EDIT Aug 27: based on feedback from various feedback from the community, for which many thanks, we have concluded the idea brought forward in this post is incorrect:
Contrarily to what this post suggests, large pools can grow all the way up to saturation point, without any negative consequences for their rewards. Even if they get lucky to produce more blocks than they are supposed to receive on average (apparent performance > 1), they receive the same additional rewards (percentage-wise) as any smaller pool also would get.
I will leave the contents of my post below intact for future reference.
After taking a closer look at the widely used term “pool saturation”, I came to the conclusion that the risk of getting less than optimal rewards is not just relevant for operators of --and delegators to-- pools marked as “saturated”.
Due to the Ouroboros randomized slot leadership distribution to stake pools, also delegators to pools which are considered to be far below the calculated “pool-saturation” size, in Epoch 212 estimated at 207M ADA, are at risk of occasionally getting their rewards capped.
To illustrate what is going on, please refer to the chart below:
What the chart demonstrates, is that a pool with an active stake of “just” 138M ADA will miss out on rewards, whenever it gets a very lucky slot leadership assignment and is allowed to mint many more blocks than usual.
Smaller pools on the other hand, with an active stake significantly lower than 138M, can take the full benefit of exceptionally generous slot leadership allocation, without any risk of losing out on any rewards.
As a result, I would like to present my theory that the perceived higher profitability of large (135M+) pools compared to smaller pools could be much smaller than generally assumed.
Although this needs further mathematical research, the downside of losing out on rewards on a regular basis, for large pools actually might have a greater negative impact on yearly ROS, than the upside of being able to divide the minimum fixed pool cost of 340ADA among their relatively larger delegator base.
I am looking forward to your comments on the suggestion that also pools far below saturation, will see their rewards capped every now and then. For the full article I wrote on this subject, read this blog post.
edit 26/8: please treat the idea presented above with caution, until verified against feedback as well as contradictory data from the ITN.