I just did a quick tally (and anyone feel free to correct me) and this is what I came up with:
(Red) Security personnel: 19
(Red) Support Services: 8
(Blue) Sciences: 3
(Gold) Command: 7
That's the total for the series with the bulk of those happening in the second season. Of those 37 casualties 27 of them are redshirts and 8 of those are Engineering or Support Services. Overall casualties averaged over 3 years = 12.3 deaths per year.
The Redshirt effect is not about the TOS universe, but about what is shown on screen. So, 37 hands lost in all series, it's almotst one casualty each two episodes. 27 dead redshirts, it's one victim each three episodes.
Of course, it's not how it happened, it doesn't follow any specific frequency, but at the end, it's still a lot of redshirt killed on screen and they're indeed the classic casualties.