Example of properly charted gathered sleeve implementation, illustrating sleeve drafting principles

Puffy, Gathered Set in Sleeves

Puffy or gathered set in sleeves are classic.
You don't need a special pattern to knit them. Learn to chart your own .. with little or math!

garment shaping garment style sleeve

The classic gathered sleeve cap can be easily charted by hand.
The best way is to use knitters graph paper.

Decisions

How much fullness at the top of the cap do you want?
I suggest using fabric (or your swatch) to estimate the amount of additional fabric you want to gather. (15%)

How much additional length in the cap?
Additional length will allow the gathers to stand above the shoulder.

How much additional fullness in the upper arm?
For a smooth transition between the sleeve cap and the rest of the sleeve, consider the added width needed in the upper arm

Put on your seamstress hat

Consider sewing this style in fabric. Using flat pattern drafting, you would "slash and spread" the sleeve cap, then re-draw the cutting and sewing lines.
You would then gather the sleeve cap to fit into the armhole.
For knitting you can do the same thing.

If you are following a knitting pattern, draw the existing sleeve on graph paper
Slash and spread, then lay it down on graph paper again.
Outline the new shape
Using the boxes of the graph paper, establish the stitch and row shaping for the new sleeve cap
Re-chart the underarm shaping the same way or use the Magic Formula to calculate the new arm shaping.