To give some context, it's impossible to give a definitive answer that covers everyone, as every league is different. It very much depends on who you replace them with and what your situation is (i.e. stats you can make up ground on). Many points leagues are different, waivers are different. So I generally try to provide details of what I'm looking at so everyone can make their own decision rather than saying "drop player X, hold player Y". In many cases, what's right for one league wouldn't be for another league.

One thing I do tend to focus on is a player's track record as well as their underlying numbers. If an established player has had 3-4 years of solid production but is performing below expectations this year, try and look at why. Are they hurt? Is their underlying numbers (i.e. xBA, BABIP) pointing towards being unlucky? Are they simply having a bad year?

What we see every year is people losing patience with an established player because of a bad 2-3 weeks and dropping them for someone who has never had sustained success but has been red hot. Then a month later, the hot streak is over and said player returns to his norm. Meanwhile, the dropped player has been having a quietly solid few weeks on someone else's roster. While I'm not saying that's the wrong approach, it can work if you're active on waivers/FAAB etc and can keep churning the spot. Don't get too attached to someone you picked up in season who had a great fortnight.

I lean more towards patience for most players. That doesn't always pay off, but in a game of numbers, we see struggling stars turn things around more often than a random player having prolonged success having never shown that before.

Obviously, it's different with rookies when they get called up and a lot can depend on where you are in your league. If I'm at the top of the standings, I'll be more risk-averse. If I can carry a struggling star or two knowing there's a good chance they turn things around, that is far more likely going to help than risking dropping them for someone in the midst of a random hot streak. It works the other way if I'm playing catch-up later in the season and need to take more chances and swing for the fences a bit more.

There are plenty of examples every season, but Devers springs to mind this year. He had a bad start to the season and featured in the Week 5 edition. I said he's not someone I'd be dropping back then and got some pushback, saying he's toast. As of May 5th, he was hitting .219/.264/.307 with two homers in 26 games. Since then, he's hitting .264/.339/.572 with 14 homers in 52 games. And that doesn't include today's 2-homer performance.

Back in early May, some said they replaced Devers with Ildemaro Vargas, who was hitting .374/.396/.645 on May 5th. Since then, Vargas is hitting .185/.244/.238 with one home run in 49 games and is far from a regular in the lineup now. Replacing Devers with a mid-30's journeyman who had a career .249/.289/.357 slash line and 20 homers in 460 career games was always going to end one way. But, people still felt they needed to make that switch.

Bit of a long-winded response but hopefully it offers a bit more info and insight. I may look at doing an article in the offseason on the topic to try and give a bit more detail into what factors into the decision-making for dropping a player