Iâve come across a rule of thumb statistic that says 85% of the time, stocks tend to role sideways. This would mean 15% of the time, stocks tend to trend either upwards or downwards. Would this simply imply stocks trend upwards 7.5% of the time and likewise downwards 7.5% of the time, or does this split work out differently in practice?

No, it doesn't work out 50:50. Markets tend to fall twice as fast as they rise (rule of thumb) so assuming the 15% holds you are looking at something more like 10% of the time the markets trend up and 5% trend down.

Each paragraph of your OP is unfounded. You may have read the first one but you tried to reason through the second one. So, maybe, you are introducing yourself to the countrintuitive nature of the markets as measured by CW. CW means Conventional Wisdom. To best get down the foibles of CW, read taderzones to see how unhinged non critical thinking can get. Get a mentor who can straighten out how you are approaching the financial industry and, in particular, trading.

It's time for a lesson in statistics: 68.2 % of statistics are true and the remaining 56% are made up!

What's the definition of rolling sideways? Looking over the markets for the last 30 years, it would be hard to call it sideways.

Rules of thumb differ from statistical generalizations. There, that's the end of what I know. I run from rules of thumb.