you would be surprised. i have shooting shotguns in my state untill i hunted in maine and found the wonders of thr rifle.
i have taken 4 deer with shotgun. the one that ran the farthest was shot with a rem copper solid ( original design before they where changed ) shot deer at 10 paces and it ran 40yds after getting up.
i have also taken another witha rem lead slugger in the same spot i always shoot, the lungs and he ran about 30 - 40yds.
now i found out last year that the wonders of how a 30-06sprg 165gr. does better in dropping them quicker and have beter blood trails.
i think it is more apon the average i have seen deer drop and where you shoot them.
maybe try the lightfield slugs?

also how much of a blood trail you getting when you shot that deer? i got very litle when i shot mine with the rem copper soilds. took 2 shots and i saw very little but found a chunk of lung or kidney on the ground.