How much does drinking once a week effect athletic performance?

Variable. It all depends of the amount drank, 1-2 alcoholic beverages 1-2 times per week may actually have some health benefits and not affect performance. Binge drinking, which is more than 5 drinks for a male and 3 drinks for a female in one evening can be a sign of a drinking problem. That amount will most definitly affect athletic performance the next day even in a healthy fit indivdual.
Depends on how much. If you drink to get drunk, the once a week may well cause muscle inflammation and damage, and reduce athletic performance. If its truly social drinking (1-2 drinks) then it would not likely do very much. Also depends on whether you are talking about a pick=up basketball game with other older guys, or competing in the olympics. If its highly competitive, even smaller amounts of alcohol matter.