I've done over 50 runs (did not record data), and at an eyes glance, I'd get an orb around every 1.33 runs and the occasional double orb run.
While I do not have any data to show for this, I'd like to share my experience in farming this was very positive
Edit: They drop Advanced and Elite orbs
http://wiki.spiralknights.com/Lancer_Knightz_%28Guild%29/Mission_Rarities
They have 15 measurements of orbs for Rise or Fall. That's not as many data as you, but they are carefully curated.
They average 0.2 3-star orbs and 0.07 4-star orbs per run. In other words, they got a total of 3 3-star orbs and 1 4-star orb in 15 runs. So they get 1 orb every 3.75 runs.
But 15 measurements is few enough that the uncertainty is still pretty high. They don't show confidence intervals.
And it's conceivable that the drop rates have changed over time, although the bottom of the page shows that it hasn't for Radiants.