Disclaimer: I have no formal education in Greek.
Setup (If you are familiar with Romans 12 you can skip to "The question" below)
Throughout the Roman empire (and in all the world) both Jews and gentiles were accustomed to the idea that worship involved sacrifices. What deity in their right mind doesn't appreciate BBQ, seasoned with salt? And having eaten a good meal the deity is then more disposed to be merciful and provide rain and military victories to the worshipers.
The gentiles of Athens, when wanting to cover their bases, set out offerings on an altar with a note saying essentially "These gifts are for any deities not covered by gifts to the deities we already know about":
KJV Acts 17:23 For as I passed by, and beheld your devotions, I found an altar with this inscription, TO THE UNKNOWN GOD. Whom therefore ye ignorantly worship, him declare I unto you.
Paul, like the Jewish prophets points out that the one true God doesn't need anything and isn't properly worshiped by gifts of food and drink or gold or silver:
KJV Acts 17:
24 God that made the world and all things therein, seeing that he is Lord of heaven and earth, dwelleth not in temples made with hands; 25 Neither is worshipped with men's hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things;
NIV Psalm 50:
7“Listen, my people, and I will speak; I will testify against you, Israel: I am God, your God. 8I bring no charges against you concerning your sacrifices or concerning your burnt offerings, which are ever before me. 9I have no need of a bull from your stall or of goats from your pens, 10for every animal of the forest is mine, and the cattle on a thousand hills. 11I know every bird in the mountains, and the insects in the fields are mine. 12If I were hungry I would not tell you, for the world is mine, and all that is in it. 13Do I eat the flesh of bulls or drink the blood of goats? 14“Sacrifice thank offerings to God, fulfill your vows to the Most High, 15and call on me in the day of trouble; I will deliver you, and you will honor me.”
Paul's new approach: "divine service according to knowledge"
In Romans 12 Paul sets forth the new paradigm of worship to God that involves a "living sacrifice" where one offers one's own body, alive for divine service (λατρείαν). He exhorts them to sweep away the thinking characteristic of those who don't know God and think in a new way, according to a knowledge of the true God so they can please God and determine the will of God based on understanding:
NET Bible Romans 12:
1 Therefore I exhort you, brothers and sisters, by the mercies of God, to present your bodies as a sacrifice—alive, holy, and pleasing to God—which is your reasonable service (τὴν λογικὴν λατρείαν ὑμῶν). 2 Do not be conformed to this present [ignorant] world, but be transformed by the renewing of your mind, so that you may test and approve what is the will of God—what is good and well-pleasing and perfect. 3 For by the grace given to me I say to every one of you not to think more highly of yourself than you ought to think, but to think with sober discernment, as God has distributed to each of you a measure of faith.
In verse 3 or Romans 12 Paul ties "sober" evaluation of one's divine service to the following Greek phrase:
...ἑκάστῳ ὡς ὁ θεὸς ἐμέρισεν μέτρον πίστεως.
In the NET Bible (and other English translations play the same suit) it is rendered:
...as God has distributed to each of you a measure of faith.
To my mind (and see disclaimer above) the sentence fragment (in English) above does not fit the context and makes no sense at all. For example, should I say "I have a lot of faith so I think I'll be an apostle"? Or "I have very little faith so I guess I have no gift"? I mean, who knows how much faith/faithfulness they have? How do they measure that?
So how does Paul expect one to use the μέτρον πίστεως that God has allotted to each (ἐμέρισεν to ἑκάστῳ) to think "soberly" about their gifts?
Click HERE for the LSJ entry for μέτρον (which I believe is the key to understanding this properly).