Basically, the active form of chlorine is hypochlorous acid that does most of the disinfection killing bacteria, inactivating viruses, killing algae and oxidizes organics. Hypochlorite ion is far weaker by orders of magnitude, but most (about 97%) of what is measured as Free Chlorine (FC) is actually in the form of chlorine combined with Cyanuric Acid (CYA) in a series of compounds called chlorinated isocyanurates that are almost inert. They do not disinfect nor oxidize to any great extent. They do, however, release the chlorine as hypochlorous acid as this gets used up.
shows the traditional industry graph of hypochlorous acid concentration as a function of pH when there is no CYA and then shows the true graph when CYA is present. The NSPF CPO and APSP TECH courses don't teach this for whatever reason.
The amount of active chlorine, hypochlorous acid, is proportional to the FC/CYA ratio. So if you double the amount of CYA in the water, then you need to double the amount of FC to have the same level of disinfection, oxidation and algae prevention. It's easy to have CYA rise when using stabilized chlorine since the following are chemical facts independent of concentration.
For every 10 ppm FC added by Trichlor, it also increases CYA by 6 ppm.
For every 10 ppm FC added by Dichlor, it also increases CYA by 9 ppm.
For every 10 ppm FC added by Cal-Hypo, it also increases Calcium Hardness (CH) by 7 ppm.
The technical derivation for the FC/CYA ratio is described here
and some qualitative descriptions are also found here
in extracts from the original paper presented at a 1973 symposium and published in 1974.
The stabilized chlorine industry has been touting the mantra "CYA doesn't matter; only FC matters" for whatever reason and unfortunately this has also led to the belief that "CYA should not be used in indoor pools; it only protects chlorine from breakdown from sunlight" which is only a half-truth since it leaves out the significant fact that it reduces the active chlorine concentration. This means that pools without CYA, such as indoor pools, are over-chlorinated by orders of magnitude with 10-30 times the amount of hypochlorous acid concentration needed. This leads to much faster degradation of swimsuits (elasticity gets shot), flaky skin and frizzy hair as my wife experiences during the winter at a community center indoor pool while in our own pool during the summer there are none of these problems even after 5 years.