FOXBOROUGH, Mass. -- Quick-hit thoughts and notes around the New England Patriots and NFL: 1. Maye Effect: A simple truth in free agency is that a team offering the most money usually gets the player. It also doesn't hurt to have a promising young quarterback. That was a hard-to-miss theme from the initial Patriots' 2026 free agent class, a group headlined by receiver Romeo Doubs, safety Kevin Byard III, guard Alijah Vera-Tucker, outside linebacker Dre'Mont Jones, fullback Reggie Gilliam and tight end Julian Hill. Call it the Drake Maye Effect. Byard, entering his 11th NFL season, summed it up after spending the last two seasons with the Chicago Bears and being part of Caleb Williams' rise. "An ascending quarterback; it's one of the hardest things to get right in the NFL, and everybody is trying to do that. New England has it right with Drake Maye. I'm excited to be able to play with him," Byard explained after officially signing his one-year, $9 million contract in New England on Thursday.…