Relative Bitterness Ratio (RBR)

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Hop

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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.

Beer A would have an RBR of 0.517 while Beer B would have an RBR of 0.417--a fairly big gap in perceived balance.

In the pages linked below, you can find 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 RBR calculator if you just want to input some numbers and get the results.

To quickly explain the formula:

RBR = Relative Bitterness Ratio. ADF = Apparent Attenuation. 0.7655 is the average ADF of all beer styles (according to the BJCP style guidelines). 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.

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

You can see the full original post (basically the same as this one) over at Mad Alchemist, but I'll be happy to read and respond to posts here.
 
I used 60% and 80% to illustrate a point (and I do get ADF in those ranges depending on the beer). I specifically tailor my mash schedule, yeast selection, and fermentation temperature in part to determine my intended attenuation.

I'm not sure if ADF is what you're talking about here, though--ADF is Apparent Attenuation. I think you are talking about Brewhouse or Mash Efficiency since you mentioned "standard mashes."

Apparent Attenuation (ADF) is the percentage of fermentable sugars converted by yeast to ethanol and CO2.
 
I think this has been kicked around and it is also tied to mash temps. Getting a good number on how that will affect any given brew session seemed to be the sticking point.
 
I've found that I can fairly accurately predict my apparent attenuation before brewing based on a combination of knowing my equipment, changing my mash temperature (higher temperature means less attenuation, lower temperature means more attenuation), and choosing yeast with attenuation in mind.

I've found that BeerSmith is quite accurate at predicting my likely ADF now that I know what to expect. I would recommend using that or similar software to aid in the calculations--it'll make your life easier.

That said, you can't be absolutely certain what your Relative Bitterness Ratio is until after fermentation is complete, but I've found it useful in planning recipes.

RBR isn't something you should bother trying to calculate until you know your system well and are fairly advanced at homebrewing. Basically, BU:GU wasn't quite cutting it alone, so I decided to tackle the problem head-on and have found it to be quite useful in the past several batches I've brewed.
 
Oh, no not at all. Apparent Attenuation is highly dependent on mash temps. I must have misunderstood your comment entirely if I led you to believe that.
 
What number represents a 'noticeable' difference on your scale? Given the numbers above you might have to multiply by 100 because peoples bias towards thinking decimals aren't very meaningful. Think percentage. ;)
 
Ha! Well, you're looking at a 20%+ gap there.

Relative Bitterness Ratio (RBR) numbers are very similar to BU:GU in that 0.5 is roughly balanced between sweet and bitter.

(On average) The sweetest-balanced beer style is Fruit Lambic at 0.113 RBR. The most bitter is the Imperial IPA at 1.135 RBR. An American Amber Ale is 0.611 RBR and an Irish Red Ale is 0.430 RBR.

Hopefully that gives a little clearer picture on the numbers. If you use BU:GU already, the numbers will be familiar. I did consider multiplying the values by 100 because they are easier to understand that way, but I decided to leave them as-is because many of us are used to the BU:GU numbers already, and RBR is simply BU:GU corrected for attenuation relative to other beers.
 
I do pay attention to bitterness ratio when I design my recipes. Since your RBR requires ADF, it's really not possible calculate it until after fermentation. So, while it's an interesting and accurate way to characterize the beer after it's made, it's not a good tool for recipe creation (unless your ADF is well outside the norm, and you know for certain what it till be).
 
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?"
 
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