07 Oct 2009 @ 3:34 PM 

Part 1 of this little series happened a while back. It was my original foray into trying to figure out a good simplified set of statistics for beer. Feel free to head back there if you need a refresher.

You may have thought that I forgot all about this. In reality, I have been percolating.

The problem with my original post is that a lot of the math I’m using is fairly arbitrary. Basically, I was experimenting to try to find something meaningful. Mind you, that covers a good portion of actual statistics, but what I keep going back to in my head is that what I really want to do is come up with a good way to represent the relationships between the existing numbers in an easy to read statistic for the layperson.

So today, I’m heading back to IBUs because this, I think, is the root of a portion of the problem.

IBUs are calculated in a sensible manner… ish. The original calculation (for metric units) is meant to predict how many mg of iso-alpha acids there are per liter of beer. For example, 30 IBU = 30mg of iso-alpha acids/liter.

The non-metric unit formula – which deals with gallons – listed in Wikipedia (yeah, I’m referencing Wikipedia), looks like this:

Wh × AA% × Uaa ⁄ ( Vw × 1.34 ), where

  • Wh refers to the weight of the hops used, in ounces
  • AA% refers to the alpha acid percentage [of the hops in question]
  • Uaa is the percentage of alpha acid that is actually used during the boiling process
  • Vw means the volume of the wort, in gallons
  • 1.34 is a constant factor that adjusts the measurement to account for the use of U.S. customary units

There’s a little bit of a woogy bit on Wikipedia. They note in their text:

The bittering effect is less noticeable in beers with a high quantity of malt, so a higher IBU is needed in heavier beers to balance the flavor. For example, an Imperial Stout may have an IBU of 50, but will taste less bitter than an English Bitter with an IBU of 30, because the latter beer uses much less malt than the former.


Then they note:

The technical limit for IBU’s is around 100; some have tried to surpass this number, but there is no real gauge after 100 IBUs when it comes to taste threshold.

This is where referencing Wikipedia comes around and bites you in the ass. On the other hand, it’s like someone is asking me to write this post.

The problem here is that other elements in beer do (of course) effect bitterness. 100 IBUs might be very hoppy but, as they note, the more malt there is the less the bitterness is perceivable. By that logic, if something is very highly malted you should technically be able to detect a bitterness difference above 100 IBUs. Certainly, there is a significant difference between Dogfish Head’s 90 Minute IPA (90 IBUs) and Dogfish Head’s 120 Minute IPA (120 IBUs). I’m having a hard time believing that the difference would be the same if it were only 10 IBUs more instead of 30. Maybe I’m deluding myself.

In any case, a measure of hop bitterness within a beer is not an accurate measure of the actual bitterness of the beer. However, the formula stated above does accurately measure the bitterness being contributed to the beer from the hops. We have to assume that there are other factors, but we’ll get to those another day. For now, let’s keep talking IBUs.

The BJCP guidelines (which are just a tick more static than other guidelines right now) show us that in the full range of beers in the world, acceptable IBU values range from 0 (at the low-end of Gueuze) to 120 (at the high end of American Barleywine and Imperial IPA). For the sake of argument, let’s consider those as our range. We have to accept the theory that there can be beers above 120 IBUs, because they can exist mathematically, but let’s call 120 our arbitrary upper limit because in order to standardize things, we need one.

Just for giggles, here’s a quick plot of all of the upper and lower limits of the BJCP beer styles, sorted by the mean IBU of each style (in green).

Far left is Gueuze, far right is IIPA. You can click it for a bigger version.


What you can really get off of this is that the vast difference between the middle and the top vs. the middle and the bottom.

I broke all of the styles into three values: Bottom IBU, Top IBU, Average IBU. They are the stated bottom of the acceptable range for the style, the top of the acceptable range for the style, and the average of the range.

The mean of the Bottom IBUs is 21. The mode is 20.

The mean of the Top IBUs is 37. The mode is 40.

The mean of the Average IBUs is 29. The mode is 30.

So what does this tell us? That the line between “hoppy” and “not hoppy” is much thinner than it might seem when the upper end is 120. As we’ve already noted, this has a lot to do with factors other than hops, and that IBUs aren’t the best way to measure the bitterness of the beer itself, just how many hops were put in.

Okay, cool. That first part is interesting and the latter part is fairly obvious. We know we need to use IBUs – at least in part – in order to calculate an overall bitterness, so let’s see if we can breakdown the range of IBUs a little better. From this point out, I’ve actually discarded the average for anything but sorting, and I’ve put the highs and the lows together in the same variable to give us the upper and lower limit of the acceptable range all in one place.

The mean of all of the IBU values across all of the beer styles is 29, the median is 25, and the mode is 20. The standard deviation of values from the mean is ~19.

This seats the middle of the range of IBUs in beer styles squarely in the 20’s, and I would say that the average (29) probably represents what we could call our middle in terms of perceived hoppiness. The standard deviation from the mean gives us a high end of 48 – let’s say 50 – and a low end of 10. Anything above 50 would definitely be hoppy (but not necessarily bitter) and anything below 10 would probably not have any hop character at all.

