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What is Tom Thibodeau's value?

The Chicago Bulls are doing it again. Without injured star Derrick Rose, the Bulls have used elite defense and just enough offense -- the same formula that won them a playoff series last year -- to stay in the mix for home-court advantage in the Eastern Conference.

The Bulls have gone 11-4 in their last 15 games entering their nationally televised matchup against the Houston Rockets on Thursday night, and center Joakim Noah has drawn some MVP consideration. Though Noah has unquestionably been Chicago's most valuable player this season, he might not be the most important part of the team's overachieving success. Instead, that honor might belong to coach Tom Thibodeau.

Thibodeau's four years in Chicago have resulted in two first-place finishes in defensive rating, and second place so far this season, not to mention a Coach of the Year nod (in 2010-11) and twice posting the league's best record during the regular season. While statistical analysts have yet to make much progress in valuing coaches, let's take a look at what various approaches indicate about Thibodeau's value to the Bulls.

The Del Negro comparison

Since Thibodeau has served as a head coach only in Chicago -- not counting one season at the helm of his alma mater, Division III Salem State in Massachusetts -- the obvious place to start is the Bulls' improvement from 2009-10, when they won 41 games under Vinny Del Negro, to their 62-20 record the following season with Thibodeau.

Of course, the coaching change wasn't the only alteration Chicago made to its roster. The Bulls spent lavishly in free agency to bring in Carlos Boozer and rebuild their bench with unheralded contributors like Omer Asik, Kyle Korver and C.J. Watson. And the development of Derrick Rose into an MVP at age 22 was a major factor in Chicago's improvement from 28th in the league in offensive rating to 11th.

With a core of Luol Deng, Joakim Noah and Taj Gibson in place, the Bulls were already an above-average defense under Del Negro. But using Thibodeau's system, which helped the Boston Celtics win the 2008 NBA title, Chicago allowed 5.4 fewer points per 100 possessions than in 2009-10. If we credited the entire improvement to Thibodeau -- adjusting for league average -- it would translate to about 4.4 points per game and a remarkable 11.8 wins out of the 21 the Bulls actually added to their total.

Thibodeau effect?

Giving Thibodeau all the credit for the defensive improvement is a bit of a stretch. Chicago's newcomers were defensive upgrades, too. A more conservative measure would look only at lineups featuring the team's four holdover players -- Deng, Gibson, Noah and Rose. The chart at right shows how groups of three of these four players performed defensively relative to league average, per NBA.com/Stats.

Weighted by minutes played both seasons, the Bulls' defensive rating improved just 0.9 points per 100 possessions with common players. (More of the improvement, in plus/minus terms, was due to bench units and to the change from Brad Miller to Asik at backup center.) Translated in the same way, that suggests Thibodeau's defense was worth about two wins to Chicago. That could safely be considered the floor to his possible value.

The RAPM approach

The most intriguing method for valuing coaches is including them in adjusted plus/minus as a sixth "player" on the court for both teams. That's what Jeremias Engelmann, who has consulted for an NBA team, has done with his version of RAPM (Regularized Adjusted Plus/Minus).

The results don't always match conventional wisdom, and they seem to give too much credit to coaches who wring decent performances out of less talented players while leaving more talented ones on the bench. Still, Thibodeau's numbers generally pass the laugh test. He rates as a slightly negative influence on offense (0.4 fewer points per 100 possessions) but is tied with Scott Skiles as having the most positive impact on defense (4.1 fewer points per 100 possessions).

The combination ranks Thibodeau third among active coaches and makes him a hugely valuable contributor. His plus-3.7 overall rating would rank Thibodeau 14th among players, tied with LaMarcus Aldridge of the Portland Trail Blazers. If Thibodeau was really as impactful as RAPM suggests, he'd be worth about 3.7 points per game to the Bulls and nearly 10 wins over a full season.

A bargain contract

The question of Thibodeau's value first came up in last week's chat. I answered that Thibodeau was worth three to five wins over a replacement-level coach. (Incidentally, since six of this year's nine new head coaches rate as average or better by RAPM, replacement level might be average.) A closer look at the numbers suggests that three wins is a fair lower bound, but the upper end of Thibodeau's value might be even higher than I guessed.

We're looking only at a fraction of the ways a head coach can affect his team's record. In particular, the lingering question with Thibodeau is whether his tendency to ride his starters for heavy minutes has a long-term impact on their health. While Chicago has been about average in terms of games and minutes lost to injury under Thibodeau, the effects might not be felt for years.

That quibble aside, Thibodeau's value is hard to deny. Given solid defensive talent, his scheme essentially guarantees an elite defense. In the defensive rating category, his teams have seven consecutive top-five finishes and counting, dating back to his time as an assistant to Jeff Van Gundy with the Houston Rockets. No individual player in the league can boast such a streak.

If Thibodeau were a player, given the cost of $1.6 million per win in free agency, his production would be worth about $5 million at the low end and easily more than $10 million at the high end. That makes his salary -- a reported $4.4 million per year, with bonuses up to $5 million, per Spotrac -- a bargain, especially since an elite coach doesn't count against the salary cap (or the luxury tax) like an elite player.

Thibodeau might not be quite as valuable to the Bulls as Noah, who has posted 10.4 wins above replacement player by my metric so far. But given the gap to the next most valuable Bulls player (Jimmy Butler, at 4.2 WARP), Thibodeau likely ranks second in importance. Not bad for someone who hasn't scored a single basket all season.