NOTE: In the 2015 BJCP Style Guidelines, Doppelbock is now Style 9A in Category 9 Strong European Beer which contains more strongly flavored and higher alcohol lagers from Germany and the Baltic region. Most are dark, but some pale versions are known.
Doppelbock or "double bock" started out as a beer brewed by the Paulaner monks in Munich for their Lenten fast. Since they could not eat anything for 46 days between Ash Wednesday and Easter Sunday, there was no use baking bread that they could not eat. Instead they used the grain to brew a strong beer which they felt cleansed the body and soul during this long taxing period of fasting. The beer they brewed was called Salvator, or Savior, and was initially brewed only for themselves. Apparently some was sold for extra money periodically because there were many complaints of public drunkenness in the streets surrounding the monastery. Eventually the brewery (now owned by a civilian brewer named Franz Zaver Zacherl, the owner of Münchener Hellerbräu) received an ordinance of favor from King Ludwig I of Bavaria himself which allowed them to brew Salvator and dispense it to the public.
Soon many breweries began brewing copies of Salvator. As soon as the German copyright law was passed, Franz Xaver's successors, the Brothers Schmederer, received the registered trademark for Salvator and all the other breweries using the name had to come up with new ones. Almost all selected names with "-ator" in the suffix. Beers such as Celebrator, Triumphator, Maximator, etc. were being brewed in Germany and were recognized by the "-ator" as a doppelbock style beers.
Even though the name means double bock, by German law, it is required to only have an OG of 1.074 or 18°P to be labeled a doppelbock. This is 2°P over a standard bockbier. This is the minimum however and many of these beers can reach strengths between 10 and 13% ABV. Apparent attenuation is less than a standard bockbier, in the range of 65-72% making the beer seem quite sweet. Even though the alcohol may not be substantially more than a regular bock, the beers are usually perceived as being much stronger.
Brewing a doppel bockbier should start with good continental malts with low protein, below 11.5%. Munich malt can make up 65% of the grist, the other 35% being a continental pilsner malt. Use dark caramel malts sparingly due the the astringent nature they contribute in this beer. German brewers perform a decoction mash and to be more authentic you should too. Choose a well attenuating lager yeast that produces low levels of diacetyl, aerate the cold wort well and perform a diacetyl rest after fermentation has completed. Follow these tips and you will brew a wonderful example of a German Doppelbock Beer.
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