title_body: What is the impact of espresso tamper base shape?
upvoted_answer: If you only use a double (14g) portafilter basket then you're best to use a 58mm convex tamper. This is because if you look at the basket, in most cases, the sides will slope in. Therefore, if you had a flat 58mm tamper then the you are compressing to outer more than the inner. Obviously the whole point of tamping is to compress the grounds consistently throughout the whole puck, so this would achieve this the best. If you want to use a flat tamper for any reason in this situation, you would be best using a 57mm flat tamper and tap the edge of the portafilter to knock any loose grounds back down into the basket and then rotate the tamper over to produce a flat surface for the water to pass through.
  
  If, however, you are using a single (7g) portafilter basket then the 58mm tamper would probably be too wide to compress the grounds evenly as it may not go far enough down in the portafilter basket to tamp it at all. Therefore, you would be best using a 57mm tamper. 
  
  If you're using a triple basket then a 58mm convex rules would apply the same as the double basket.
  
  This is all based on the assumption that the basket is 58mm. This is the most common size but other sizes do crop up, commonly on older machines which may use a 53mm basket. In this case the flat/convex rules still apply, just with the smaller diameter.