In Stake PAN for Your Community, we laid out the staking cluster model that we’re pursuing for Panvala. In brief, communities can start staking clusters to earn donation matching capacity for their communities. Communities aim to stake a share of the staked tokens that exceeds their share of the donations they raise. Communities with excess capacity will be matched at the highest rates. Communities that exceed their capacity will be matched at lower rates, but it’s always better to raise as many donations as possible.

We’ve put together a spreadsheet that calculates each community’s matching based on the tokens staked in clusters and the tokens that each community donates. This post will explain how each community’s subsidies will be calculated for Batch Seven. The details can get a little bit complicated, but like any new game you’re trying to learn, the best method is to play for a round or two to get a feel for the game.

Here’s the spreadsheet that calculates matching budgets for each community in Panvala’s league. The scenario we’ll discuss uses the staked token totals for each community as of June 11, with an extra small cluster to match PAN donations to projects that none of our communities have chosen to support. We’ve put in example donation totals for each community so you can get an idea of how staked tokens and donations interact.

In this scenario, the average multiplier for all donations is 12.95x. Four clusters stay within their capacity and earn the highest multiplier of 15.69x. The Hashing it Out cluster exceeds its capacity and earns a reduced 13.75x multiplier. The cluster for Other Donations vastly exceeds its tiny capacity for a much smaller multiplier of 4.49x.

Let’s dive into the calculations that produced these results. To start with, we calculate the **preliminary capacity**, which is the share of staked tokens that each cluster has. A cluster’s donations will be fully matched to the point where the share of donations equals the cluster’s capacity. The donations that overflow the capacity will be matched at lower rates. The preliminary capacity isn’t the final number, but by comparing donation shares and capacities at a glance, you can get an initial idea of which clusters have exceeded their capacities.

The second phase of our calculations drops excess staked tokens from each cluster. In the “Policies” tab of the spreadsheet, we’ve set the **maximum staking advantage** to 1.5. That means a cluster will only be credited for up to 1.5 times the median tokens staked per donation for all clusters. This limits the influence of whales: staking millions more tokens than other clusters won’t make a difference, but it’s still good to have more staked tokens per donation than the other clusters. After we’ve dropped the excess staking, we can calculate the final **capacity** values, then find out their **utilization**: the donation matching capacity that was actually used by each cluster. Those utilization numbers reflect the summary results for each cluster in the first screenshot above: four are below 100%, one is nearly 150%, and one is way over capacity at over 1200%.

Next, we want to account for the reduced matching that gets applied to each cluster’s **overflow**. First, we separate the overflow percentages from the **fully-matched utilization** that is 100% or lower. Next, we calculate the **diminished overflow**, which applies an increasing marginal cost to each percentage point over 100%. Each additional percentage point of overflow will be matched at a lower and lower rate. The **overflow penalty factor** in the “Policies” tab determines how fast that cost increases, which is set to 5 in this example: the percent overflow needed to be credited for a percent of **effective donations** increases at a rate of 5 times the overflow percentage, or 5x + 1 . We solve its integral \frac{1}{2}5x^2 + x at the value of overflow, which is \frac{-1 + \sqrt{1^2 - 4(5)(\frac{1}{2})(\text{-overflow})}}{2(5)(\frac{1}{2})} . Hashing it Out’s overflow of 47.30% is reduced by about half to 27.88%. The Other Donations cluster has its large overflow reduced to almost a sixth of where it started. Multiplying the sum of the fully-matched utilization and the diminished overflow by the original donation total for each cluster gives their **effective donations** that will be used to calculate their share of the subsidy.

To determine each cluster’s subsidy, we start with Panvala’s **total quarterly budget** of 1,899,401.76 PAN. Our governance process allocated 75% of the total to Panvala’s league of communities for donation matching, which gives a league budget of 1,424,551.32 PAN. Any donations sent during the round have already been sent directly to their recipients, so we subtract the 110,000 PAN donated from the league budget to get the total subsidy, then multiply it by each cluster’s share of the effective donations to get the cluster’s **subsidy**. (In Panvala, all donations end up back in Panvala’s token supply, so the 110,000 PAN subtracted from the league budget represents 110,000 PAN that will literally be deposited back into Panvala’s token supply contract to complete the cycle of our token model.)

Adding each clusters’ donations to their subsidy gives their full **budget**, and dividing the budget by the donations gives the **multiplier**, the metric that matters most in Panvala.

With these results, how should each community respond? Well, it always makes sense for all communities to encourage as many donations as possible. Hashing it Out has exceeded their capacity in this example scenario, so they would want to encourage their community members to stake more tokens to get an even higher multiplier than 13.75x. DXdao was nearing their capacity in this scenario at 80% utilization, so they probably want to encourage more staking as well so they have room for growth.

On Monday, Panvala’s donation matching campaign on Gitcoin Grants begins! You and your community can earn the most funding for the projects you support by donating to them in PAN. Last quarter, PAN donations were matched at an average of 12.9x. This quarter’s multiplier depends on how much you stake and how much you donate. We’re looking forward to seeing each community’s results!