A cocktail batched in advance is not the same recipe scaled up. Two things change: the water has to be added deliberately, and ingredients that do not keep have to be replaced.
The dilution has to be built in
A drink mixed to order picks up water from ice during stirring or shaking, typically a substantial fraction of the finished volume.
A batch poured from a bottle receives none of that, so water is added as a measured ingredient before storage.
The exact amount is determined by mixing the drink normally, measuring what the finished volume became, and working backwards.
That figure is taken by scale rather than by jigger, because the gap between a correctly built batch and a thin one is a small fraction of the total volume.
Fresh citrus stops being an option
Fresh juice loses its aromatic top notes within hours and develops a stewed character within a day.
Batches intended to keep therefore use an acid solution made from citric and malic acid, which supplies the sourness without the perishable aroma.
The result tastes cleaner and less complex than fresh juice, which is why acid solutions appear in long-life batches rather than in same-day ones.
Separation and sediment appear at scale
Ingredients that stay mixed in a shaken drink can settle over days, particularly syrups with fruit solids and anything with suspended particles.
Batches are usually filtered before bottling, and heavier ingredients are added at service instead of in the batch.
Dairy and cream are excluded altogether, since they separate and spoil on a timescale far shorter than the batch is built to last.
Cold storage does part of the work
A batch held in a freezer is served at the correct temperature without ice at all, which removes the last variable from service.
Alcohol content keeps a properly built batch liquid at freezer temperature, and a batch that freezes solid indicates the dilution was pushed too far.
Refrigerated rather than frozen batches need a brief stir over ice at service, which reintroduces a small amount of dilution the recipe must allow for.
Why bars batch in the first place
Service speed is the obvious reason, since pouring from a bottle takes seconds where building a drink takes a minute or more.
Consistency matters more. A batch removes the variation between bartenders, between busy and quiet periods, and between the first and last drink of a shift.
The cost is flexibility, since a batched drink cannot be adjusted for a customer who wants it drier or sweeter, which is why bars batch their highest-volume drinks and build the rest to order.