9 6 – 2 0 1 2 : ▁First ▁official ▁meet ings ▁and ▁inter le ague ▁play ▁ ▁One ▁year ▁before ▁their ▁first ▁official ▁match up ▁in ▁inter le ague ▁play , ▁both ▁teams ▁retired ▁the ▁number ▁of ▁Hall ▁of ▁F amer ▁N olan ▁Ryan , ▁who ▁had ▁successful ▁runs ▁with ▁both ▁teams . ▁During ▁the ▁ 1 9 9 7 ▁off - season , ▁" rad ical " ▁real ignment ▁plans ▁were ▁band ied ▁around ▁about ▁possibly ▁re arr anging ▁teams ▁from ▁one ▁league ▁to ▁another , ▁especially ▁Houston ▁and ▁Texas . ▁In ▁order ▁to ▁cut ▁down ▁on ▁travel ing ▁costs ▁and ▁align ▁teams ▁together ▁based ▁on ▁ge ography , ▁the ▁ML B ▁own ers ▁came ▁up ▁with ▁many ▁plans ▁to ▁put ▁the ▁Ast ros ▁and ▁R angers ▁in ▁a ▁more ▁suitable ▁pla cement ▁together . ▁However , ▁the ▁American ▁League ▁and ▁National ▁League ▁would ▁lose ▁their ▁respective ▁ident ities ▁in ▁the ▁process . ▁( The ▁only ▁move ▁was ▁the ▁B rew ers ▁from ▁the ▁AL ▁Central ▁to ▁the ▁N L ▁Central .) ▁One ▁of ▁the ▁plans ▁in ▁ 2 0 0 0 ▁even ▁featured ▁the ▁Texas ▁R angers ▁in ▁a ▁six - team ▁AL ▁Central , ▁so ▁that ▁they ▁would ▁be ▁with ▁other ▁teams ▁in ▁the ▁Central ▁Time ▁Zone , ▁while ▁the ▁fled g ling ▁Arizona ▁Diam ond back s ▁would ▁have ▁had ▁to ▁leave ▁the ▁N L ▁West ▁for ▁the ▁AL ▁West ▁to ▁replace ▁the ▁R angers . ▁During ▁the ▁ 2 0 0 5 – 0 6 ▁off -