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Relative Bitterness Ratio (RBR)

2012 January 13

I have a new calculation that I’ve been using when determining the expected balance of my beer recipes. It is a child of the commonly-used Bitterness Ratio (BU:GU), and the numbers output can be read in the same way as BU:GU. However, the one thing that is taken into account with the Relative Bitterness Ratio (RBR) that BU:GU does not account for is Apparent Attenuation (ADF).

The higher the degree of Apparent Attenuation (ADF), the more fermentable sugars are consumed and the less residual sweetness is left behind. That means that as ADF gets higher, beer balance tends more toward the bitter end of the scale. As ADF gets lower, beer balance tends more toward the sweet end of the scale.

For example: A beer that starts out at an OG of 1.050 at 25 IBU would be said to have a Bitterness Ratio of 0.5. If it were split into two batches and one had an apparent attenuation of 80% (Beer A), while another had an apparent attenuation of 60% (Beer B), Beer A would be perceived to be more bitter than Beer B, as the latter has considerably more residual sweetness.

In the pages linked below, you can find out a plethora of information explaining details about the Relative Bitterness Ratio (RBR). If you aren’t interested in the details, I’ve included the formula for figuring out RBR as well as a simple calculator if you just want to input some numbers and get results.

To quickly explain the formula:

RBR = Relative Bitterness Ratio. ADF = Apparent Attenuation. 0.7655 is the average ADF of all beer styles. Since the Relative Bitterness Ratio takes into account balance relative to all beer styles, it uses this as a constant. You are comparing your beer’s ADF against the average ADF (0.7655), then adjusting the standard Bitterness Ratio accordingly (it goes up if your ADF is higher than average, down if your ADF is lower than average). Just like BU:GU, higher numbers mean more bitter, lower numbers mean less bitter, and 0.5 is roughly average balance.

RBR = (BU:GU) x (1 + (ADF - 0.7655))

Relative Bitterness Ratio Calculator
BU:GU Ratio
Apparent Attenuation (%)
Relative Bitterness Ratio
RBR = (BU:GU) x (1 + (ADF - 0.7655))
by Ryan “Mad Alchemist” Shwayder
4 Responses leave one →
  1. January 14, 2012

    A very interesting concept. A drawback I can see is that you have to have an idea of what your attenuation will be before you can use it. That can be problematic, especially with a new recipe.

  2. January 15, 2012

    Thanks for getting the discussion started, Denny.

    The Mad Fermentationist (not me, I’m the Mad Alchemist!) emailed me and proposed that we start thinking along the lines of the residual extract (which I believe is the same thing as real extract, so that’s what I ran with).

    To push this discussion further along, here’s some thoughts I sent him about that approach.

    I added columns for Real Extract in both Plato and Specific Gravity to the far right of the data chart.

    https://docs.google.com/spreadsheet/ccc?key=0Ai1Yv492QZYUdFN1YWpYZTFxUm1reWN2WEx2a0xpUkE

    I originally used RDF (Real Attenuation) instead of ADF (Apparent Attenuation) for similar reasons. Ultimately, since I decided to adjust the Balance according to a beer relative to all other beers, using ADF vs. RDF became inconsequential (because your beer’s RDF in comparison to the average is the same as your beer’s ADF in comparison to the average). I switched back to ADF so people didn’t have to bother with RDF = ADF * 0.8192.

    Real Extract is ultimately a similar approach, though might be more accurate in terms of perceived sweetness of the final beer.

    If we were to decide to create a new number scheme from BU:GU entirely, I think it might yield some useful results (part of my decision to go with what I did for RBR was to make it more accessible since many people are familiar with BU:GU already, and the numbers are essentially the same).

    Anyway, I also dropped in a thought on a potential method to calculate this under “Perceived Bitterness?” in the last column.

    It is IBU/RE (°P)

    International Bitterness Units / Real Extract (degrees Plato)

    RE = (0.1808 × °Pinitial) + (0.8192 × °Pfinal)

    Interestingly, this (IBU/RE (°P)) gives numbers roughly on a scale from 1 to 10, with the outlier being Imperial IPA at 13.4. It’s actually the only beer style above 10 using this equation.

    I went ahead and colored the columns as well, which allows us to see that beers relative to one another look roughly the same as BU:GU and RBR.

  3. January 16, 2012

    Denny Conn linked the info over on the AHA forums. I’m mirroring it here since some people aren’t AHA members and can’t post over there.

    Summary: All attempts to accurately quantify beer balance objectively before brewing will fail because of the many contributing factors. For example, grain bill (some things that aren’t hops are bitter), attenuation (difficult to calculate before fermentation), carbonation, etc.

    Perhaps instead of attempting to predict balance more accurately than BU:GU already does, it would be valuable to codify balance for what objective data we DO have access to–but to direct those efforts toward expanding our ability to communicate with other brewers about an existing beer rather than using it to help define a recipe upfront.

    Meaning, let’s come up with a useful number so I can go over to the AHA conference and say, "Hey, try my beer. Its perceived bitterness is 5, so it’s well-balanced. I have some roasted barley in there too, which increases the astringency a little, but check it out!"

