I’m a little confused on why you think a harmonic mean would be more apt here?
You state:
But this isn’t true, at least not from my knowledge of harmonic means I learned while learning engineering.
A harmonic mean would be used when averaging different rates being performed together, not simply when a task is being performed together.
You use the terms parallel and series, so I’ll apply it to circuits since that’s something I know fairly well: the reason that a resistor network would use the harmonic mean when the resistors are parallel is because the current flowing across them is at a rate of time. The change in charge with respect to time across the network is occurring simultaneously but at different values, and so you would need to use a harmonic mean because these rates are different between elements of the circuit.
Because these things are time derivatives with different denominators (the currents), we have to use a harmonic mean which would allow us to ignore common denominators, otherwise the resistance values would not hold up.
However, in Overwatch our ranks are not time derivatives. They aren’t rates at all. At least not explicitly.
The assumption here is that two individuals, ranked differently, would need to use a harmonic mean in order to determine the correct average of their ranks, but this requires that we have these values as a rate of something. A rank, however, does not determine the rate at which an action is performed for instance: it is only used to determine someone’s general efficacy on the ladder.
Harmonic means are also used in instances to mitigate the impact of an outlier, but it actually doesn’t do that in this instance, it agitates the impact of the outlier as per your own calculations.
Perhaps you could use harmonic means when averaging the ranks of individual roles in the match, but it would be very difficult to do so across roles. I could see an argument, for instance, that a rank indirectly represents a DPS’s ability to kill a target within a period of time, and the higher the rank the faster they would achieve that goal. I don’t believe this would be a correct usage, though. Contrast that with a DPS vs a Support, what task would you compare across them?
I may be misunderstanding something, as my knowledge in statistics is not well polished, but my understanding of harmonic means would suggest it isn’t the correct answer in this situation.