Thinkers had to wildly guess (4,2,3,4)
I believe the answer is:
shot in the dark
'guess' is the definition.
(I have seen 'Wild guess' mean 'shot in the dark' so perhaps 'guess' could also mean 'shot in the dark')
'thinkers had to wildly' is the wordplay.
'wildly' indicates anagramming the letters.
'thinkers'+'had'+'to'='thinkershadto'
'thinkershadto' anagrammed gives 'SHOT IN THE DARK'.
(Other definitions for shot in the dark that I've seen before include "Pure guess" , "Guess based on little information" , "Wild guess" , "Blind guess" .)