Were the Golden State Warriors 'lucky' to win the NBA title?

— -- It's the story that won't go away, thanks to the vocal critics of the Golden State Warriors, particularly Los Angeles Clippers coach Doc Rivers and his shooting guard, J.J. Redick.

Some four months after the conclusion of the NBA Finals, the Warriors are still shouting down those arguing they were fortunate in the playoffs because of the players and teams they didn't have to face along the way to the title.

Only a little. It would be more accurate to say that the Warriors would have been very unlucky to have faced the gauntlet their critics wanted them to see.

Let's take a look at how the Warriors' playoff opposition compared to what they might have faced -- as well as the paths past champions have taken.

Yes, Golden State got lucky

To some extent, the notion that the Warriors got some lucky breaks along the way shouldn't really be a controversial one. Of course they did!

All four opponents Golden State faced were missing key players for part or all of their series:

• New Orleans Pelicans starting PG Jrue Holiday was limited to 55 minutes total and missed one game of the Warriors' sweep entirely coming off a stress reaction in his right tibia.
• Memphis Grizzlies starting PG Mike Conley missed Game 1 of the series with Golden State because of a facial fracture, and starting SF Tony Allen played just five minutes over the last two games because of a sore left hamstring.
• The Houston Rockets played without starting PG Patrick Beverley and backup F/C Donatas Motiejunas, while starting C Dwight Howard played through a torn MCL and torn meniscus suffered during the Western Conference finals.
• In the NBA Finals, the Cleveland Cavaliers were without starting PF Kevin Love because of shoulder surgery early in the playoffs and lost starting PG Kyrie Irving to a fractured patella late in Game 1.

We can estimate how much the absences helped the Warriors by using the multiyear, predictive version of ESPN's real plus-minus (RPM) to estimate the ability of each opposing team.

I calculated this in two ways: first, weighted by the minutes players actually played in their series with Golden State, and then a projection of what their playing time might have looked like had the entire roster been healthy.

These methods estimate the net rating per 100 possessions of each team compared to an average NBA opponent. By this measure, all four teams the Warriors faced were at least 2.4 points per 100 possessions weaker because of injuries -- about equivalent to the difference between the San Antonio Spurs and the Portland Trail Blazers during the 2014-15 regular season.

So when it comes to opponent health, things certainly could have been worse for the Warriors.

Yes, Golden State's 'luck' might have helped

We can estimate the likelihood of Golden State winning each series based on the Warriors' strength and their opponents' strength. From there, we just multiply each series together to get the total likelihood for Golden State to win four series in a row.

Here's what that looks like, comparing the actual opposition the Warriors faced to a hypothetical healthy set of opponents.

Had Golden State faced each team at full strength, we estimate they would have been barely better than a 50-50 bet to win the title despite their regular-season dominance.

But that is surely a bit unfair to the Warriors since we're rating based on their actual postseason playing time.. Had they been tested more seriously, coach Steve Kerr could have tightened his rotation further to keep his best players on the court. That's precisely what happened in the Finals, and indeed Golden State's estimated net rating improved from plus-16.3 points per 100 possessions, better than any of the teams they faced would have rated if healthy, to an even more dominant plus-17.2.

Still, there is perhaps a 20 percent chance that health was the decisive factor in the Warriors' title.

No, Golden State's title path was not easy

At the same time, looking just at the Warriors' opponents doesn't really get to the true sense of whether their luck is really damning. For that to be the case, Golden State's playoff opposition also would have to be easier than the typical champion has faced. And it turns out that's not the case.

It's easy to run the numbers and "play" the champion Warriors against the same opponents other champions have faced in recent years. For instance, what if Golden State had tried to make it through the same path that San Antonio did a year earlier?

When we do that, we find that the Warriors' path was actually slightly more difficult than average, and a lot more difficult than San Antonio's and Miami's the previous two years.

Against the typical competition for a champion over the past 13 seasons, we'd expect Golden State to win a championship 77.4 percent of the time -- slightly more frequently than going through last year's four actual opponents. The distribution ranges from a high of the Warriors winning an overwhelming 82.4 percent of the time against the opponents the L.A. Lakers faced in 2010 -- when they played a 54-win Phoenix team in the conference finals and a 50-win Boston team in a seven-game NBA Finals -- down to 63.7 percent of the time with the same path as the 2008 Celtics.

Considering the actual paths of recent champions is a better way to frame the Warriors' run. Recent history says that, in fact, had the Warriors faced healthy competition throughout the playoffs -- let alone tougher matchups like the Clippers and Spurs -- they actually would have been exceptionally unlucky. None of the previous 12 champions have faced such a difficult set of opponents. To some extent, that reflects a stratified league where the best teams have loaded up as weaker ones rebuild, but it's also a good reminder that every champion gets some fortunate bounces along the way.

So the Warriors shouldn't worry about what anyone else says. They were an extraordinary team with only ordinary luck.