I guess this is like asking about the best trap, but here goes:

Why go with any given chain length?

So, if short chains mean less room to run and gain speed, but more potential to pump a stake, and long chains mean more room to gain speed, but greater difficulty in pulling a stake (pulling across more, and up less) .... how do you win? Seems like there's no winning with physics.

Cross stake your traps and You won't get any pumping.

Earth anchors + short chains= no pumping, less damage to trap and animal. Imo

You still get earth anchors pumped if you get enough rain with earth anchors.

Could be, I carry two lengths of cable stakes for just such occasions. Haven't had any issues yet,(knock on wood).

I like 18-30" of chain. I double stake or cable to a tree

I think chain length depends on several factors. Target animal, terrain, chance of theft, dry land or water sets, fur trapping or live market, and shock spring usage or not and probably many factors I haven't mentioned. I don't believe any one length of chain can handle all situations.

So what's the formula to figure it out, other than trial and error?

There is no formula. It is trial and error to some degree and it depends on one's style of trapping. One thing that must be considered is what type and size of trap you are using. Smaller traps using a short chain doesn't let the animal test the trap like a longer chain would. Where a larger trap that has a base plate and laminated jaws will take more of a beating from a larger critter. They can't pull them apart as easily.

There are so many factors to consider as to what length of chain to use. This season I used some drags with longer chains and anchored some traps with longer chains to trees back off the roadway edge to hide the catches. What I found out is that the longer chain in most of these cases allowed the animal to get tangled up in forest ground vegetation and cause more damage to themselves. This was in thicker forested areas. If in more open country this wouldn't have been as much of an issue but then you need to track the animal further, in case of the drag, than you would in thicker areas. So I think it really depends a lot on the area and terrain you trap in along with what equipment you are using.

I think I'll wait before I comment..Later

Don't be shy bus lol.
Staked traps, 24 to 36 hr check time,
I like 10" on my 1.75s and 3s
18" om my 1 1/2s for water and coon sets.

This has been a topic since the beginning of the internet.
I have tried what others like and settled on the above.
Not because others are wrong, but like Grey said, variables.

If I went shorter than ten, I would struggle since I stake under the trap and usually in a cereal bowl type hole. If I went longer, more swivel fouling.

A lot of mine have chestnut type dbl stake rings.
One time I went to cable stakes, the ring lengthen my chain a couple inches over what two rebars in the ring. I noticed right quick that little difference and that confirmed I had it right for me.

Good swiveling is more important than the magic length.

Oh and I learned the DPs can be shorter, but not longer. I two swivel those, too.

Well I don't use drags so I don't worry about that.
All my traps and I mean all of them have no more then 14" of a combination of swivels anchor points and chain. I have never had a problem with that length being to long or to short.
90% of the time I double stake whether I'm using earth anchors or steel stakes.

Eastwood I never did hear you say what trap setup and what species your after ?

Also what ground conditions?

Mixed line, mostly coon and coyote. Running mostly 450,550, Bridger 2, and occasional dp. Ground typically hard dirt, some yellow clay. Moving to new ground that's sandy as much as anything.

I trap sandy soil. I cross stake with rebar out in the fields, and cable with wolf fangs in the cover where tractors don't roll. All my 550's, and Bridgers have stock chain length with an extra swivel added. No stake pumping, and no problems.

There may be a benefit to a longer chain in my conditions...but I don't see it.

I'll explain later LOL

I was a short chain guy up until I tried long chains. now all my land traps have at least 18 inches of chain. When the trap captures the coyote first thing he does is go straight up. 18 inches they run out of steam. Then the attack the trap with there mouth, then the lunging starts. By this time a well constructed trap has locked. With 18 inches of chain you also get less mounding in snow and loose soil witch can hinder the swivels. Thus the catch circle is much flatter so the remake is smooth. So the next animal will enter the circle without as much distraction. Longer chains also hold incidental coon better because the have more to chew on and are more free. The true teller is the fellers that have extended checks. At least 5 swivel points. I can also move the trap around in the set proper with longer chain if need be. Thanks Red

All my coon/mink footholds have 24 inches of good chain and lots of swivels. All my drags have 10 foot of the same good chain.

Makes sense.
except the mounding aspect. I know this Isn't the same but with a 7 foot snare the mounding at the anchor point Is major. In fact there won't be a thing at the edge of the catch circle It will all be at the anchor point. What happens Is the coyote Is digging at the edge trying to get away and moving every thing back to the center.
That also happens In certain conditions with mid length chains. But It all depends on the ground cover.

Ok here is snow