when combining hot sauces with different Scoville Heat Units (SHU), how do I estimate the resulting SHU? Say I combined 100 grams of a sauce that was 1,000 SHU with 100 grams of a sauce that was 2,000 SHU. Would the resulting SHU be the average: 1,500?
I'm trying to make a super hot sauce (perhaps around 400,000 SHU) using something like Frank's as the base and adding some (a drop?!?) of those sauces that's like in the millions of SHU. I need help with the math.
You cannot calculate it, you can only measure it.
Scoville is a subjective scale. Wikipedia tells you how it is measured - by testing with human panelists, using a certain protocol.
As all subjective scales, Scoville is ordinal. Even though it is expressed in numbers, these numbers are best understood as ranks - you cannot assert that "1000 SHU is twice as hot as 500 SHU", for example, or that "the hotness difference between 500 SHU and 1000 SHU is the same as between 1000 SHU and 1500 SHU".
If you take statistics, you will find that many methods are treating ordinal scales as if they were interval, and go on calculating averages and whatnot. This tends to work well enough for some applications. But in your case, you are dealing with human sensory perception. I am not 100% sure for the specific case of hotness, but typical human responses to a stimulus are logarithmic, not linear. So if you try to simplify your life and make a linearity assumption for Scoville, your estimates are likely to be so far off as to be unusable.
If you really need an exact Scoville number for your sauce, it is not math you need, but the resources to conduct proper testing in several iterations. I fail to see the relevance of such goals for the home cook though. You eat sauce, not numbers.
What SHU measures is (at least intended to be) the ppm by mass of capsaicin in the sauce, and there is a rough conversion factor of 1µg/kg capsaicin = 16 SHU. The concentration of capsaicin can be measured relatively easily by chromatography or other means so precise scientific data is available for many peppers and sauces. Guinness World Records certainly measures the SHU value of the world's hottest peppers and sauces this way.
I didn't find information online about how exactly commercial sauces measure their SHU, but given the pressure to put out a consistent product and how variable the pungency of chili peppers can be, it is hard to imagine that they test their sauce the way Scoville intended.
Anyway, the concentration of capsaicin in the mixture is the weighted average of the concentrations of the two sauces, so the SHU should also be averaged in the mixture. Your intuition that the result of your example should have 1500 SHU is exactly right.
Of course the other answerer is correct that the relationship between SHU and perceived hotness is complicated. It's probably not linear, it definitely depends on the taster and it interacts with other spices and foods in ways that can be hard to predict. But if it's the SHU you want then it's just algebra.
