Let’s start with elongation or the more commonly used term “chain stretch”. Chains really do get longer as they are used, but it’s not due to anything stretching, it’s simply the accumulated wear between the pins and the bushings formed into the inner sideplates. It is also the only type of wear that increases the pitch of the chain, beyond its nominal .500 inch. It’s commonly recommended to not allow a chain to elongate more than .5% , which is 1/16 inch per foot or ¼ inch over four feet of chain. I like to think that ¼ inch over the full chain length of 52-54 inches is close enough. Where this figure came from, I have no idea. It’s not a bad number, but only relevant to chains that exhibit significant elongation. Some brands will elongate quickly, so adhering to this recommendation might work with those chain (like Shimano). Others will show very little elongation, even after 5,000 miles (Campy is one example). If you wait for a Campy chain to elongate by .5%, you’ll be waiting a long time and causing cog damage long before that much elongation is ever reached.
The only good way to measure elongation is with a 12 inch or longer scale, a full length comparison with a new chain, or some other properly made gage for measuring length, that does NOT rest against the rollers. The 12 inch scale is most common tool, but the least accurate. Place the end of the scale on the edge of a pin. The pin at the opposite end of the scale will be totally covered when the chain is new. As the chain wears, this pin will begin to “peek out” from under the scale. When half of this pin is exposed, you’ve reached a little more than 1/16” of elongation per foot. Full length comparison with a new chain is not a bad method either, but I have found that some new chains may be up to 1/16” shorter than nominal when new. That amounts to 25% of the ¼ inch that you’re trying to measure. What looks to be .5% elongation may really be .38%.
My tests have proven that cogs can be worn to the point that they will not engage with a new chain (chain skips), even if the only chain used on the cassette never exhibits more than a fraction of the commonly recommended .5% elongation. The culprit for this cog wear is not elongation (change in pitch), but roller wear. Rollers always wear much more than the pins and their mating bushings, regardless of brand.
A well worn roller might have an OD reduced by .006 inch, or about 20 times the wear on the pins. If you’ve ever disassembled a chain link, you’ll see that the roller rides on a bushing, formed into the inner side plates. This is a 2-piece bushing with a gap in the center. A severely worn roller will have a diameter in the center that’s about the same as new (since it never touches the bushing), but an area on both sides, where it contacts the bushing halves, that is much larger. It’s quite easy to see the depth of the wear with the naked eye, since they are so deep. You may find the ID of a roller increased in diameter by .010 inch, which is about 30 times the wear on a pin. When I measured the distance between rollers (inside to inside) on a worn chain (6,000 miles), I found an increase from .200 inch when new to .235- .240. IMO, that chain was worn out to the point it should be tossed. The official recommendation from Campagnolo is to toss a chain when the roller spacing has only increased by .020 inch. IMO, that sells a lot of chains, but is much too conservative. I use dial calipers to measure the distance between rollers, so I can compare the new and used dimensions. Shimano and KMC chains have a significantly longer .210 inch roller spacing, compared to .200 inch for Campy, so that should be taken into account when figuring the roller wear.
The last wear area that can be monitored is the side clearance. When new, you’ll most often find a side clearance in the .004-.008 inch range. With a lot of use, that clearance might increase into to as much as .013 inch or more. If you’re into that range, then the chain will exhibit a lot of side flex that may affect shifting precision. Side clearance is easy to check with feeler gages.
Now that you have some idea of how to monitor chain wear, there’s the more complicated issue of how often to change a chain and when to trash it, in order to maximize cog life. Some people change chains very frequently, probably long before they are fully worn, and get more cog life by doing so. The only problem with this approach is that at some point, a new chain will be installed and chain skip will still occur on one or more of the most worn cogs. The cost of all the chains thrown away in an effort to increase the cog life could easily exceed the price of a new cassette and most likely, it is not the most cost effective approach to chain and cassette management.
The most cost effective method of managing chains and cassettes is to use at least three and perhaps more chains, in a regular rotation. The idea here is to get some use on all of the chains, before enough cog wear occurs to produce chain skip with the last new chain in the rotation. I like to get the most from my chains and never seem to notice deteriorated shifting from side wear, so I like to use only three chains expecting about 5,000 miles from each (Campy) chain. If I was using some other brand, I’d buy 4 or 5 chains and expect to get about the same 15,000 miles from them. The primary requirement for a practical chain rotation schedule is a reusable link to join the chain. A Campy chain can be joined with the HD-L pin for its first use, but after that, a reusable link is needed. Shimano chains can be joined several times, using the special joining pins, available from Shimano, but I’d probably choose a properly fitting reusable link. You don’t need to log a lot of miles on any one chain on its first use. 1000 miles is plenty, but I tend to use each of three Campy chains at least 2,000 before rotating. Once each chain has some mileage on it, chain skip should never occur when rotating to one of the other partially used chains. Each chain can gradually be used until it reaches one of the dimensional limits for elongation, roller wear or side wear. Some brands will hit the elongation limit first and others may hit the roller or side wear limit, but all brands eventually hit the trash can.
About cassette life; there is no reason to change a cassette unless a new chain is installed and skipping occurs on one or more cogs when pedaling with heavy pressure.