DISCLAIMER: I trust Miguel's number to be far more accurate, and am just using OTC for a rough number example. I'm not sure exactly what Miguel's current number ($12.482M) accounts for. I know that he breaks it own in detail on BSJ, but I don't have access.
On OTC, the number is roughly $14.022M, but they have yet to list Trent Brown ($1.90M). Adding Brown would knock Will Tye's $705k cap hit off the bottom of the 51, making the
current cap space roughly $13.317.
After that, the lowest three cap hits of the top 51 are:
Cardona = $730k
Grissom = $720k
Bolden = $720k
Total is $2.170M.
Bentley's cap number for 2018 (drafted at #143) will be $556k. So Bentley, and everyone drafted after him or signed as a UDFA, is already well below the top 51 and won't count against the cap (except for any signing bonuses paid to UDFAs, I think).
The gross cap numbers for the Pats' top three picks are:
Wynn = $2.087M
Michel = $1.756M
(corrected)
Dawson = $865k
Total is $4.708M. (corrected)
Subtract the total of cap numbers of the three guys who will be knocked ($2.17M) off the bottom, and you get $2.538M.
(corrected)
$13.317M minus $2.538M = $10.779M ..... roughly.
(corrected)
Since Miguel's cap number is $835k lower, cap space could be as low as
$9.944M after the top three draftees are signed.
There may be some contract re-structurings in the works that would add some cap space, but that's roughly the amount of cap space that the Pats would probably like to have going into the regular season. IOW, re-structurings would likely be necessary to cover any free agent signings.
EDIT: As was graciously pointed out by
@ctpatsfan77 , I'd originally used an incorrect number for Sony Michel's 2018 cap hit. Everything above should now be correct (see explanation in post below).