This is the second time since replacing tires that I have come back to my jeep after a 6 mile ride to find a rear rim brake pad rubbing. I noticed pedaling seemed harder the last half mile ir so.
When I put my bike on the carrier I spun the tires looking for stickers and the rear only turned about 6”.
It’s a 2013 Spec Roubaix with Ultegra groupset.

Grab the entire brake caliper in your hand, rotate it until isn't centered on the rim. If it rotates too easily, tighten the 5mm mounting bolt that attaches it to the frame.

Make sure you have the wheel fully seated up into the dropouts and the qr fully tight.

It doesn’t rotate easily. I centered it a few days ago after it did the same thing. I made sure there was the same space between the pads and rim on both sides.
I thought I had the wheel all the way up in the dropouts but since I did have it off then reinstalled it I will check that first.
Is there any situation that can cause the brake to rotate to one side?

Which generation of Ultegra? Is there a centering adjustment bolt? See Acrobat file (for Ultegra 6800) at URL below on pp. 13-14.

DM-BR0003-09-ENG.pdf

This is the first thing I would check. After that, check that your wheel is spinning straight and not wobbly.

For example:
1. See above re: centering adjustment bolt.
2. You keep hitting your brake caliper on one side.
3. Assuming you have a dual-pivot brake caliper, one pivot is binding. Disassemble, clean, and grease all moving parts.

Hitting it with the tire when putting it in. Or the cable pressure if it is too loose on its mounting bolt.

Let's be clear about this. When Kontact said to rotate the brake, he meant that the brake body must actually move relative to the frame. Lots of people just push on one of the brake arms and think that they are centering the brake. That's not how it works and after a few applications of the brakes, they will be off-center again. If you can't move the brake body by hand, then loosen the attachment bolt, center the brake, and tighten the attachment bolt while making sure that the brake body doesn't move. You might need to do this a couple of times to get it right. I always tighten my brake attachment bolts such that the brakes can't easily be knocked off center, but so that I can move the brake body with significant hand force.

I will check that later. I may have been only moving one side.

The mount bolt was tight. I managed to get it moved just enough. I must have moved it when I installed the rear tire.
Someone mentioned what series Ultegra it is. It cam on my ‘13 Spec Roubaix. I have no idea what series that is. Here is a pic.

In the photo above you can see a small chromed Allen head screw just above and to the right of the "A" in Ultegra. That is for fine tuning the centering of the brake pads. You can see them get closer/further away from the rim as you screw it in or out.

It was me in post #4. Your brake caliper appears to be a BR-6700. Dealer manual: SI-8G60A-003-ENG.pdf

From your photo, the cable adjustment nut (see dealer manual at step 5) seems to be too far up. Screw it back down and pull the cable further down into the pinch bolt. You may also want to consider steps 4 and 7.

Thank you! That manual is very helpful!

2013 and 10-speed equals 6700. But it really doesn't matter. Check that the pads are hitting the rim squarely. It looks like the right-hand pad is half way into the spokes.

The small allen-head bolt on the right side is a centering screw. It's been loosened so much that it might fall out soon. You have to tighten this before that happens. Tighten it so you can't see the threads anymore, and give it an extra turn. Then re-center your caliper as Kontact told you to. Then tighten the allen-head mounting nut on the other side of the bridge.Then re-adjust the pad height so they both hit the rim squarely. Then fine-adjust the cable tension if necessary. Then fine-adjust the centering using that centering screw, so both pads hit the rim from opposite sides at the same time. You shouldn't have to give it more than a quarter turn in one direction or another.You can tell it's right when you feel a solid "thunk" of the pads hitting the rim simultaneously. Also, the rim won't move sideways when you apply the brake. And if you did everything right, you've done a better brake job than the average shop pro. The reason I instructed you to do it in this order is because that centering screw affects cable tension and pad level.

I will put it on my work stand in the morning and check front and rear brakes.

Just curious how you were able to determine that it is 10-speed. Ultegra 6800 was released in 2013, so going by model year that I had pulled the BR-6800 manual in post #4.

Might as well start with new brake pads too. Hard to tell if one side is more worn than the other from the angle of the photo, but if they were misaligned for a long time, uneven wear may have occurred.

It is an 11 speed.

I adjusted it this morning. I used the balance adjustment screw and watched to make sure the pads touched the rim at the same time. I moved the right pad up slightly and set it more level. I set the cable adjustment to match the front. It was at the end of its adjustment range. I will buy new pads. These don’t look really bad but they are probable old and it’s cheap peace of mind. One pad did look like it was worn at a slight angle.

My mistake, good catch. I'd long forgotten when 6800 came out, but I should have guessed by the shape and anodizing pattern on that caliper.

Riders will continually knock the caliper to one side when they replace the wheel, and then recenter it using the screw. Some mechanics will do this too, I've noticed. After a few of these adjustments, one pad will be too high and the other too low, and the screw will bottom out or fall out. It's best to center the caliper like Kontact said, and then use the screw for fine adjustment, like after a few hundred miles of pad wear.

After re-installing the wheels I just pushed the calipers to center them. I didn’t know about the screw.
One pad was at the correct height but the other was low.
I know what to watch for now.

I just did a 6 mile loop around a local lake.
The bike rides much better with the brake off!😄

Hmmm?

Now I am confused. The photo shows a BR-6700 based on the location of the centering adjustment bolt. Maybe pepperbelly has a mismatched groupset? (Nothing wrong with that. My main road bike is a mish mosh too.)

No- you are correct, it is a 10 speed rear cassette.
I have no idea why I was thinking it was an 11 speed all this time. I must have miscounted when I first got it.
I have passed up deals on spare parts because they were for a 10 speed.

Well, Shimano 11-speed non-Di2 drivetrain components are now relatively inexpensive, and work with your existing 10-speed crank and chain rings. (Like I said, my main road bike is a mish mosh.)

I don’t need to replace anything right now but I passed on a Shimano 10spd Dura Ace cassette for a steal- new in box.

Whatever. They adjust pretty much the same.