I found this after reading and responding to this post here about early Trek fans' prejudicial negative reaction to TNG. One of my responses (see here) was to point out that any fans of the progressiveness of Trek ought to have been mindful of the room for improvement over TOS, with female representation being an obvious issue. I posed the question "when did Trek start consistently passing the Bechdel test", thinking that it didn't start happening until Voyager, which those hard-line TOS fans would never have allowed to be made (along with TNG and DS9).
And of course, someone's done the analysis with graphs and everything! Awesome! (though note the links to tumblr posts at the bottom that are now behind a sign-in wall ... fun).
The results aren't surprising to me, generally. I expected TNG to do worse, but also thought it did a pretty good job with female guest characters so it might score higher than I thought. DS9, I expected to do better than TNG, which, to my surprise is only marginally true. But I didn't expect, from memory, how much of that is attributable to so many characters breaking off into (hetero, yes even Odo) couples. Voyager obviously does very well. And Enterprise ... well we shouldn't expect much of that ... honestly, for me, this cements the show's status as a blight on this era to lean so masculine straight after voyager.
And of course TOS shows its age, which, surely by 1987, good Trek fans should have been aware of?
Beyond that, I can't help but think of SNW here, which, IMO has a wonderful cast/crew that's well balanced and which I'd expect to be doing well on the Bechdel (as low and superficial bar as it is). But, as it starts to transition into a TOS prequel/reboot (as it is trending from S2 and as the show runners are indicating), all of those TOS characters are going to carry that 60s baggage with them. They'll all be men (Uhura is already there!) and all be special miracle workers. La'an's story has already been sidelined into a Kirk romance. Pelia the engineer was already somewhat substituted by Scotty the engineer. As it goes on (presuming it does), I think it could begin to look awkward once you squint.
EDIT: For those asking about new seasons/series ... I found this page/blog by the author of the parent blog post ... which provides data for some new Trek (Disco and Picard S3 and SNW S1 it seems).
Somewhat notably to me (though only one data point) ... the one episode of SNW S1 that (clearly) fails the test is the one with Kirk in it.
In a similar vein though, while Disco generally does well (best of all Trek so far it seems), the author notes that Season two had the most episodes that were close to the line, because Michael’s arc was so intertwined with her search for her brother, Spock. That is, the more new Trek leans into TOS nostalgia, the worse this gets.
I take your point. DS9, as the linked article's author points out, scores worse on the bechdel over time because characters get paired off into couples more and more, which would arguably show in the reverse bechdel too.
Given the numbers and the low bar of the bechdel, some quick sampling could probably be done to get a picture. Select 10 episodes that pass the bechdel test and 10 that fail, maybe some from TNG ans some from voyager, and we here collectively try to see if they pass/fail the reverse bechdel test in a group effort?
My personal bet is that until the bechdel pass rate goes up into ~90%, your point won't really fly and the reverse will be passed all of the time ... still interesting to find out.
Test definition
In the era of "just asking questions", I certainly understand any implicit assumptions that I'm oh-so-cleverly concealing some ill-conceived "point" about feminism. Certainly a case can be raised that by presenting a possible chink in the supporting evidence of your post is an inherently disruptive and destructive act; clearly your broader point about closet bigotry affecting fan biases is both correct and worth emphasizing. I'd far rather strengthen your argument than tear it down. I hope that's ultimately what I'm doing here.
I don't think I would trust the results of this, unfortunately, as there's probably a reverse correlation between the Bechdel and reverse Bechdel tests; in a sample this small that would pollute the results. For example, take any episode where two characters of the same sex are stuck together in some sort of trouble. That episode will surely pass one of the tests (Bechdel for two women, reverse for two men) but has an increased chance of failing the other because much of the dialogue for the rest of the characters is likely to revolve around the plight of the imperiled pair.
...which isn't to say that what you suggest isn't worth the attempt. Certainly raising an issue and then shooting down a proposed solution to it isn't very helpful. Episode transcripts are out there; maybe there's a software solution here? Automatic identification of conversations between two characters would be imperfect but manageable, running that dialogue up against a list of names of male/female characters and then manually checking up on the episodes that missed to avoid false negatives would probably be the most technically efficient way about this?
Circling back on your actual point, though... You are absolutely and unambiguously correct that TOS did a horrible job with gender representation, much worse than TNG did (or could have been expected to by fans when it was about to air). It's also clear that Voyager did much better than it's contemporaries, and ENT was a pretty harsh step backwards. You don't need to know the base rate to establish if one number is bigger than the other, only to draw more nebulous, general conclusions about how well shows are doing with gender representation.