Follow me on my math to see if I’m missing anything here
Dryhop math
23 L = 23,000 ml
50 g / 23,000 ml = 0.00217 g/ml hopping rate
Bottled tincture
1g / 50 ml = 0.02 g/ml
Then you used 2 ml so added 0.04 grams to you bottles. But it would now get diluted when added to the bottle.
0.04 g / 600 ml = 0.00006 g/ml hopping rate
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So your dryhoped bottles would end up having 1.3 grams per bottle (0.00217 x 600)
And the tincture bottles would what 0.04 grams per bottle. I can’t personally see how this could possibly produce more of a hop character.
But this will all change if the tincture beer was from the same batch with that dryhop and then you just added tincture to one of those beers. If so, of course it had more flavor because your adding more hops to that bottle. Those bottles now have 1.34 grams per bottles
That said it’s only a 3% increase in hops which is interesting that you anecdotally believe it had a massive impact. I wonder if you did a blind triangular test with some friends if they could distinguish the difference
Water is a polar substance. Even a mixture, like beer, of water and 5-8% of ethanol still a strong polar solvent. Essential oils and soft resins, like polyphenols, alpha and beta acids are apolar, and their solubility in water is minimal. Because of this we boil hops, to isomerize AA, and turn them a little more soluble in water.
Ethanol molecules are polar in one end and apolar in the other. So it solubilize the essencial oils and the resins of hops, and still miscible with water. There is an article that describes the extraction by ethanol. They used 1/15 proportion in a more complex extract operation, and achivied around 90% of efficiency. I used 1/50. Probably got close to they results.
The main difference between the dry hopping method and the extract addition, is the polarity of the medium. Only a small quantity of essential oils solubilize in beer, the other components just don't. While all apolar substances of hops solubilize in ethanol.
When the extract is added to the beer at bottling, it produces a ouzo effect, because of the solubilization of the mixture of ethanol and hops compounds. So, all that has been extracted will be in the final beer. 1 g of Polaris has 4-5 % of oil, 16% aa 5% ba. It's near 200 mg of bitter substances. Divide by 50 mL. It's 4 mg/mL. For 2 mL, 8 mg. In 600 mL beer, it would be like 13 IBU addition, or 13m g/L. And it doesn't completely explain how bitter it turns the beer. Maybe the polyphenols does.
Refer to the essential oils, 5 mg, means 0,1 mg/mL. 2 ml, 0,2 mg. In 600 mL, 0,33 mg/L As a reference, many oil compounds of hops have threshold limits ranging from 0,010 mg/L to 0,100 mg/L. Considering that, it should be detectable in my experiment.
The aroma and flavour of this specific hop is mint like. And it really shows up. I didn't try a triangle test. What I have done is open both beers and served to an friend and to my wife, and asked what they think about. My wife prefers the extract beer. My friend the original. Visually, they look like the same to my, but the mint notes was very distinct, as well the bitterness.
So, why don't you give a try and do something like this. It's nice to do experiments sometimes. That's what fascinated me about homebrewing, in the first place.