the k effect (from 150 to 500)

The Cardano main network was set at 150 with the parameter k in August 2020. This is the desired number of pools. It is not a hard cap, but reward and ranking formulas use this parameter to achieve a so-called Nash equilibrium around this value.

On 5 November 2020 and after some discussions with the Community, the researchers and engineers involved, there was a decision and communication to increase this value from 150 to 500 and to put it into effect on 6 December 2020.

This is a big step but makes sense. Many small steps would require both pool operators and stake delegators to permanently adapt on a new epochs desired state, in order to avoid ending up in over-saturated and less rewarding pools.

We have refreshed our previous work showing the development of pools and pool clusters and will look now at the effects after this new k value announcement.

As expected it wasn’t that easy for all pool operators to quickly reach out to their delegators. It took many epochs and weeks to rebalance the stake to more pools at less size.

At k=150, the saturation point of a pool was about 210 million ADA. At k=500, the new saturation point is 64 million ADA. This pushed many pool operators to create additional pools. However, this also prompted some delegations to flow into existing smaller pools.

the progress over time

The following animated graph shows the pool growth and resizing progress over time. Pay special attention to the period from epoch 227 to 234. You can easily jump to every epoch by clicking on the desired position on the timeline.

what did it achieve?

We make snapshots at the beginning of October and 6th December. Then we compare the silhouettes, in order to see the effect of re-delegations to smaller sized pools.

At the first view, it looks good because the red line now is more equilibrated. The ideal Nash Equilibrium would be reached with all 500 pools at equal size (almost flat line).

Update 11.December 2020
after another epoch, we repeated the snapshot and draw another silhouette at the end of epoch 234.

We see that now – after the new k-value has become active – some delegators have reacted a little late but nevertheless. The red curve has clearly flattened further. But there are still 35 pools that are very clearly above the new saturation point and are thus experiencing significant losses in yield.

Whether this red line also means more decentralisation is another question. Pool operators who have created additional pools and directed their delegations to the new pools are not acting in a decentralised way because they are owned and managed by the same entities.

All data used for this visualization comes from