Had to get rid of my entire collection back in 2008 that I put outdoors in the backyard. We had lots of other fruit so all those sucking insects probably spread it around. Haven't noticed abundant offsets, except for H. JohnsonII which did have a lot of offsets, though I think that is normal for that variety.

I have had several papilio clones (which is known to be resistant to virus) produce up to 10 offsets in a year, so I don’t think virus has an effect. The hybrids I have grown that had virus didn’t produce many at all, maybe 1-2 a year. I suspect pot size may have something to do with it - larger pots encourage more of them to grow. How much space is there between the mother bulb and side of pot?

I've definitely had bulbs with red blotch that offset like crazy. I had a Chico bulb that eventually bit the dust, but produced a lot of offsets before dying.