battery dies after a few hrs ??!! help..

[87prjctpony]

well bud... i have my 87 5.0 and when i barely had gotten it i thought it was normal the way it would start up (very Lazzy) and then i heard other ponies fire up and they would fire up right away!
i would run my car hard just 1st 2nd gear and stop, turn the car off and try to restart it and the battery would be dead! i was left with ????? i bought a new battery, that wast it. checked the alternator, that wasnt it. so someone told me to change my starter. i though ,"no it cant be my starter because when starters go bad they tend to grind., well i changed it and turned it on . wow it fired up better than ever. that was my problem. i would try that .