You need to provide a more precise description of your system and real-time
If you are interested in only the timeliness and timeliness predictability of
the response to the first event, your question is about that one event response
and not about the subsequent events responses and thus the system.
You didn't specify your required timeliness and timeliness predictability for
responding to that event. It sounds like you are satisfied with your empirical
measurements for subsequent responses to varied numbers of recipients. So for
the first event response, you need to specify your desired response time
constraint, such as a deadline. Then you need to specify the desired
predictability of that response's timeliness.
Perhaps you want to a' priori know that the deadline will always be met--i.e.,
that the response is deterministic (deterministic is one end-point on the scale
of predictability). If so, you need to identify what presumptions about your
system and its execution environment you make for that prediction; that is
called a system model.
Your question indicates that your measurements do not cause you to expect that
subsequent responses be deterministic--instead you expect that if the first
response is deterministic, your subsequent response measurements have been
empirically predicted accurately.
There is a large body of literature about determining worst case execution times
(the first response latency in your case), and the presumptions that are
necessary for those times to be accurate. Formal proof that your first response
time is deterministic may or may not be feasible, depending on the unstated
presumptions you are making. (In general, such proofs get rapidly more difficult
as more things are presumed to be more dynamic instead of all being static.)
But if instead of requiring that the first response time be deterministic, you
are either satisfied with or forced to concede that your system model provides a
non-deterministic first response time, you have to explicitly deal with the
response time predictability.
There is a vast body of theory and practice on that topic in general (although not in the conventional real-time computing field).
In your case, you could simply do sensitivity experiments to measure and establish bounds on the variability of the first response timeliness, by varying parameters of your system model.
To convert that into analytical predictability, you can do probability distribution function fitting. For example, perhaps your measured first response times are normally distributed with means and variances based on your measurements. While not a proof, that gives you an analytical way to reason about that response time.