"Carry dollars at work" relation to annual carry distributions

How do "carry dollars at work" translate to actual annual carry distributions? Heidrick & Struggles 2018 survey mentions that they calculate "carry dollars at work" based on stated assumptions and expected returns, then they provide percentiles and mean figures for carry broken down by AUM for "all funds" and "most recent" fund. So are "carry dollars at work" an allocation--a theoretical value based on a set of assumptions (e.g. under a 2/20 model with 8% hurdle and $500mm AUM with a fund ROIC of 3X, the partner will receive "X" dollars in carried interest distributions based on the number of bps allocated to that partner?) So how do the annual carry distributions work in relation to the theoretical allocation? For instance, in a Holt-MM&K-Buyouts Insider survey (2016-2017) under the categorical variable "Large LBO/Growth Equity" firm average dollars at work for a Managing Partner/CEO was $56.3mm for "most recent fund" and $118.1mm for "all active funds." Under the same variables, the Managing Partner/CEO received an average of just over $8mm in annual carry distributions (not broken down for "most recent" or "all active" funds). Is it correct then to assume with these variables that the average annual carry distribution received by the large LBO firm CEO would be either 1/7th the carry dollars at work (if the distribution figure they provided was based on "most recent fund") or even 1/15th (if it was based on "all active funds")? Is the relationship between "carry dollars at work" and annual carry distributions linear?