So it was conjectured that if all elliptic curves over $\mathbb{Q}$ are ordered by their heights, then the average rank is $\frac{1}{2}$.

Brummer initially showed assuming BSD and GRH that the average rank is bounded by 2.3. Since then many improvements have been made. In my search, I found the slides for a talk by Manjul Bhargava (linked here: http://www.dpmms.cam.ac.uk/research/BSD2011/bsd2011-Bhargava.pdf), where he talks about his result showing that the average rank is bounded by 1.5 unconditionally.

My question is has there been any improvement on his result since then? A reference to such a paper would be appreciated as well.