As hinted by the title and the flavortext, this puzzle is about minor league baseball teams. Specifically, each diagram represents one of the eleven divisions of Minor League Baseball.
Circles drawn in the same non-black color in different diagrams represent the same description and black circles each represent one of the unique descriptions.
(For example, the only circle type that appears six times is green solid, so it must represent "Geographical name contains two capital letters".)
Determine which division is represented by each diagram and where the teams are located in that division's diagram, then use the jersey number as an index into that team's nickname.
Those letters, taken in diagram order, spell DASH'S PARENT, a reference to the High-A East team the Winston-Salem Dash, whose parent team is the WHITE SOX.
Low-A East
WOOD DUCKS (4) = DBlack: In the South Division
Dark blue: Nickname has two capital letters
Green dotted: Nickname has nine letters
Light blue: Home ballpark contains the word "stadium"
High-A West
INDIANS (5) = ALight blue: Home ballpark contains the word "stadium"
Large black: Nickname begins with a vowel
Small black: Located in Oregon
Triple-A East
RED SOX (4) = SYellow dotted: Home ballpark contains the word "field"
Yellow: Nickname has one syllable
Black: Nickname is identical to parent club's
Gray: Home ballpark contains the word "park"
Double-A Central
HOOKS (1) = HGreen: Geographical name contains two capital letters
Yellow dotted: Home ballpark contains the word "field"
Green dotted: Nickname has nine letters
Dark blue: Nickname has two capital letters
High-A East
CRAWDADS (8) = SDark blue dotted: Nickname has eight letters
Light blue: Home ballpark contains the word "stadium"
Green: Geographical name contains two capital letters
Black: Geographical name contains the word "green"
Double-A Northeast
FIGHTIN PHILS (8) = PLeft black: Located in Pennsylvania
Light blue: Home ballpark contains the word "stadium"
Dark blue: Nickname has two capital letters
Right black: In the Northeast Division
Low-A Southeast
CARDINALS (7) = ABlack: Nickname contains the name of an animal
Green dotted: Nickname has nine letters
Green: Geographical name contains two capital letters
Low-A West
PORTS (3) = RGreen: Geographical name contains two capital letters
Yellow: Nickname has one syllable
Gray: Home ballpark contains the word "park"
Triple-A West
RIVER CATS (4) = EGray: Home ballpark contains the word "park"
Black: In the West Division
Green: Geographical name contains two capital letters
High-A Central
LOONS (4) = NLarge black: In the East Division
Green: Geographical name contains two capital letters
Yellow: Nickname has one syllable
Dark blue: Nickname has two capital letters
Small black: Located in Iowa
Double-A South
BISCUITS (7) = TDark blue: Nickname has two capital letters
Left black: Located in Alabama
Dark blue dotted: Nickname has eight letters
Right black: Geographical name contains multiple pairs of double letters