These two charts show how resulting pool reward is affected by changing o and s values. You can try changing the a0 value and see how charts are changing.

Different s as o grows (left or top chart)

This chart shows how rewards for pools with different leader stake (s) change as their delegated share (o) grows. You can see how rewards for each pool logically goes up along with its share up until it hits the "cap" of (z0), and after this even if pool gets more delegated stake - reward stays the same.

You can notice how all lines have different length. This is because you cannot have parameter o to be less than parameter s. This is explained by the fact that when a leader already puts 0.05 of total stake of personal stake (s) into his pool - the total pool reward (o) is also already equal to that number, which means that this pool is already "half-full", and there's only another 0.05 of total stake available for delegates to "fill".

The most interesting property is how all lines are capped at different height. This represents exactly the effect of leader stake on the pool rewards - the bigger personal leader stake (s) a pool has - the bigger eventual reward it will be able to get. You can see that the topmost line only starts at o=0.01 and is already capped - this means that the only way for a pool (or a node) to get the maximum possible reward is to set the personal stake at the maximum possible value. BUT! For a pool this would also mean that there's no "empty stake space" left in there for others to delegate, because any further delegation will move such a pool over capacity and will reduce profits for everyone.

Different o as s grows (right or bottom chart)

This chart shows the same data but from another angle. Each horizontal line here shows the same data as corresponding vertical line on the first chart. So the top line represents any "full" pool (o=0.01) this means that this pool has reached its maximum capacity and will not be able to receive any more reward, even if more people will delegate to it.

You can see top line representing how rewards would grow for a capped pool as leader stake represents bigger and bigger share of it. The leftmost point (s=0) means that there's no leader stake at all - the pool is capped, but all the coins in it are delegated by other people. In the middle (s=0.05) - half of stake is owned by the leader, and half of it is delegated by other people. And in the right part (s=0.01) - all stake in the pool (node) is owned by its leader and reward reaches possible maximum (z0).

Second from the top line represents a pool filled for 75%, it is shorter than the top line, because it is impossible for a pool to have leader stake more than a total stake at all (leader stake is regarded as a part of total stake), so chart would not work that way. This pool will never be able to reach the maximum possible reward, just because it doesn't have enough stake share at all. But you also can notice how this line is a bit flatter than the top one, and the next one is even flatter. This shows how delegated stake affects the total pool reward. Namely - it's something like it adds value to the option of having leader stake. Meaning that if you own a "half-full" pool (o=0.005) - then it is more profitable for the whole pool if you would personally own half of coins in it (0.0025). But if you have a completely "full" pool (o=0.01) - then the profit for the pool of you owning the same amount of coins (0.0025) is even better now, and the whole pool would receive more reward.

Conclusions

The leader stake is important for a whole set of reasons, e.g. - it disincentivises whales to split their stake; it makes pools with a real locked stake more valuable than just empty pools that anyone can create, because former are less likely to brake any rules or be negligent; it also disincentivises whales from creating empty pools and putting their coins in there as delegates, instead of locking it in as leader pledge.

Interesting fact is that any pool in reality will never be able to receive the same share of rewards as its share of the stake is (cuz only maximum possible leader stake can guarantee maximum possible reward). This means that after each epoch there will be "left-over" reward. Do not worry, part of it will go toward the treasury, and the rest will be added to rewards for the next epoch.

Significance of a0

Both presented charts do not plot the a0 parameter. This means that you can change its value in parameters form and see how it changes the charts. Basically, this parameter determines - what will be the difference in rewards between a full pool with no leader stake and a pool created with maximum leader stake. As you move this value around - you can see how capped maximums on the left (top) chart are either drawn together or drawn apart, and also how the top line on the right (bottom) chart gets more and more steep or flat. This means that as a0 grows - the profit from each single leader stake ADA is getting bigger and bigger. And it gets bigger not because top pools are making more money, but because bottom pools are making less. Which is obvious, because they can't have more than 100% of total rewards to distribute.

Note! That detailed a0 plotting can be found on the next page with charts.

These two charts show how resulting pool reward is affected by increasing the a0 value with different o and s values. You can change o or s parameters in the input form and see how charts are changing.

Different o as a0 grows (left or top chart)

On this chart each line represents a stake pool of different stake share (o). You can see how their rewards change as a0 parameter grows. The leader stake (s) is not plotted, so you can change it's value in the input form and see how it changes the chart.

You can see that the leftmost part of the chart (a0=0) is perfectly proportional to the o value, for example, o=0.005 gets 50% of rewards, and o=0.01 gets 100% of rewards, even if you change the s value. This is because a0=0 means that leader stake (s) has no effect at all and can be ignored. This is how one would expect pool rewards to be distributed in a naive system.

But as a0 value grows to the right, you can see rewards getting lower and lower, and the more stake a pool has - the more value it loses. So watching on this chart you can estimate how having a pool of different saturation with no leader stake will be affected by different values of a0.

Different s as a0 grows (right or bottom chart)

On this chart all lines represent pools with the same total stake (o) (by default, they are all full, so o=0.01), but different leader stakes (s). The pool stake is not plotted, so you can change this value (o) in the input form and see how this chart changes.

You can see that in the leftmost part all pools have the same maximum reward of 1.0 (means 100%). This is because at a0=0 difference in leader stake plays no role. But as a0 grows to the right, you can see how the pools with maximum leader stake stay on the same position of maximum rewards, but pools with lower leader stake shift down to lower and lower rewards. And you can see how the lower leader stake a pool has - the greater downshift in rewards it gets.

Conclusions

These two charts demonstrate how majorly maximum rewards can be affected by increased values of a0, an why it is important for stakeholders, which exactly value will be selected by IOHK for the final implementation.

They also show how hard it is to chose the right value, because as a0 grows - security is improved, because it gets more and more costly for an adversary to split stake (one of the main problems the leader stake is designed to solve). But at the same time you get the problem that pools get worse and worse rewards as their leader stake goes down, which results in the whole sector being largely dominated by "whale pools", and anyone without a large pledge would not have a chance to build a sustainable pool. At the same time, as a0 reduces - the environment gets more and more "fair" and "flat", but at the same time a possible Sybyl attack get cheaper ad cheaper to perform. So selecting the proper value for this parameter is non-trivial, but very important task.

Note, that as you change value of s or o on the input form you can notice some lines disappearing from the charts. This happens because o can never be less than s, just because the personal stake of the pool leader is included in the total pool stake. So it does not make any sense to say "what is the reward at s=0.005 and o=0.0", because this situation is impossible.