The type of people who put their gender on their profile could be different from the type of people who don't
The paper's conclusion that "women are more competent overall" doesn't seem very plausible to me. If there was really a significant, consistent boost simply from being female then we'd see software companies that consist mostly of women or which are run by women outcompete opposite companies at least some of the time, and it'd be an effect that'd have been detected before. I'm struggling to think of any examples of this.
Based on my own experience of github and open source, however, the only times I have ever seen women contribute to open source, they were always being paid to do so. I cannot recall a single time that I came across a pull request or even just a regular patch from a hobbyist woman. Not sure why that is, but it has been a constant throughout my career - men do hobby programming and women don't.
Given this difference I'd expect contributions from women to be larger overall, tackling grunge work that volunteers wouldn't want to do, solves some real business problem, and more frequently be code that was tested for a while internally first so is less likely to have quality problems.
The fact that men are also less likely to have pull reqs accepted when their gender is known also seems likely to be a correlation with submitting from personal gmail accounts vs corporate accounts.
Possibly related anecdata: from my not insignificant, but still far from comprehensive experience nearly all the women who are developers in my area (not SF—I know nothing about that market aside from what I read) are with bigger companies (not necessarily software companies), and in fact there are quite a few women working as developers with those companies.
OTOH, startups and small software businesses around here do hire lots of women—but mostly as graphic designers, or in sales/marketing, or as project managers. Very, very few women even interview for startup software development jobs here (for whatever reason—I don't claim to have an explanation).
At Google there was (when I worked there) perhaps about 20-30% female engineering staff. Or maybe it was a bit lower, I don't recall, but it was pretty high. Yet as far as I recall, the new projects were typically started by men, I mean the bottoms-up ones. I never noticed it at the time, but thinking back, I'm struggling to think of cases where a woman started a new project with her 20% time (or even took it, actually). That might be just lack of data points of course. Projects created by employees weren't at all rare there, but it still wasn't something that happened every day.
Many women in software, by my experience, are from slightly poorer parts of the world: eastern Europe, Russia, China, India. I suspect to them programming is just a job; a way to earn good money. But it's not something they're especially passionate about in the single minded obsessively focussed way that men can be (and I'm guilty of that).
There's also probably a bit of a gravity affect happening. My entire career I've never been on a team with even a single other woman and it would certainly be a nice thing to go somewhere where that wasn't the case, so maybe it's just easier for companies that employee women to hire more women.
One possible reason: Women have less free time available for hobby programming. There are some statistics on this at http://www.ashedryden.com/blog/the-ethics-of-unpaid-labor-an....
Another possibility: Women are in such demand in the industry that a hobbyist contributor will soon be hired by someone, and no longer be a hobbyist.
This is also something I have observed in my job. I am in a typical enterprise software shop and I feel like women are more likely to see programming as "just a job", while men are more likely to put more passion into it. But most people in general see it as "just a job", so maybe hobbyist female programmers are just rare because female programmers in general are rare.
Who knows.
For me it's a combination of not wanting to deal with the very abrasive personalities idolized in some open source communities and just preferring to spend my free time hacking on throw away code to experiment with new ideas. I write clean readable tested production code at work, I want my hobby programming time to focus on impractical educational exploratory programming.
It also just feels like I have a lot less time to write code than my coworkers, even though I'm the only person on my team without kids. Traditional gender roles are evolving but it still feels like I'm left with more life stuff to deal with.
The reasons for being more careful could be all over the place, ranging from actually being better programmers to being more likely to receive criticism for a bad pull request.
In an industry that's somewhat hostile to women, it wouldn't be surprising that only the most competent women stick around, whereas less competent men stick around more than less competent women, dragging average competency of men in the industry down, even if the total number of competent men might be higher than the total number of competent women.
You're saying this in response to a study that showed the industry being less hostile to women, at least on this particular axis.
I'm explaining how hostility to women can result in a higher acceptance rate of their pull requests. As you could have seen from the numbers in this study, women do far, far fewer pull requests than men. Why? Perhaps, because only the best women remain, and they only submit their best pull requests. That drives the average for women up, while driving the total number down.
And I don't think the acceptance rate of pull requests is a likely vector of discrimination anyway; they're fairly anonymous and focus on the code. But the hostility absolutely does exist in other areas: small talk, jokes, hiring practices, sexual harassment, etc.