Warren (2008 pp. 327-329) reports a workshop encounter with a banking executive who described her bank’s strategy for increasing disadvantaged minority representation amongst senior managers from the current 6% to 20%. The plan was to increase the level modestly, year-by-year, by approximately 3% over a 5 year period. In person terms, it would mean lifting the current number of minority senior staff from 60 to 200 out of the bank’s total number of 1000 senior personnel. It sounds reasonable, but Warren pointed out that the “physics of the system” wouldn’t be able to support this goal. To see why, we need to understand the stocks in the system and the flow rates between them and out of them. The model has the three main stocks of disadvantaged minorities in this system: Junior Staff (new hires); Potential Senior Staff (Junior Staff identified as having nascent Senior Staff qualities); and Senior Staff. Potential Senior Staff are split into four separate stocks to account for each year of their development. The flows between these stocks work as follows: 

• Junior Staff might get promoted to positions nominally considered to be indicating that they are Potential Senior Staff, or they might leave, or they remain as Junior Staff. 

• Potential Senior Staff routinely move between each year of their development unless they leave

• Potential Senior Staff in their fourth year may also be promoted, or they may leave, or stay as Experienced But Not Promoted staff.

• Senior Staff either stay or leave.

At the time of the proposed strategy there were 60 minority Senior Staff. Promotion to this stock from the stock of Potential Senior Staff was typically running at 25% per annum, or 16 persons. If we just focus on the year one goal of achieving a 3% increase in the relative number of minority drawn Senior Staff per annum we are actually asking for a 50% increase - from 60 Senior Staff to 90 (3% of 1000) - in one year, showing that small percentage point increases can translate into large relative increases in actual numbers, especially from a small base. But the situation is worse than this as it doesn’t take into account minority Senior Staff that leave, which at the time the plan was made was running at 25%, or 15 persons in year one. So the actual promotion figure from Potential Senior Staff to Senior Staff has to find 15 additional promotable people from the Potential Senior Staff stock as well. That would mean promoting 45 of the 65 persons in that stock, or 69% of the total number, way beyond the current 25% promotion rate and certain to promote those who have insufficient experience (i.e. are sourced from earlier years in their development rather than the usual fourth year candidates) or might otherwise not have been considered. This, of course, echoes down the pipeline of stocks, requiring much more vigorous hiring and promotion than currently exists, or is likely to be desirable, or even possible, in the short to medium term. And this is to say nothing of the hypothetical effect on attrition (leaving the firm) by minorities who are promoted to positions that are beyond their current capabilities. The firm could, on this reckoning, find itself working hard to pull levers intended to increase minority representation among senior managers that either don't work, or don't work very well. This model illustrates how this could eventuate, and contains key metrics that the reader can adjust to perform experiments on what policy formulations might work best, and/or how the policy goal needs to be adjusted to the actual mechanics of the staff pipeline.

Reference
Warren, K. (2008). Strategic management dynamics. John Wiley & Sons.