TwiggyTracking player improvement over time : i suggest you ask directly GentlemanJon who has done prior "research" in this field.
I would be interested in stalemates data : can you recognise from the logs that a stalemate happens, and what are the most common ways it gets unlocked, on what maps in what zones does it happen, etc. Although you'd have to work with very incomplete data because the log gives you player positions on kill events and not on damage.
You can tell if scouts have low DPM that a game was slow. I'd imagine that, if you could see the damage outputs within a certain timeframe, you could do this to pinpoint stalemates. You could also look at offclasses.