“Why the 40,000 Token Cap?” : The Analysis Behind the Cap
By Ava Masucci
The Telos network is a new, distinct network based on a code-fork of the EOSIO software that also powers EOS. Telos will use a token distribution identical to the EOS genesis snapshot except that each account will be capped at a maximum of 40,000 tokens to greatly decrease centralization of token ownership, and therefore voting, on the new Telos network in an attempt to make DPOS sustainable and governable.
The 40,000 token cap was decided upon after analyzing the EOS genesis snapshot. This analysis showed that the data was heavily skewed to the right. In lay terms, this means a large majority of token addresses contain a small number of tokens, with few addresses holding large numbers. The mean (or average) is also larger than the median. Given these statistics, the EOS distribution is highly centralized. In the EOS snapshot, the average token address holds 6080 EOS and the median token amount is about 102 tokens. The median value means that half of all EOS addresses contain less than 102 tokens and half contain greater than 102 tokens. Or 81965 addresses have less than 102 tokens, and 81965 addresses have more than 102 tokens. This further emphasizes how skewed the token distribution is.
The largest address (block.one) has roughly 16,450x as many tokens as the average address.
A box plot (shown above) or box-and-whisker plot, shows the distribution of quantitative data in a way that facilitates comparisons between variables or across levels of a categorical variable. The box shows the quartiles of the dataset while the whiskers extend to show the rest of the distribution, except for points that are determined to be “outliers” using a method that is a function of the inter-quartile range. (https://seaborn.pydata.org/generated/seaborn.boxplot.html)
Any EOS account with more than the inverse log(10.5) or 36315 is deemed an “outlier”.
Telos’ Solution: A More Equitable Distribution for Voting
Various cutoff numbers between 5,000 and 70,000 were analyzed to determine the most effective, least intrusive token cap amount. The 40,000 cap was found to be the best number for transforming the token distribution from highly skewed (“abnormal”) to “normal.” This analysis was conducted by log transforming the EOS snapshot data, a common technique used by data scientists and statisticians to better analyze highly skewed data. From the above data visualizations, you can see that the log transformed distribution looks close to a normally shaped bell curve up until ~ log 10.5 or 36,315 tokens. Rounding up to a whole number that’s psychologically significant brings the ideal cap to 40,000 tokens.
The 40,000 cap radically alters the token distribution from EOS in the following ways:
• Removes 86.5 % of token supply, or 865,000,000 tokens
• Reduces the holding of just 0.67% addresses, or 1,098 individual addresses, registered at the snapshot.
• The circulating supply is reduced from ~996,691,000 EOS to 178,473,249 TLOS tokens.
40,000 is that “sweet spot” that alters a low number of addresses to achieve a more equitable, statistically normalized distribution that’s similar to the familiar bell curve:
Note that there are no “outliers” in the Telos distribution with the 40,000 token cap!
Standard deviation is the square root of the average of the square distance of measurements from the mean. The standard deviation in the EOS token distribution is over 100 times greater than in Telos. In EOS, the token amounts are greatly spread out. In Telos, token amounts are closer to the average of 1088 tokens.
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