    My intent with spending all the time working on this article was largely to start a conversation on finding ways to predict and target beer balance. I’m glad the conversation is starting.

    Ultimately, the best way to make the beer you want is to brew it once then make corrections in pursuit of your intent, but I’m always interested in methods to frontload that effort with calculations (the fewer repetitions needed to perfect a recipe the better).

    The Mad Fermentationist (not me, I’m the Mad Alchemist!) emailed me and proposed that we start thinking along the lines of the residual extract (which I believe is the same thing as real extract, so that’s what I ran with).

    To push this discussion further along, here’s some thoughts I sent him about that approach.

    I added columns for Real Extract in both Plato and Specific Gravity to the far right of the data chart.

    https://docs.google.com/spreadsheet/ccc?key=0Ai1Yv492QZYUdFN1YWpYZTFxUm1reWN2WEx2a0xpUkE

    I originally used RDF (Real Attenuation) instead of ADF (Apparent Attenuation) for similar reasons. Ultimately, since I decided to adjust the Balance according to a beer relative to all other beers, using ADF vs. RDF became inconsequential (because your beer’s RDF in comparison to the average is the same as your beer’s ADF in comparison to the average). I switched back to ADF so people didn’t have to bother with RDF = ADF * 0.8192.

    Real Extract is a similar approach, though might be more accurate in terms of perceived sweetness of the final beer.

    If we were to decide to create a new number scheme from BU:GU entirely, I think it might yield some useful results (part of my decision to go with what I did for RBR was to make it more accessible since many people are familiar with BU:GU already, and the numbers are essentially the same).

    Anyway, I also dropped in a thought on a potential method to calculate this under "BU:RE" in the last column.

    It is IBU/RE (°P)

    International Bitterness Units / Real Extract (degrees Plato)

    Real Extract (RE) = (0.1808 × °Pinitial) + (0.8192 × °Pfinal)

    Interestingly, this (IBU/RE (°P)) gives numbers roughly on a scale from 1 to 10, with the outlier being Imperial IPA at 13.4. It’s actually the only beer style above 10 using this equation.

    I went ahead and colored the columns as well, which allows us to see that beers relative to one another look roughly the same as BU:GU and RBR.

    I’ve added some data to the chart for us to look at:

    • "BU:RE (°P)": Bittering Units/Real Extract in degrees Plato
    • "BU:REU (SG)": Bittering Units/Real Extract Units in Specific Gravity (Real Extract Units = (SG – 1) * 1000)
    • "BU:FG (°P)": Bittering Units/Final Gravity in degrees Plato
    • "BU:FGU (SG)": Bittering Units/Final Gravity Units in Specific Gravity(Final Gravity Units = (SG – 1) * 1000)
    • "BU:FG (SG)": Bittering Units/Final Gravity in Specific Gravity

    Light American Lager and Gueze both get a little broken because their average FG is actually less than 1 °P (unless you look at the Real Extract numbers, which look a bit better).

    My favorite of the bunch is BU:RE (°P). The numbers make my brain happy because it is basically on a 10 point scale. The average of all beer styles is 5.4, so I suppose it could be corrected to make 5 be dead average, but that’s just manipulating the data to make it prettier.

    The formula looks a little nasty if you don’t break it up into its constituent parts.

    Effectively it is just IBU / RE in °P.

    Real Extract (RE) = (0.1808 × °Pinitial) + (0.8192 × °Pfinal)

    If you want to write the entire thing out into a formula using Standard Gravity (since most homebrewers use SG and not °P)… Well, this is going to look nasty in forum text, but I’ll attempt to write it out.

    (IBU / ((0.1808 * (259-259/OG)) + (0.8192 * (259-259/FG))))

    Yeah, looks nasty. Hooray for calculators. This includes the conversion of SG to °P right in the equation for both OG and FG. It also includes the conversion from FG to Real Extract in the equation. It certainly looks like a mess, but the results are elegant and seem pretty accurate to me on a 10 point scale.

    This still suffers from the need to either measure your FG or try to predict it accurately if using it to formulate a recipe. Perhaps it would be more useful when communicating with each other as to the balance of our beers rather than in planning a recipe.

    "Here, I brewed up this Irish-American Red. Its BU:RE is around 7, so it’s more bitter than your average Irish Red. I lovingly call it the South Boston Red. What do you think?"

    "Try my Imperial IPA. It’s got a BU:RE of 9, so it’ll taste a little less bitter than you might be used to in such a bitter style. I call it Archduke IIPA. Got enough bite for ya?"

  4. February 10, 2012

    Interesting. The only high level observation I’d submit is the disregard for other “modulating” flavor/aroma components that work against pure bitterness (i.e. alpha acids). We have received numerous comments from brewers using our super high aroma hops that their bitterness is less pronounced when the variety is handled properly during processing for high aroma. Granted some of the aroma components are heavy in sesquiterpenes and specifically pinenes which will add to the bitter perception, however several other components are quite pronounced which seem to dampen the apparent bitterness.

    Nice follow-through with the analytics!

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