Either your memory is bad or you are a troll. The first draft lottery was held on 12/1/69 for men born 1/1/44 - 12/31/50. This would determine who would be called up in 1970. Unless you graduated college at age 20 or less, this would include you. The last men called up had #195. Starting in 1970, your draft chances depended on your lottery number. The last people drafted were from 1972, born in 1952, #95 or lower. Before 1970, you would have been subject to the draft, but I presume you had a student deferment. Even if you didn't, the local boards generally went by a oldest man first rule, starting with the 26 year olds.
Thank you for the details. I was trying to summarize the way things worked in 1971 without going into the details of the draft. FYI I graduated in 1971 at the age of 19.