Nylon Calculus had a very cool article breaking down the differences of playoff basketball and regular season basketball using statistical regression to try and prove out which cliches were true and which weren't.
Mika Honkasalo wrote the piece as part of their Freelance Friday section, I'd recommend reading the whole thing in detail because it's really quite good.
It's worth noting that the article is aimed at maximizing playoff wins not just analyzing champions.
However, the quick conclusions of the article are this:
1: Defense is really important, much more so than offense.
In the playoffs, teams who get there via high offensive rating and average defense almost always flame out and disappoint. Teams that get there with average offenses and elite defenses usually get further than expected. While the article doesn't state it, I will, to win it all, you typically need to be great on both ends.
However, a great defensive team is likely to make it a round further than a great offensive team.
2: If you had three teams that were equally good overall, the team with multiple stars would be most likely to win, but the team with no stars would be better than the team with one.
Effectively, the team with multiple stars can't be shut down. The team with no stars can continue to play like they normally do and is close to break even, but the team with one star will have that player swarmed and taken away leaving the rest of the team in an uncomfortable position.
Granted, it's really, really, really hard to build a great team with no stars, so again, this likely projects more towards winning in an early round than winning a title, because the odds of becoming a 60 win team without a superstar aren't very good.
3: Veterans matter (older teams tend to do better)
Because playoff basketball really is played differently than regular season basketball, experience does matter. There's an adjustment players need to make to the pace of the game, the intense scouting of every opponent, the adjustments made from game to game, etc, that is an adjustment for younger teams which can cause them to struggle.
4: Passing matters, but rebounding does not
This is perhaps the biggest shocker of them all. Having a large rebounding advantage in terms of rebound rate isn't a predictor of success, but good ball movement is. This makes sense to me in that better ball movement will get better looks in half court games while teams are running less and protecting the basket more, offensive rebounding probably loses some of its importance.
5: The ability to make baskets matters more than overall scoring rate.
This probably gets down to teams who can score baskets in clutch situations win while teams reliant on getting free throws for their points are in more trouble.
So how does this relate to the Bulls?
The Bulls are great defensively every year which is actually the #1 predictor of playoff success. In that sense, the direction of team building is very good. They've sought out a secondary star each but have failed to get one. For an elite team, they're on the toughest path with the single star route, though Dirk Nowitzki proved it's possible.
Chicago has generally been a great interior passing team and Pau Gasol will only help that trend. On the perimeter, they're more pedestrian as Rose isn't an elite passer as a PG, Butler and Dunleavy aren't anything special out there, and we'll have to see what McDermott can do moving the ball given that he was almost exclusively a scorer in college.
Chicago's strong rebounding won't mean as much as people think it would, and the Bulls lack of ability to get baskets the past few seasons definitely killed them. Will they be a team that reverses that last trend this year with improved offensive players? I'd think so, but we'll have to wait and find out.
Overall though, the article states the far and away biggest contributor to playoff wins is team defense. The Bulls should have that in spades, and interestingly enough, it's quite possible the Cavs won't have that much at all. Cleveland could possibly be set up as a team with a massive offensive rating and an average defense, that's the type of team which typically gets upset in the playoffs.
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