13 is more like a tight IC than a mod.
I know a couple of guy's that would swear on a stack of bibles that 12-13 is some kind of magical choke number though.
chokes are an odd thing I have good luck with IC in one gun shooting 3 drams of Clays, 7-1/2's, and the rem fig-8 wad.
it also does well with a load of titegroup and 1-oz of 8's still a 10-K load but only moving about 1150 fps, and with the RL-12 wad [like the RXP only for 1oz] loaded with 1-1/16 oz of shot, with red-dot.
I'm kind of surprised at how well it does with those various loads, since it's set up for duck hunting and has a 3-1/2" chamber.
in my model 1300 the mod choke is stuck in place and will smoke clays at 35-40 yds like a full choke, and will cleanly snipe the head off a grouse at 25 yds using the Fed 12-SO wad, the fed 209A and titewad.
it also does well with the 1-1/8oz windjammer wad and red-dot with 1.05 oz of shot, but it doesn't pattern as tight, it throws a good strong core just not close to 70-75%.
it still shoots steel shot just fine if I stay with #2's, or does well with fast [like near 1400 fps] #5's if I use a steel shot wad and long shot powder.
the choke change thing threw me off for a bit because most of my trap guns have fixed chokes and standard .729 bores.
I don't have the 'help the load out option' on them, so have just learned to tune the load to the gun and stick with what works method over the years.
all the above loads I mentioned have been various guns pet loads over the years,.
the r-12L load is for the 3200.
the windjammer load is both of the girls preferred load in different guns [one a semi-auto and one an over under]
the titewad load is for littlegirls pump gun.
some guns shoot them all good enough, and some just preferred them to anything else.
the choke thing kind of caught me by surprise on this one, it was the exact opposite of what I would have expected to have to do.