I was an extract brewer for a few months to learn the process. This was about 5 years ago when I started homebrewing. During that time , I did straight extract beers, steeped grain beers and a process like the mini mash procedure currently popular. Let me say that extract brewing in it various forms (extract alone, steeping grain, smal amounts of grain mashing, etc) all make excellent beers. In fact, in home brew competitions, beers using extracts often are indistinguishable from all grain brews and are often the winning recipes. I moved from extract brewing to all grain for several reasons, none of which had to do with the quality of the beers it made. The reason I made the switch was;
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Educational Purposes. I wanted to learn more about the process of all grain brewing and the variables associated with the process on the final beer.
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Mashing Experimentation. I wanted to experiment with mashing times, temperatures and other conditions to better understand the influences of the enzymes in malt on the finished beer.
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Base malt Experimentation I wanted to try various base malts in beers to see their effects.
I guess all of these fall into more of a "scientific experiementation" mode which fits my scientific background. Some of the advantages I see with all grain brewing are that it is particularly advantageous when you are making light colored and light body beers. Things such as pale lagers and blonde ales can be brewed to better fit the style profile for color and body. It also allows you to adjust your base malt to fit the beer profile you want. For example, an all Maris Otter ale is not as easy to do with extracts and mini mash.
So if you are an experimenter and you have exhausted trying different things with extract brews, then all grain might be what you are looking for. However, from my experience, unless you are focused on lagers or blonde ales, you will not see a dramatic increase ( say a magnitue of 10 or 100 fold) in beer quality characteristics going to all grain.
I am sure others may have a different opinion and I look forward to reading them.
Dr Malt