Is there a way to know historically how often do we see >5% one day rally? Maybe you could download historical data from finance.yahoo.com in "csv" format, pull it into a spreadsheet, and calculate the one-day change for all days in history. Then you could pick a time interval that you think is relevant (1960 to today? 1985 to today? 2003 to today?) and count up the number of >5% rallies in that interval.
biggest jumps are always in a bear market bulls give up and sell slowly bears cover quickly, and violently