The rule, in full

Plummy's weight should move less, and the reason is the one you have already seen working.

Cabernet's unit is 1, so that weight has its full say in the guess. Plummy's unit is 0.5, so that weight only ever gets half a say. When the guess comes out 10 dollars too low, cabernet is twice as responsible for the shortfall as plummy is, because it was doing twice as much of the talking.

So the weight that caused more of the error should absorb more of the repair. Moving them in proportion to how loudly they spoke is simply aiming the correction at where the error actually came from.

There is a second reason, and it matters later. A unit of 0.5 is weaker evidence about the plummy weight than a 1 is about cabernet. Making the smaller change from the weaker evidence keeps the model from overcommitting on a faint signal. The two reasons happen to agree, which is a good sign for the rule.

So cabernet should move more than plummy, and viognier and apricotty should not move at all. That settles the proportions. It does not settle the size, and the size is where the last three bottles came apart. Every correction so far closed its gap completely, and each one undid the bottle before it.

So whatever we build now has to come out gentler than that. The question is what decides how gentle.

Start with the proportions and see where they land on their own. Only two numbers are available, and each has a job. The error, 10 dollars, says how big the total repair needs to be and in which direction. The unit says how much this particular weight had to do with causing it.

Multiply them and both jobs are respected at once. A bigger error means a bigger correction everywhere, and within that, each weight gets a share sized by how active it was.

The proportions are right. Cabernet moves twice as far as plummy, and the silent two do not move.

The size is the trouble we expected. Run the bottle through those new weights and the guess comes out at 24 dollars 50, against a wine that costs 22. It has sailed straight past, and too far in the right direction is still too far.

Which is worth seeing clearly, because it says the proportions were never the problem. The shape of the correction was right the whole time. It was only ever too large.

So keep the shape and shrink the whole thing. Take the same four numbers and use only a fraction of each. A tenth, say.

Now the numbers are small enough to be a nudge. Cabernet gets 1, which is a tenth of the full correction its unit called for, and plummy gets half of that. Same two to one ratio, a tenth of the size.

That fraction is the answer to how gentle, and nothing about the bottle decides it. It is a separate dial we set ourselves, and it has a name, the learning rate. A tenth is being used here, and how the number gets chosen is worth a slide of its own, which is coming shortly.

Which gives the whole rule, in one line:

weight change = error x unit x learning rate

Three numbers, multiplied. The error says how wrong the guess was, the unit says how much this weight had to do with it, and the learning rate keeps the whole thing to a nudge.

Apply those four changes and the weights are no longer identical.

Cabernet goes from 8 to 9. Plummy goes from 8 to 8.5. Viognier and apricotty stay exactly where they were, at 8.

9, 8, 8.5, 8

Cabernet moved a whole point and plummy moved half a point, matching the two to one gap in how loudly they spoke. And the untouched pair are still sitting at their starting value, waiting for a bottle that has something to say about them.

One bottle has gone through, and the model already knows something it did not know before.