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I am planning to age a big Russian Imperial Stout for about a year. I understand that during this time, the bitterness imparted by the hops will dissipate. If I want to maintain a balance, I'll need to overshoot my bitterness somewhat.

How much bitterness should I expect to lose in a year? 5%? 25%? half?

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I have never thought of RIS being balanced. Its a pretty malt forward style. And the depth of roasted malt also serves to give some bitter counterpoint to the malt sweetness as well. – brewchez Sep 1 '11 at 16:16
I didn't mean to imply that the style should be "balanced." It's just that I want to be able to control whatever kind of imbalance I planned to have. – Dustin Rasener Sep 1 '11 at 18:26
up vote 9 down vote accepted

Paraphrasing from Fundamentals of Beer and Hop Chemistry (text below), 2/3 of the hop bitterness in wort has a half-life in excess of 5 years, and the remaining 1/3 as a half-life of 1 year. From that, I've made a table showing the amount remaining over time. The total column shows the percentage of bitterness compared to the total at the start:

months  cis-    trans-  total
0   68.00%  32.00%  100.00%
3   65.68%  26.91%  92.59%
6   63.45%  22.63%  86.07%
9   61.29%  19.03%  80.31%
12  59.20%  16.00%  75.20%
15  57.18%  13.45%  70.64%
18  55.23%  11.31%  66.55%
21  53.35%  9.51%   62.87%
24  51.53%  8.00%   59.53%
30  48.08%  5.66%   53.74%
36  44.86%  4.00%   48.86%
48  39.06%  2.00%   41.06%
60  34.00%  1.00%   35.00%

So, if you leave a beer for 1 year, it's IBUs will have decreased to 75% of its original value. For example, an 80 IBU beer will have 60 IBUs after 1 year.

Here's the relevant part of the text:

The ratio of the isohumulones depends on the reaction conditions. In the wort medium it is normally 68:32 in favour of the cis-compounds. However, the cis-compounds are much more stable (half-life >> 5 years) than the trans-isomers (half-life of ca. 1 year) during the course of time. This affects, obviously, the cis:trans ratio and has significant consequences with respect to taste and flavour stability.

Of course, other variables do come into play, so these figures can't be taken as exact, But then, as we all know, that's how it is with brewing. Our malt isn't exactly the color on the label (usually a range of values), and hops aren't the bitterness on the pack since they degrade from the get go. So, although not exact, these figures should offer a good estimate.

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Holy crap this is specific and scientific. Excellent answer. – Graham Sep 6 '11 at 12:37

I realize that this isn't really an answer, but I don't think there's any way to quantify it. I've never seen a study done and I think it would vary from beer to beer.

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And storage conditions! – brewchez Sep 1 '11 at 17:04
Since this isn't really an answer, wouldn't it be better as a comment? – mdma Sep 1 '11 at 19:00

Adding to MDMA's informative chart - the Trans/Cis isomer ratio can be calculated using the following chart taken from A Kinetic Study on the Isomerization of Hop r-Acid - Jaksula, et. all

x = time at temp y = temp value = T/C ratio

Table 3. T/C-ratio (%)a as a Function of Reaction Time and Temperature: Experiment 1

      5min 10m  15m  20m  30m  45m  60m  90m

80C        153  111  89.7 84.1 70.7 53.9 57.6 

90C  100.0 77.5 75.6 55.4 55.4 49.3 49.1 46.7 

100C  60.8 54.1 61.8 54.9 47.3 47.3 47.1 46.3

This becomes more important with recent trends toward extreme late hopping

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