Based on the available data, managers of indexes typically make changes that reflect the peaks and troughs of the respective market conditions. This means that the most stock changes to the index occur when the market is at a high and fewer stock changes occur when the market is at a low.
Below are the changes to the S&P 500 index from 2003 to 2019. The S&P 500 is managed by S&P Dow Jones Indices (here).
see also: S&P 500 additions and deletions