From 1957-58 to the end of his career, Bill Russell didn't miss too many games, usually 2 per season. It's a lot harder than with Jerry West to measure how great his impact was. But that doesn't mean I can't try. Bill missed 28 games over that time. Normally I would not feel comfortable aggregating games missed over a bit more than a decade, because the quality of his team could change. This is not the case with Bill's team though, as they were consistently great the whole time he played.
With Russell in the lineup, excluding his rookie year as well as 1966-67 (no games missed) his team averaged 115.8 points, and allowed 108.9. They won 602 and lost 232.
When Russell missed the game, the 11 time champion Celtics were only 10-18. They scored 122.1 and allowed 123.2 (which is better than 10-18, a team with that point differential probably should go 13-15 in 28 games.)
They might have been better offensively without Russell, never a good shooter, or they might have just played at a faster pace. They were definitely much worse on defense. Overall, Russell was worth an extra 8 points per game, or 9 per 48 minutes.
Fluke? Maybe. Or maybe the rest of the team wasn't so great after all, and those who claim Russell was the greatest player of his time are correct. Look at the 1963-64 team. Those Celtics were actually the worst shooting team in the NBA. They not only shot a league worst 41.3%, they didn't make up for it at the line either. They were dead last in getting to the free throw line. So how does a jump shooting team that can't shoot and can't get to the rim finish? 59-21, then plays two postseason series, winning each 4-1, over Oscar Robertson and Wilt Chamberlain.
How did they do it? Rebounding, turnovers (probably), and defense. They had about 500 more rebounds than the average team. They had about 800 more shot attempts than average (so they pretty much had to have a huge turnover margin, though the stat was not tracked back then). And finally, if they were outscoring people that much while shooting like crap, their opponents must have shot even worse. Russell, being the shot blocking center, is the most important player for the defense, and led the league in rebounding. He might have had an impact forcing turnovers, but that's a total guess.