Long cage derailleur
The longer arm allows more chain wrap. This is needed for triple chainring bikes, for instance, since the small chainring - small cog needs way less chain than it's big - big combination.
A shorter cage arm doesn't have enough "chain wrap", so the bottom return chain could go slack, and will rub against the wrapped chain at the top pulley, since the cage is rotated all the way up.
Chain sizing
Normally, chains are sized by the "big-big +1 inch" method -- see this
Park Tool guide. This is the minimal chain length that will work correctly when doing a big-big cross chain shift.
Derailleur pulley clearance
The upper derailleur pulley needs to be positioned far enough away from the biggest cog so the chain can shift to that cog. This is a derailleur design and/or derailleur hanger length problem, not affected by the cage length.
From a table of cog radius, measured to the center of the chain pin:
28 tooth cog is 56.7 mm
32 tooth cog is 64.8 mm
That's
8 mm larger diameter.
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I have
Ultegra 6800 11-speed, and the bike came with
34/50 front,
11-28 rear.
I installed a
11-32 cassette, and the derailleur arm length was fine. It measures 58mm between pulley centers -- this is longer than a lot of older short cage derailleurs, which likely were designed for smaller cog sizes.
There's still a gap between the bottom return chain and the upper pulley's chain when shifted to the low-low 34-32. (Even if the chain wrap wasn't quite good enough, there would be some noise from the chain rubbing against itself in the small-small combination, but that's rarely used.)
My chain that was used on the 11-28 was still long enough for the 11-32 cassette. But
carefully, by hand cranking,
check the big-big combination -- the derailleur cage should still have some bend to it, or you could jam the chain. To check: hold the bike upright with the rear wheel off the ground and shift in and out of the big cog and big chainring.
11-32 worked for me, but it's a tight fit.
But the gap between the upper pulley and the 32 cog is very small. I adjusted the "B" screw to rotate the derailleur a little more, which helped. I think this 11-32 is bigger than the recommended cassette sizes, but I've had no problems shifting in or out of the 32 cog, either on the 34 chainring or cross chained on the 50 chainring.
This probably depends on the exact dimensions of the derailleur hanger. It might not work on every bike.
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Bigger than 11-32 cassette?
Want even more range? I think you need a mountain bike rear derailleur. I haven't looked into it.
I do like my 34-32 low gear on steep hills. I can stay seated on 10% grades, and I've even used it to spin up a 5-6% grade with a cadence above 90 rpm. But the tradeoff is bigger gaps between shifts in the middle of the range. That makes it harder to get the "just right" cadence on flatter roads.
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11-32 gaps (50 chainring in black, 34 chainring in red, at typical spinning cadences) :
The 18-16-14 cogs with the 50 chainring makes big jumps at 20-25 mph, right where I'm working hard to keep the speed and want the best cadence. On the other hand, the big ring can easily go down to around 12 mph, and the small ring is good all the way to 20 mph, so the front derailleur doesn't need to be shifted very often.