A 13-year-old takes about 11.5" at second base or shortstop (11.25–11.5"), 11.5" at third and 12.25" in the outfield. At 13 a player can be in Senior League (60.5 ft pitching, 90 ft bases). Typical hand: 7–7.75"; median height 5'3".
Two charts at 13
Rawlings lists adult 12+, infield at 11.25–12"; Baseball Monkey’s baseball, ages 11–13 band gives 11–11.5". They overlap at 11.25–11.5", and the sizer picks the middle: 11.5".
At 13 a pitcher’s glove (11.5") wants a closed or basket web, a middle infield (2b / ss) glove of 11.5" an I-Web, and a third baseman’s 11.5" an H-web.
The game at 13
In Little League a 13-year-old plays in Intermediate 50/70 (ages 11–13, 50 ft pitching, 70 ft bases); Junior League (ages 12–14, 60.5 ft pitching, 90 ft bases); Senior League (ages 13–16, 60.5 ft pitching, 90 ft bases). Pitchers are limited to 95 pitches a day at this league age.
CDC growth charts put the median 13½-year-old boy at 160.3 cm (5'3") and girl at 159.2 cm (5'3"); the 5th to 95th percentile for boys runs 4'10" to 5'8". 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 13 in Adult Small (7–7.25") and Adult Medium (7.25–7.5") and Adult Large (7.5–7.75"), 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 11.5", a shorter one toward 11.25".
For comparison, the 12-year-old sheet starts from 11.5".