We know the Celtics are an analytics focused team (as are most teams at this point, but the Celtics have been doing it for longer). Some of the analytics LOVE Derrick White. Hoopshype did a survey of front office executives in the pre-season about their favorite publicly available advanced rankings. Four rankings were deemed by at least one executive to be their favorite/one that they turn to first when evaluating. All of the top ones had something in common, that being that they relied more on what happens when the player is on the court, take into account lineups, etc., as opposed to only being box-score dependent. Those rankings were RAPTOR, EPM, DPM, and LEBRON.
Of the 321 players with at least 500 minutes so far this year (to avoid small sample-size issues), White ranks as the following:
RAPTOR: 25th
EPM: 24th
DPM: 50th
LEBRON: 67th
There's a bit of disagreement there. Two metrics think we got a borderline All-Star. The other two indicate a solid starter. The pick swap in 2028 is probably an overpay for a solid starter, although the rest of the package is good, especially given that the contract is reasonable and has 3.5 years left. But if the metrics that have him as a top-25 player? That's a steal. I'm pretty sure the Celtics have their own proprietary metrics, but my guess is they have White somewhere between the 24th and 67th best player, and probably towards the higher end of that. Combined with the fact that his style of play fits in very well with what the Celtics are trying to run, it's easy to see why they made the deal they did.