Average in figure 6 and 7

[XofEE]

I recently read your paper, "Modeling the Profitability of the Rocket Pool Smoothing Pool," with great interest. It provided valuable insights into the advantages of pooling over solo staking in terms of profitability.

However, I am having difficulty understanding the disparity between Figures 6 and 7 in your paper. Why is the average reward for solo staking lower than that for staking in a pool? I expected that the median reward for solo staking would be lower than that for a pool, but I assumed the averages would be similar.

I may not have the full expertise to deeply understand the calculations in your paper, but I would greatly appreciate it if you could help me understand this point.

Thank you in advance for your time and assistance.

[htimsk]

Thank you very much for the kind words on the paper. I think I caused the confusion in picking the name solitarius, which is not the same as solo staking. Both graphs show the output of participating in a smoothing pool vs. running your validator without participating in the smoothing pool (SP) (Calling that later case a solitarius validator). For example, in Figure 6, the purple lines are a plot of each of the 1,000 Montecarlo tries for a non-SP (e.g., a solitarius) validator. Here, most of the tries earn less than 5 ETH over the 5-year period. (The purple lines all combine and make the large purple smear on the bottom of the chart.). In some of these tries, the single validator is very lucky, and they earn a lottery block. These lottery-winning validators end up with 10 or more ETH after 5 years of validating. You can see these lines because they skyrocket up, and you can see the individual lines from the smear. So if you take all these 1,000 tries, the average earn is 4.93 ETH. But if you take the median, it's only 3.31 ETH. The reason the median is lower is because the luckiest validator, 220 ETH earning validator, cancels with the most unlucky 0.1 ETH earning node. Do this another 498 times, leaving you with the validator in the middle of the list with the median value. The large discrepancy between the median and mean makes a soothing pool attractive. If you participate in a smoothing pool, you are guaranteed to earn the average of the rewards, but you have zero chance of winning a lottery block for yourself. If you do NOT participate in a smoothing pool, you have equal odds of earning less than or more than the median and a slight chance of winning and keeping a lottery block. The short answer is that if the pool is much larger (90% greater) than the number of validators that you have in the pool, you have a (4 out of 5) 80% chance of doing better in the SP. This is because 1 out of 5 (20%) of the SP participants will be lottery block winners (to some degree), and their winning will help raise the earnings of 4 out of 5 groups. Hence, most people (80%) will do better since they earn the average. 20% of the participants were the lucky ones who now are sharing their windfall with all the pool's members and are performing less. So by joining the SP, you get a guaranteed earn, but you risk the chance of being lucky and having to give up your lottery winnings.

…

On Wed, Dec 20, 2023 at 2:49 AM XofEE ***@***.***> wrote: I recently read your paper, "Modeling the Profitability of the Rocket Pool Smoothing Pool," with great interest. It provided valuable insights into the advantages of pooling over solo staking in terms of profitability. However, I am having difficulty understanding the disparity between Figures 6 and 7 in your paper. *Why is the average reward for solo staking lower than that for staking in a pool?* I expected that the median reward for solo staking would be lower than that for a pool, but I assumed the averages would be similar. I may not have the full expertise to deeply understand the calculations in your paper, but I would greatly appreciate it if you could help me understand this point. Thank you in advance for your time and assistance. Figure.6.png (view on web) <https://github.com/htimsk/SPanalysis/assets/83547957/9d36f5bc-4e35-4404-9284-70a892c18d2b> Figure.7.png (view on web) <https://github.com/htimsk/SPanalysis/assets/83547957/f446c16d-5073-4407-bf0f-bb7be38c7168> — Reply to this email directly, view it on GitHub <#1>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AD6CEUBP4RL6RSLFQ53ZE53YKK7DVAVCNFSM6AAAAABA4TTP22VHI2DSMVQWIX3LMV43ASLTON2WKOZSGA2TAMZQGU2TSMI> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

-- [image: C7T_logosmall] Ken Smith CHP Principal Consultant 510-882-3499 ***@***.***

[XofEE]

Thank you for this response, it has helped me to better understand your work.