Stay straighter to the right of the carrydown.  Its going to hurt him worse than you.

In a league setting, 1 urethane ball may create some carry down. 4 or 5 guys throwing reactive will chew  up the pattern, much more and faster.

I would think main way that urethane will mess up your bowling, is if you think it is, or blame poor shots on it. If you go in thinking this guy is messing up your shot -  you  probably messed up your shot b/f he throws a ball down the lane.

That being said - probably a solid reactive ball would work better, just whatever you have that rolls a little earlier. If there really is carry down, you need to get around it by going a  little further inside and getting your ball outside of his line. Realistically,  you may just notice the shot breaking down a little less than usual.

Some other things that effect carry down besides just urethane are rev rate and what "urethane" ball is being used.

If he doesn't have much hand - well anyone with a lower rev rate will alter pattern much slower.

Also, what ball? A black hammer that isn't going to flare or a Fever Pitch that will?

This summer I used almost only "urethane" in two sport shot leagues. Thankfully, no one seemed to notice, care, nor complain about me messing up the shot.

Technology marches on. If you want a Urethane like reaction without the Urethane carrydown baggage, look at the new Brunswick Phantom.
 
After being completely unimpressed with EBI's attempt at this type of ball in the Hammer Web Tour, I was reluctant to try Brunswick's version. They nailed it. The Phantom is a ball worth looking into.   

Havent tried the Phantom,  but there is a reason people are going to the purple hammer in droves.  It fights carrydown better than any urethane I have seen, yet still retains a strong urethane look.

Why weren't you a fan of the Web Tour?

Mostly for the reason shakezilla9 outlined. The Web Tour wants to hook at your feet, so it's a very condition specific ball. When there is enough oil for it, I personally find oilers with a higher differential to be more useful. Different styles will come to different conclusions. But I live in an EBI dominated area, and it's a ball rarely used by better bowlers.
 
As for Urethane, I have the Purple Hammer, Black Hammer and the Hot Cell. The Purple is the best of the bunch, but it's still Urethane. It suffers the same carrydown warts as other Urethanes.
 
I'm not a fan of Brunswick for many reasons, and the Phantom was a buy to keep my proshop guy from continuously hounding me about how much I'd like it. He was right. It's every bit as good as the Purple on fresh with clean backends, but still chews through later block carrydown in a way the Purple (or other Urethane's) can't.

Don't meant to turn this into the "dunk on the Web Tour" thread, but I mostly feel the same, though taking the surface up to P3000 is an improvement in getting me closer to my preferred line.

I took mine up to 3000 as well. It's almost as strong as my Rip'd Solid. When it's in play, it's AMAZING, but it rarely ever is. Maybe would be a good choice for tweeners on semi-long patterns. The shape is really nice, if it weren't so damn strong...

I think urethane is curremtly being over used on house shots, but there is a place for it on occasion for us tweeners.  When we can stay a little more direct just outside the oil line our carry can be better than resin.  Doesnt always work, but worth a s try when flat 10s start popping up, as we have to start a little too deep on the oil