What do the tanks below have in common?

They're tanks that can sort of get away with an AP build on top of their tank build.

  That's why Sorc Shoes show up in their stats. But Sorc Shoes don't only work if you go full AP.

Here are the engage-focused AP-based tanks, excluding Ornn, Sejuani, and Shen.

The eight champs above have Sorc Shoes in their stats (though Mundo this year only has them in ARAM).

Why?

Is it just trolls picking tanks and forcing AP builds?

Nope!

First, let's look at boots

   Tanks don't just grab Tabis when the enemy has lots of AD, or Mercs when they have lots of AP.

Why? Because spending 1200+ gold for 20-25 armor or MR is stupid. You buy boots for their effects.

With the current meta seeing a lot of Kai'Sa and Lee Sin, and fewer frontliners, let's say the enemy team looks like this.       Are you going Tabis? Or Mercs?

The answer is neither is great.

Reducing basic attack damage by 10% doesn't really cut Kai'Sa or Lee Sin's DPS that much. Even with Mercs, Tenacity doesn't reduce airborne or grabs, and it doesn't reduce ground-targeted slows either.

So if the AD damage is high, go Tabis; if the AP damage is high, go Mercs, right? NO! Don't waste your gold. Look at other boots.

Ionian Boots are better if you want to reduce cooldowns more, or if you're against someone where you can get off more than one rotation of your combo in a fight.

Boots of Swiftness give high movement speed for positioning, plus slow resistance, and they even help against ground-targeted slows.

So what about Sorc Shoes? Why would you buy them on a tank building tank items?

  They only give 12 magic penetration, no AP.

In the current meta, where people rarely build magic resist, ADCs and mages have around 30-50 MR, and bruisers have around 30-65 MR.

If a tank has a magic damage skill with no scaling,

Against ADCs and mages, their DPS goes up by about 9%-10%.

Against bruisers, their DPS goes up by 7.7%-10%.

Similar to damage amp options like First Strike (7%), Press the Attack (8%), Last Stand (11%), Riftmaker (8%), Liandry's (6%), Abyssal Mask (12%), you can sacrifice a boot that wasn't giving you much value anyway for a flat, unconditional, no-warmup 9% damage amp that works on everyone.

An extreme example: look at Mundo's Q.    Mundo's Q is magic damage with no scaling at all. But Sorc Shoes can still increase its damage. Of course, Swifties are still better on him.

If you're playing a tank with good kill pressure or the ability to lock down a single target, like the ones below,

you can build tank items and still consider Sorcerer's Shoes depending on the situation.

It's generally best when the enemy team is squishy or lacks a strong frontline, making it important to dive and lock someone down.