Since 1928, when the S&P 500 has risen in January, it's climbed an average of 8.3 percent for the next 11 months and was up over that span nearly 78 percent of the time.
When the S&P 500 has fallen in January, it's risen only 58 percent of the time for an average return of a mere 2.8 percent.
Here is a chart of this from Ned Davis Research:

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