I am taking athletic data historically from Pats draft picks and starters to try and paint pictures of what they look for in guys.
Let's start with wide receivers.
Looking at the non-slot WRs for the Pats. Here are there Average, Standard Deviation, and Median Numbers: 40 Yard: 4.46, 0.11, 4.45. They like them fast... lots of 4.3's here. 3-Cone: 6.86, 0.17, 6.82. They do make some exceptions for bigger taller guys who are really fast but might not have the best cod testing. So don't rule out some of the Moss, Gordon types just because they have worse CoD. They like freaks here. Shuttle: 4.14, 0.19, 4.16. Broad: 0972, 0048, 1001. Vertical: 36.46, 1.94, 36.00. Of the guys who had a lower Broad they would have a better vert or the opposite. Of the RAS from the year they were draft which helps smooth the averages out because receivers have gotten more athletic: 8.22, 1.98, 9.14. Median is 9.14... wow. So athleticism jumps out at me.
Who fits from this year?
Miles Boykin 9.92 RAS. 4.42 40, 43.5 Vert, 1108 Broad, 4.07 shuttle, 6.77 3-cone. Big size. Hakeem Butler 9.92 RAS. 4.48 40, 36 vert 1008 broad. Huge size. Did not do agilities. Emanuel Hall 9.91 RAS. 4.39 40, 43.5 vert, 1109 broad. No agils. Above average size. Parris Campbell 9.76 RAS. 4.31 40, 40 vert, 1103 broad, 4.03 shuttle. Terry McLaurin 9.64 RAS, 4.35 3-cone, 37.5 vert, 1005 broad, 4.15 shuttle, 7.01 3-cone. Isabella has the 40 time and checks the boxes for vert and broad but his agilities were mediocre for his size. 3-cone at 6.96 but a decent shuttle of 4.15. 8.37 RAS overall. Edit: this is not including guys who profile as slot only. Slots will be looked at later.
These are their top tight end picks and receiving tight ends - not just draft picks but guys like Marty B too. Here is what stands out. They like top end athletes. Average RAS was 8.94 and media 8.63. They love top end speed. Average 40 was 4.63, median was 4.64 and the worst was 4.68! 3-cone average 7.23, median 7.18, and worst was 7.64. Shuttle average 4.33, median 4.34.
Thinking about what they like Fant-Hock/Moreau might be their favorite pairing although honestly I think Hockenson's top speed is faster. Read or heard he struggled with form for the 40. Knox has the shuttle and 3-cones they like but we don't know his 40 yet. If he gets in the high 4.6s pencil him in too.
Who fits the profiles?
Fant blows about everything out of the water which says a lot given their standards. In no particular order: Alize Mack is borderline, Hock, Foster Moreau, Kahale Warring, Irv Smith Jr (he will get knocked for his lack of size - I think given their history), Josh Oliver is borderline, Caleb Wilson is borderline,
I wouldn't rule them out trading up for Fant or Hockenson if Knox doesn't run a good 40. I say that because of the most polished TEs in this draft only Fant and Hockenson fit their usual requirements in athleticism. They have valued drafting that position in the past and I'd bet they continue to meet with a ton of tight ends.