generous to Champions than the game is by making the player's effective crit rate be higher than stated. Or by making it lower than stated, because then consistent benefits become even more important.
Oh, pretty sure your numbers actually skew in the Champion's favor. A few reasons for this.
1) Riposte. This can result in you getting a reactionary attack on a turn you might not otherwise have one. And that means you aren't just getting the bonus die, but a full on attack, with all that entails. Easily 4x the direct damage benefit from a single die spent.
2) Indirect damage. A prone enemy can result in an ally having advantage, which now lets them hit when they might otherwise have missed.
3) Control/overkill. Say you have an enemy with 10 hp remaining. A Battle Master will not use a move for damage upping reasons there, because dead is dead. But the champion's +1 to crit rate could lead to a crit on said enemy, a hit that will technically do more damage, but damage that is meaningless, pure overkill.
I agree that Champion is kind of lackluster even in tabletop, but I think in game it suffers even more. There are very few things with effects like the Sword of Life Stealing, something that adds value to crits beyond "2h weapon make big number!" So there isn't much itemization that broadens what it means to crit, but chasing crit rate limits your gearing options, so it has a higher opportunity cost. Beyond that, there's the issue of resource management. In BG3, I can whack a room at the Gith base, click short rest, and then go whack another one with all my Battle Master charges available. Table top? That wouldn't fly, because a short rest is an hour long rest. The Gith will interrupt the party before they get that. And that means that the Champion is much more likely to get to the point where the quantity of crit hits exceeds what the BM can do. So yeah, when you can easily replenish your resources, that means "limited resources" is much, much less of a drawback, and it is no surprise then that classes/subclasses that have those mechanics come out on top.
