Apologies, was away from my DM Screen and the ole memory ain't what it used to be. The modifier is 15% (not 20%), per 5pts of the Athletics check.
So, if you get a 31 on your check [20 roll + 5 Str mod + 6 prof bonus], divided by 5 is six increments of 15%; total of [.9 * your 20 Str score] for 18ft added to your baseline of 20ft. Grand total of 38ft. Still smashing records, but that's a 20th level PC rolling perfectly...
As for the gear mention, I use the variant encumbrance rules, and keep track of what the PCs are carrying. If the plate wearing, backpack carrying fighter wants to jump a chasm, I will alter the 5pt/15% modifier on a case by case basis. Throw in the Disadvantage from encumbrance, and things can get real tricky real quick.
Actually, I really like the concept of your house rule, but I would simplify it a bit.
Strength plus Athletic check / 5 (normal round down). First level PC with 8 Strength and no Athletics? 8 feet to 11 feet (20 becomes a 19 with a -1 modifier). First level PC with 16 Strength and Athletics? 17 feet to 21 feet. 17th level PC with 20 Strength and Athletics? 22 feet to 26 feet. Much better than the 8 to 20 feet of the normal rules. And by squeezing the roll like this, it's not a situation of jumping 15 feet one round and jumping 28 feet the next. Except for a 8 or 9 Str PC, there's always a difference of 4 feet between best and worse jump (which makes sense, although we do use the DMG optional rule of 1 something bad can happen, 20 something good can happen for checks and saves).
Btw, in my game, things that PCs have to jump over are not increments of 5 foot like the 4E grid system. A chasm can be 6 feet, 9 feet, 11 feet, whatever depending. So, every +1 can help. Also, my rooms are not always 10x20 rooms. Lots of times they are 8x21 or 17x18 or any other dimensions, often weird blob shaped caverns of whatever size.
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