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The Pistons did want to re-sign Wood — and he was interested in sticking around — according to James Edwards III and Kelly Ilko of The Athletic:
During this process, the Pistons also offered Wood a contract, per sources. Detroit wanted him to be part of this retooling, as well. However, there was a specific price in mind. Detroit had Wood’s “Early Bird” rights, which meant that if it were able to sign him to a deal that paid, roughly, $10 million annually, Wood’s salary would only count as $1.7 million against their cap. Anything more would count toward the cap in full. Per sources, Detroit didn’t offer more than the annual amount that it would take for the smallest cap hit. The priority for the Pistons under Weaver was to acquire Grant, who, especially defensively, fits more of the mold of what the revamped front office was looking for
so it just looks like the money didnt work out, makes sense.