October has a bad name because that is when a lot of selloffs have stopped, not because the month itself is usually bad. Since 1945, a drop of 5% or more has ended in October 33 times, more than in any other month. March and September are next, with 23 each. Since 1950, 6 of 12 bear markets bottomed in October.
An ordinary October is nothing special. Since 1950 the S&P has gained about 1% and finished higher a little more than half the time. A lot of those selloffs were already over in September or early October.
A midterm October is different. The Stock Trader’s Almanac puts the average gain at about 3% for the S&P and 3.2% for the Dow. November is close behind, about 2.7%, and up more often.
The real split is not the month. It is the half-year. May through October is roughly flat in most markets and down in bear markets. November through April has been up in bull markets, bear markets, and everything in between. That is the stretch that has paid.