I think the main point is that stratum on its own doesn’t say much about accuracy. One S1 server can be less accurate than an S4 server from a different server chain. Even in one chain it is possible that a higher-stratum server can be more accurate than a lower-stratum server if it has a more stable clock and is averaging measurements over longer interval (assuming the network/timestamping asymmetries between the two servers are smaller than their clock instability).
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Exactly.
It depends on so many factors, that it’s far from sure S1 is more accurate then S4.
A DCF77 will be S1 but it’s by far as accurate then an S4 that’s connected via HW-stamping-hirachy to an S1 GPS with PPS on RS-232.
Still both are S1. To remove this accuracy-problem you should select multiple sources, no matter if they are S1 or S2. It’s the combined sources that will make your server more accurate.
As mlichvar also writes, there are too many factors.
Therefor you need to combine sources to get the best accuracy. Don’t use only S1 servers, unless you know what hardware they are using. Not all are PPS-RS232-accurate.
Sample of a high-accurate S2 server, it wll beat many S1 servers: https://ntp.teambelgium.net/ntpstats
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