I read the test of the M1A Socom 16 in American Rifleman and the performance loss really was amazing.  On the Remington 150 SP they got 2474 velocity and 2038 energy at the muzzle. The factory rated ballistics from a 24" bbl are 2820 velocity and 2648 energy.  I didn't go check the other two rounds tested for factory ratings. Somebody figure out what percentage of performance loss that is.   That is getting down into 6.8 territory.

From the 45th Edition of the Lyman Reloading Handbook:

For rifles with muzzle velocities in the 1000-2000 fps range, the change in velocity for each 1" change in barrel length is 5 fps.
For rifles with muzzle velocities in the 2001-2500 fps range, the change in velocity for each 1" change in barrel length is 10 fps.
For rifles with muzzle velocities in the 2501-3000 fps range, the change in velocity for each 1" change in barrel length is 20 fps.
For rifles with muzzle velocities in the 3001-3500 fps range, the change in velocity for each 1" change in barrel length is 30 fps.
For rifles with muzzle velocities in the 3501-4000 fps range, the change in velocity for each 1" change in barrel length is 40 fps.

According to the above info, a .308 barrel that has had 8" cut off (24" to 16"), the velocity loss should be 160 FPS. Perhaps the discrepancy in the M1A test is due to the fact that Remington probably does their testing with a bolt action rifle, while the M1A is semi-auto.

It seems that the above scale is intended to guide changing barrel lengths to a smaller degree and in a different range.  24 to 26, 24 to 22, etc.
24 to 16 is more in 'cutting a barrel in half comparison guide' territory.

 Celt 1 posted a chart showing 308 barrel /velocity after cutting and chronoing, a lot.  It was informative,  and gracious of him to contribute.

I've seen that chart before but consider this.

All propellants do not burn in a linear fashion.  The first 16 inches might be more significant than the 4 beyond that.  Sometimes powders are mixed.  The fast powders won't be affected as much from shortening a long barrel as much as the slower powders.

If I remember correctly, the original .45 ACP ball load was optimized for 5".  Cutting it down from 6" to 5" is not going to result in the same loss as from 5" to 4".  I'd have to double check that as it has been a while since I looked at the charts.  I have 45-70 cartidges that are specifically optimized for short barrels such as those on contender pistols, loss of velocity on a full length rifle barrel by cutting length is not going to be linear, the propellant power curve is past long before it would get to the end of a long barrel.

The chart above is a good rule of thumb, but does not account for all loads/propellants.

From what I recall, .308 was optimized for 18+ inch barrels.