ALBA was one of 37 clubs from Denmark that had teams playing during BMS Herlev Cup 2021. They participated with three teams in Boys U15 2007/08 , Girls U13 2009/10 and Boys U17 2005/06 Invitational respectively. The team in Boys U17 2005/06 Invitational made it to the the in Gruppespil, but lost it against Horsens ic by 51-53.

In addition to this, ALBA have participated in BMS Herlev Cup before. During BMS Herlev Cup 2020, ALBA had two teams playing in Boys U15 2006/07 Invitational and Girls U13 2008/09 respectively. Two teams played until Placeringskamp 7-8 plads in Placeringskampe; Boys U15 2006/07 Invitational won over Skovbakken Bears by 63-34 but Girls U13 2008/09 lost against SISU 3 Rød by 13-26.

ALBA comes from Allerød which lies approximately 17 km from Herlev, where BMS Herlev Cup takes place. The area around Allerød does also provide 28 additional clubs participating during BMS Herlev Cup 2021 (Among others: BMS Herlev, SISU Basketball, Virum Basketball Klub, Glostrup I.C Basketball, Jonstrup Basketball Klub, Hørsholm 79’ers, sisu, Hørsholm, Hørsholm 79ers Basketball and Falcon Basketball).