The red cross claims that donating blood can 'save up to three lives' That seems a highly exaggerated best case scenario. I'm curious, how many lives are really saved from a unit of blood? Specifically, what is the odds of one pint of whole blood producing a product which will be used to successfully treat an otherwise fatal injury/illness etc, and that if the donor had not donated that pint a death would have occurred due to lack of sufficient supplies, or being forced to use fewer resources of less computable ones?

What I would love is the ability to do get as nuanced and exact numbers as possible, as part of the motivation of this question is to have the numbers needed to address another question on Skeptics. If an answer doesn't want to do the exact math pointing me to the resources I need for me to do the math would be fine as well; but I don't even know what products are produced from a whole blood donation much less how to calculate the benefit of any one of those products.

I know that blood type of the donor could play a factor here, but to address the question I'm interested in I'd prefer to know about the 'average' pint of blood, so in essence if all the donor of all the varous blood types in the US donated and you averaged all those various pings of different types together what would the average pint do?

Of course being B+ myself I would be personally curious to know what the B+ blood type does, it would be cool to calculate a 'statistical lives saved' ratio for myself :)