What is the function of RD cage length?

Cage length (from wikipedia)

The distance between the upper and lower pulleys of a rear derailleur is known as the cage length. Cage length determines the capacity of a derailleur to take up chain slack. Cage length determines the total capacity of the derailleur, that is the size difference between the largest and smallest chainrings, and the size difference between the largest and smallest sprockets on the cogset added together. A larger sum requires a longer cage length. Typical cross country mountain bikes with three front chainrings will use a long cage rear derailleur. A road bike with only two front chainrings and close ratio sprockets can operate with either a short or long cage derailleur, but will work better with a short cage.

Manufacturer stated derailleur capacities are as follows: Shimano long = 45T; medium = 33T SRAM long = 43T; medium = 37T; short = 30T

Benefits of a shorter cage length:

• more positive gear-changing due to less flex in the parallelogram
• better gear-changing with good cable leverage
• better obstruction clearance
• less danger of catching spokes.
• slight weight savings.