Large long-running reporting queries are causing very slow new mysql connections

Usually, mysql's connecton time is in the 0.001 second range. However, when I run a large reporting query (that spans multiple tables with aggregates), I get tons of warnings saying that new mysql connections are taking between .5 and 2 seconds just to connect! Why would a single large query affect connection times so much?

Doing research online, I can't seem to find which mysql settings would need to be tweaked to mitigate the issue.

I'm on MySQL 5.6, using all InnoDB tables.