I've toyed with a JP supermatch 22 barrel for a couple years, haven't been impressed accuracy wise. To be fair to JP, if you read the instructions they clearly state that even with best match ammo expect at best 1MOA at 50 yards, and with less expensive match ammo 1.5-2 MOA at 50. That's pretty much been my experience, I will say it runs like a top with every ammo I've used in it. Though I'd be willing to bet that if JP put that info on the product page clearly, they wouldn't sell many at $500 a barrel. I even sent mine back to JP, and to their credit they were great, they rebuilt it in their upper/handguard, worked on the bolt, and they were able to get some 50yd 1 MOA groups with Eley Tenex, but other test ammo they tried was all in the 1.5-2 MOA range. JP did say that they didn't use a tight match chamber for reliability.
I've toyed with probably 15-20 different ammo options in it and that's pretty much been my experience. It will shoot Eley 10x about the same as my Volquartsen will shoot CCI std, tac-22, and Wolf. The big problem I see is is big fliers, even in ammo it seems to like. I generally shoot lots of 5rd groups to eval ammo, and you'll see groups with 4 rounds touching and then a 3/4" flyer. Sometimes you can get very lucky, get no flyer and have a nice 1/2" group, but it's 1 group out of 20. You'll see groups with 4 rounds in 1/2" and a 1.5" flyer. At 100 yards even the ammo that it likes at 50, falls part to 3" groups. Recently I tried out some Tac-22, Wolf (new version), some old Remington Eley Match, SK Std, SK Rifle Match, and SK pistol Special. It actually seemed to like the Rifle Match and Pistol Special at 50 quite a bit, however it would still throw 1/2-3/4" flyers. A couple targets from a recent range visit, calm conditions, shot off a front/rear rest. I usually try to dial about 1/2" high to maintain the aiming point, outer black circle is 1.5" inside edge to inside edge. There's a couple good groups, but then the group after it will be 1"+. Rifle Match and Pistol Match it clearly seems to like better than the others and groups seem to start to get to the 0.75" range, but you still frequently see 1 flyer ruin the group. At 100yds I ran 30 rounds of both rifle and pistol match, and they both ended up being 2.5-3" groups. Pistol match definitely did better and probably 20 of the 30 rounds were in 1-1.5" but the other 10 were all over the place out to 3". Rifle match was more randomly scattered over 2.5-3" with no real clustering. If the flyers were solved, it could be a hammer with SK Rifle Match and Pistol Match Special, but even those showed flyers 3/4" outside the main group. At best it seems like the higher dollar the ammo, you can reduce group size, but the flyers persist but they get a bit smaller. Eley 10x did better than Center-x, but it's hard to want to spend $20/box to get the same groups that my Volquartsen and CZ 457 will get with $4-5/box
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At first I suspected the ammo was being damaged when the action was cycling, but I did a lot of testing hand loading rounds, and releasing the bolt from the same position, and it didn't help the issue. It's also not consistent that the flyers are first, last round etc. The only thing I can think of now is that the ignition is not reliable. However I'd expect that if it was just an ignition issue the variation would be only vertical and I don't really see that. The other thing I've noticed is the chamber face/bolt gets really gunky fast, less than a box the whole bolt face and chamber will be fully coated no bare metal showing. So I've wondered if that's impacting headspace, but that would seem to cause a slow erosion of accuracy over time, not massive flyers. I've also made sure to clean that area every 20-30 rounds, and it didn't really change flyers. Seems to shoot the same barrel clean or dirty, does about the same off a bipod with a rear bag or a front rest.
At the end of the day, JP knows their product better than I do, and if they say you're unlikely to see better than 1/2" c-c groups even with the best match ammo, it's probably foolish to think that I'd be able to make it do better.
To be honest though, and I'm small sample size and far from an amazing shooter, but I haven't been overly impressed with JP's Supermatch barrels from a raw accuracy standpoint, as far as building off their barrels. I do think they make a nice accurate barrel that's also lighter weight and shoots different ammo types all pretty well. I have a 6.5, 224, 22, and 223 wylde JP barrels, and none of them accuracy wise will stay with my Bartlein or Krieger barrels for basically the same price, but they are lighter, and less picky about what ammo they shoot well (this 22 barrel aside).