Generally speaking, we wouldn’t expect anybody’s NBA title odds to improve much as a result of re-signing a 33-year-old wing who started just one game in the previous three seasons. But the Golden State Warriors are, as always, the exception. With free agency opening for business over the weekend, the champs brought sixth man extraordinaire Andre Iguodala back to the Bay Area on a new three-year contract — and it boosted their chances of defending the crown by much more than one might assume.

Iguodala is, of course, far better than your typical aging benchwarmer. According to ESPN’s real plus-minus, he ranked as the eighth-best small forward in basketball last season, thanks in part to tough defense: When Iguodala was the closest defender, opponents shot for an effective field goal percentage that was 2.1 points lower than we’d expect based on the location of the shooter and Iguodala’s proximity to him. Iguodala was also ludicrously efficient at the other end of the court, finishing the season in a four-way tie for the top offensive rating (129 points per 100 possessions) of any player who logged at least 1500 minutes.

Although Iguodala didn’t score much (only 7.6 points per game), he did just about everything else at a high level. Our CARMELO projection system sees him as most similar to Ron Harper and Shane Battier, two other under-the-radar — but important — championship veterans:

According to CARMELO, Iguodala figures to produce somewhere between three and four wins above replacement next season. That’s a pretty good total — 69th-best among the 630 NBA players we have a projection for (roughly the same as Pau Gasol or Jeff Teague) — though not exactly star-level production. But Iguodala’s value is amplified by where he helps position the Warriors in their title defense.

With Iguodala on hand — and keep in mind that rosters are still in flux since it’s still so early in free agency — CARMELO projects Golden State to win 64.4 ballgames next year. (This includes 25 minutes per game given to replacement-level players; that playing time will probably go to better talent after the Warriors fill out their roster over the summer.) However, if Iguodala had signed elsewhere — with the rival San Antonio Spurs or Houston Rockets, for example — the Warriors’ projection would have dropped to 61.6 wins.

That difference in wins can matter a lot to a team’s championship odds. Using a logistic regression, we can estimate the probability that a team will win the NBA title based on how many regular-season Pythagorean wins it has. The Pythagorean wins stat eliminates the noise of a team’s actual win-loss record in close games and can allow us to home in on a team’s real talent level. According to data since the 1983-84 season, a team with 61.6 wins’ worth of talent will win the championship about 29 percent of the time, but a team worth 64.4 wins has a 47 percent chance of winning the title — a huge upgrade for a relatively small increase in talent.

Although the championship value of adding one extra victory begins to level off as teams approach the 70-win barrier, the “sweet spot” for adding talent is a win total in the low-to-mid 60s, right where the Warriors currently sit. And among the Warriors’ free agents, Iguodala himself was also in the sweet spot — between those who are more valuable but unlikely to leave (Steph Curry, Kevin Durant) and those who are more likely to sign elsewhere but also more replaceable (JaVale McGee, Ian Clark).

In other words, Iguodala was the most meaningful wild card in Golden State’s offseason, and his return was of outsize importance to their chances next year. It’s not the summer’s splashiest move, or its most transformative in terms of sheer wins and losses. But if the Warriors are champions again, it might prove to have been the most important.