Espresso statistics

[aloening]

Are there any mathematicians out there?. I am afraid this is beyond me!.

I have an Isomac Professionale grinder which is great. It grinds direct from the beans into the basket.

I measured that a single shot is about 14g in weight. With the espresso blend I am using that is 116 whole beans.

I took this blend recipe from another post on this forum;

40% Brazilian Cachoeira
30% Sulawesi (Kalosi)
20% Harrar
10% Guatamalan Antigua

So if I put this in my grinder I would get

46.5 Brazilian Cachoeira beans
34.8 Sulawesi (Kalosi) beans
23.2 Harrar Beans
11.5 Guatamalan Antigua Beans

in a perfectly blended shot. Now there are two problems;

1. Asssuming there are no broken beans, you can't get exactly the right number of any of these beans directly from the grinder. So what is the minimum error in the blend?.

2. As the beans are randomly distributed (assuming they are all the same size and density) in the hopper there is a range of possible blends from 'perfect' (as near is allowed - see Q1.) to entirely Guatemalan Antigua Beans, as these are the least frequent in the hopper. What does this distribution curve look like and what are the chances of getting a really bad blend?.

So is the only answer to a perfect blend to grind 1/2 a tonne and mix vigorously for a week?

Thanks Bye

Adrian

[wang]

I think there's a certain amount of inevitability that you may have to deal with when dealing with blending - with harar beans every cup is different to an extent in itself. Thankfully enough - the flavour of the beans may pass to each other while the different beans mingle in the same container and even out as coffee is great at absorbing flavours and odours.

[simonp]

I think you are worrying WAY too much about it . If you really want to make sure yu get close to the blend each time, then do what I do sometimes (when I am trying different proportions) weigh beans individually out for each shot.

[aloening]

Not worried in the slightest! - just interested in the mathematics.

[simonp]

Not worried in the slightest! - just interested in the mathematics.

Ahh, seark the coffeegeek (sorry Phil, dirty word I know!) froums, there was a post on this subject once, going on about the statistical likelyhood of getting the 10% componenet of a blend in a shot.