Using information I got from the Beazley Database, I input the four styles of vessel I was focusing on along with the three most common icons represented on them. This was to see if there was any significant association between the shapes of pots and their decorations.
The results show that many of the vessels have a low score, meaning that it is most likely not random which decorations were on which shapes. For example, an amphora with Herakles on it is likely not an outlier within the archaeological record outside of the database. Comparatively, the cups with Athena on it have a higher score. This means that, in theory, there should be many more cups with Athena on them.
Dionysus is mostly easily recognized through the use of grapevines on vessels which depict him, such as on the one above. Some other decorative elements that are associated with him are satyrs, maenads, and drinking horns. (He can be seen holding a drinking horn in the above image.)
Athena is regularly shown with her characteristic helmet and shield, such as she is above. She is also often shown in scenes of war or competition, being painted alongside Herakles and other athletes on many vessels.
Herakles will most likely appear in scenes from one of his labors, being next to depictions of the Amazons or Athena. In this image he is shown wearing the skin of the Nemean lion, one of the beasts he conquered during his time before Olympus.
Amphora
Amphorae are classified through their wide belly, tapered foot, and two handles for easy transport.
Oinochoe
Recognizable by their clover shaped spout, Oinochoai were used to serve wine, much like modern day pitchers. Its name comes from the words oinos (wine) and cheo (I pour).
Cup
Cups from Ancient Greece are known for their shallow bowl shape. They were used to drink wine, and therefore contain many depictions of Dionysus, who is associated with the drink.
Lekythos
These oil containers have one handle and a mostly closed neck. Lekythoi are typically tall and narrow, but also have wider and shorter variations.