"based on" usage

Solution 1:

As Lachlan Dominic observes in a comment above, "based on" is interchangeable with "on the basis of" in many constructions. So, for example, you could say with equal accuracy and clarity

The league determines playoff seedings based on each team's number of regular-season wins.

and

The league determines playoff seedings on the basis of each team's number of regular-season wins.

The "It is divided based on glasses of milk" example is a bit difficult to interpret (because you don't provide a referent for It), but in terms of meaning it is interchangeable with

It is divided on the basis of glasses of milk.

Both the "based on" form of the sentence and the "on the basis of" form are coherent and grammatical, so here (and probably in most other cases) you are free to use the form you prefer.

UPDATE (9/16/2017) Having described real-world usage fairly accurately in my original answer (above), I feel that I should expand this answer to acknowledge a prescriptive view of "based on" that has existed for many decades.

Theodore Bernstein, The Careful Writer: A Modern Guide to English Usage (1965) gives a succinct account of this view:

BASED ON

A latter-day tendency is to use based on as if it were an absolute participle like considering or given: "Based on future prices today for October delivery, Cuba will pay about $1.5 million for the shipment," This could be corrected to, "Based on future prices ... estimates are that, etc." Another example: "Once fully certified—based on {make it on the basis of} at least four years' carefully observed performance in the classroom—the new teacher would be licensed to teach anywhere in the United States." Some day based on may become an absolute phrase; but as of now, unless it has a clear and present subject, it must be classed as a DANGLER.

In short, Bernstein argues that a teacher may be fully certified on the basis of four or more years' carefully observed performance, but may not be fully certified based on such performance.

Almost forty years later, Bryan Garner, Garner's Modern American Usage, second edition (2003) identifies two appropriate and two inappropriate applications:

based on. This phrase has two good and two bad uses. First, the phrase may carry a verbal force (base being a transitive verb)—e.g. [first example only]: "She said she based her ruling on Xiong's allegations." ...

Second, in a passive sense, it may carry an adjectival force (based being read as a past-participial adjective)—e.g. [first example only]: "A quick calculation based on U.S. data indicates a requirement of $13 billion a year for Afghanistan." ...

But traditionally speaking, based on should have neither adverbial nor prepositional force. Here it's an adverb: "American officials said they attacked the convoy based on intelligence reports." ... (Based on improperly modifies attached. Try because of or owing to instead.) ...

And here it's a preposition (a DANGLER, to be exact): "Based on those conversations, Riley said he doubts Graham will play." ... (A suggested revision: Riley said that because of those conversations, he doubts ....)

At least in the third example—the adverbial one—Garner presumably would have had no objection to "on the basis of" in place of "based on."

Kenneth Wilson, The Columbia Guide to Standard American Usage (1993), however, argues that in practical terms the "some day" at which "based on" becomes an absolute phrase (to use Bernstein's terminology) has arrived:

based on, based upon These combined uses as participial phrases, when they begin a sentence, often turn out to be dangling modifiers, although it is not necessary that they be so: Based upon the facts we have, my conclusion should stand up under scrutiny. But the fact is that based on and based upon, even when they dangle, are idiomatic in all but the most careful Edited English: Based upon {on} what we've heard, the police probably are ready to make an arrest. Most listeners will not notice such danglers at Conversational levels or in Semiformal or Informal writing.

Even fewer listeners will notice the adverbial "bad use" (according to Garner) of the phrase when it appears after the associated verb, as in "They could calculate nearby pick-up and drop-off points for their passengers based on optimized routing."

In any case, Wilson's distinction between Edited English and other forms of spoken and written English is a useful one to bear in mind.

The disapproval of "based on" in adverbial and prepositional settings persists in certain editorial precincts to this day—as I have been made aware repeatedly by colleagues at a company for which I have worked frequently in the past couple of years. But outside the rarefied air of Editorial English strongholds, "based on" used adverbially or prepositionally has overwhelmed any lingering objections to it with the sheer force of its ubiquity.

Solution 2:

your sentence is similar to this: "people are classified based on their characters." "based on" refers to "classified". as in saying :the classification of people is based on their character".