Josh Jacobs is clearly VERY lucky to be alive today ... TMZ Sports has obtained the mug shot from just after the NFL star's car wreck this week -- and you can see he suffered a GNARLY head wound in the crash.
As we previously reported, cops say Jacobs wrecked his ride at round 4:42 AM near the Las Vegas airport on Monday.
And, in new police docs obtained by TMZ Sports, officers say Jacobs smelled like booze when they found him at the crash site.
In the docs, cops claim as Jacobs was explaining to them why he had crashed .