A first-base mitt is 11.5–12" for youth players 7–12 and 12–13" for adults on Rawlings' chart; the sizer picks 11.75" at 10 and 13" for an adult. First basemen want the longest reach and a deep pocket for throws in the dirt.
Length for the stretch
Rawlings lists adult 12+, 1st base at 12–13"; Baseball Monkey’s baseball, ages 14 and over band gives 12–13". They overlap at 12–13", and the sizer picks the middle: 13".
A first-base mitt is long and has no individual fingers, for scooping throws in the dirt and reaching on a stretch. Youth mitts stay at 11.5–12" so the player can still close them one-handed.
The adult game
High school, college and adult baseball is played on the 90-foot diamond with a 60 ft 6 in pitching distance, and gloves are adult patterns throughout.
CDC growth charts put the median 18½-year-old boy at 176.4 cm (5'9") and girl at 163.2 cm (5'4"); the 5th to 95th percentile for boys runs 5'5" to 6'2". A tall player at the age is often a size ahead in the hand too.
Check the hand
Rawlings’ batting-glove chart puts hands at 7–18 in Adult Medium (7.25–7.5") and Adult Large (7.5–7.75") and Adult XL (7.75–8") and Adult 2XL (8–8.25"), measured from the base of the palm to the tip of the middle finger. Measure it 1:1 in Mode 01 (finger plus palm): a longer hand moves the pick toward 13", a shorter one toward 12".
For comparison, the adult outfield sheet starts from 12.75".