If we were to break it down on this scale we could say that we have, essentially 4 categories.

0 – 10: No apparent hop character
10 – 30: Low hop character
31 – 50: High hop character
51+: Very hoppy

If we were to sort existing beer style IBU averages into these categories we would get:

0 – 10: Guezue, Lambic, Berliner Weisse, Lite Lager

10 – 30: Standard American Lager, Weissbier, Dark American Lager, Dunkelweizen, Scottish Light 60/-, Witbier, Roggenbier, Southern English Brown, Mild, Scottish Heavy 70/-, Flanders Red, Cream Ale, Munich Helles, Premium American Lager, Belgian Dubbel, Doppelbock, Blond Ale, American Wheat, Scottish Export 90/-, Flanders Brown, Irish Red, Belgian Blond Ale, Weizenbock, Munich Dunkel, Biere de Garde, Traditional Bock, Vienna Lager, Oktoberfest, Kolsch, Northern English Brown, Belgian Pale Ale, Strong Scotch Ale, Brown Porter, Dortmunder Export, Schwarzbier, Saison, Belgian Dark Strong Ale, Belgian Golden Strong Ale, Maibock/Helles Bock, Ordinary Bitter, American Brown Ale, Sweet Stout, Belgian Trippel, Baltic Porter, Eisbock

31 – 50: Special Bitter, North German Alt, Classic American Pilsner, American Amber Ale, Oatmeal Stout, German Pilsner, Dry Stout, California Common, American Pale Ale, Robust Porter, Bohemian Pilsner, Extra Special Bitter, Dusseldorf Alt, Old Ale, English IPA, Foreign Extra Stout

51+: English Barleywine, American IPA, American Stout, Russian Imperial Stout, American Barleywine, Imperial IPA

If we made the “low hop” cut off 29 (the average) instead of 30, Ordinary Bitter, American Brown Ale, Sweet Stout, Belgian Trippel, Baltic Porter, Eisbock would all be in the “high hop” category.

If we made the “very hoppy” cut off 48, English IPA and Foreign Extra Stout would be in the last category.

It’s close. Really close. Of course, some of the beers that end up in the hoppier categories actually end up having a much lower perceived bitterness due to the fact that they’re also very malty. Sweet Stout, Trippel, Baltic Porter, Eisbock, English Barleywine and Old Ale come to mind.

So now we have some benchmarks in place. I had been treating IBUs as a continuous scale, because it is a continuous measurement. However, if you believe that 100 IBUs is the upper limit of human detection and 0 IBUs is the lower limit, that would suggest a mid-range of around 50 IBUs. We’ve shown here that the mid-range, at least in terms of what we expect out of our beer styles, is actually a little lower than that, so we may actually have to do a little bit of normalization when we’re using IBUs in a formula to calculate bitterness more efficiently.

Next up: An IBU standardization formula and how OG and attenuation fit into the bitterness equation. (Part 3 is here)

Posted By: erik
Last Edit: 13 Nov 2009 @ 11:55 AM



Responses to this post » (8 Total)

  1. Russ says:

    You could be to beer what Lord Kelvin was to thermodynamics.

  2. erik says:

    If I can come up with something sensible, I totally want it called a Myers Number.

  3. notaro says:

    Glad you came back to this. This would be super useful. And boiling it down to four of five categories seems much more useful (at least from a drinker’s perspective) than 100 point scale.

    I’m not a hop head. The ESBs I have had lately have not seemed particularly bitter to me. I certainly wouldn’t place them in the same category as an American Pale Ale. Is that because they were poor specimens of the style (i.e. ESB ought to be bitter, these weren’t) or that malt in the typical ESB masks the hops, lowering percienved bitterness.

  4. erik says:

    The latter, probably, on the ESBs. The name is really a historical reference rather than one that actually describes the flavor. They are bitter, but not in the way that an American who is used to drinking Big Hoppy Beers is used to. There is a much larger malt profile in an ESB and it definitely does serve to mask the hops.

    You’ll notice that “Ordinary Bitter” is up there in “Low Hop Profile” which is totally true, but it’s certainly more bitter than some other English style ales especially half a century ago before America discovered hops.

  5. Russ says:

    A week ago I was in Ephrata, PA and had lunch at Stoudt’s brewpub; by way of comparison on the IBUs as Erik suggests, their “Scarlet Lady ESB” is a mere 32, while their Double IPA is at 90. To REALLY put that in perspective, their “Fat Dog Stout” has an IBU of 55…and you certainly don’t think “bitter” when you think of stouts. Dry, perhaps, but not bitter.

    I am anxious to see what you come up with for maltiness; I’ll withhold questions on that topic ’til you post relevant to it.

  6. […] might argue that extreme beers above 120 IBUs (impossible to sense, but possible to make) or with irrationally high alcohol content are consumed for the torture of […]

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