There are various alloys that all fall in the catch all term of pewter.

Compositions varied across Europe in the middle ages, and also changed over time. Different alloys are used for different applications.

The Most common alloy used in english pilgrim and secular badge manufacture is around about one part lead to two parts tin. At 36.78% lead to 63.22% Tin, a Eutectic alloy is formed, PbSn3. Eutectic alloys behave as pure metals, but with a greatly reduced melting temperature. This is quite handy in casting. 

I wont waste time trying to explain, As It's been done already.

http://scitoys.com/scitoys/scitoys/thermo/thermo4.html

Slightly heavier weight science, http://www.chemguide.co.uk/physical/phaseeqia/snpb.html

and my really shoddy sketch of the liquid/slushy/solid phase point diagram, (the percentages at the bottom of the graph are wrong. Should read 36.78% lead to 63.22% Tin)

Continental European badges tended to have a higher lead content, upwards of 50%. the resulting badges tended to cast with more flaws and were cruder and less complex on account of the poorer casting qualities of the metal.

Hollow or slush cast items on the other hand were usually cast in more or less pure tin, Pilgrim bells in an almost pure tin with a touch (3%) of copper and antimony (<1%)

For all the info on this read Spencer. Essential Reading

Different alloys really do behave differently in the mould, and heat differently.

When learning it helps to find one source and stick to it. It might cost a bit more than melting down random pewter tankards, but your results will be more consistant.

That said, tankards are cheap, and a great source for cheap sheet pewter, that you'd otherwise pay through the nose for...