I have a Greek and Hebrew minor.  When I came to Christ in 1990, I was as dumb as a rock when it came to grammar.  Interestingly, I taught myself grammar from the ground up when I began the daunting task of teaching 4th, 5th, and 6th graders in 1991.  It was very humiliating in many respects.  I rewarded students for correcting my grammar in the classroom.  They learned and I learned.  It was a good deal.

When the Lord Jesus called me to preach, I thought it important to learn both Greek and Hebrew.  I always thought that Greek would be fairly logical and tight in translation work.  Then came discussions regarding genitives in reading courses.  Here is where I found all the ambiguity.  Another difficulty arises when we look at vocabulary words that occur infrequently.  Put those two situations together, and you have Romans 12.3 containing a rather difficult genitive:

“For I say, through the grace given to me, to everyone who is among you, not to think of himself more highly than he ought to think, but to think soberly, as God has dealt to each one a measure of faith.” (Romans 12:3)  Here is the discussion from many good men on this genitive:

The faith in view in this verse [v. 3] and in verse 6 seems to refer to one’s ability to view and use his or her gifts as abilities that God has given. It also involves trusting in God to work through us to bring blessing to others.  Constable, T. (2003).

Tom Constable’s Expository Notes on the Bible (Ro 12:3). Galaxie Software.

“Portion of faith” = portion (namely charismatic portion) belonging to faith (simple possessive genitive). Πίστις is personal, saving faith, and in the case of every believer it has and possesses some charisma or other that is to be exercised for the glory of God and the good of the church. Fail not to note “each one.” This relieves us of the forced and unsatisfactory interpretations which think of a partitive genitive because portion and portioning precede. “Portion” is an incomplete concept; but a genitive of a proper kind makes its governing noun definite. That is the case here. Only a few, thinking of a partitive genitive, speak of “a portion of justifying faith” despite the analogy of Scripture which never speaks of such portions and never tells us to be satisfied with a small portion of saving faith.

Lenski, R. C. H. (1936). The interpretation of St. Paul’s Epistle to the Romans (p. 755). Columbus, Ohio: Lutheran Book Concern.

ἑκάστῳ ὡς ὁ θεὸς ἐμέρισεν μέτρον πίστεως, “as God has measured to each a measure of faith.” The thought is rather compressed (Cranfield), but the meaning is clear enough so far as syntax is concerned. Despite Cranfield’s strong and repeated advocacy (followed by Fitzmyer, Wilckens; cf. also Jewett, Tolerance, 61–62, and Harrisville; against most—e.g., TDNT 4:634; Lietzmann; Barrett; Murray; Schmidt; Schlier; Ortkemper, 45–46; Zeller), it is very unlikely that μέτρον here has the sense of “standard by which to measure, means of measurement.”
    (1) Following μερίζω the phrase is more naturally taken as an apportioning of different measures—as is the case in 1 Cor 7:17 and 2 Cor 10:13 (the nearest parallel—apostles have been apportioned different spheres of service [neb]). 
  (2) The fact that the μέτρον is given to each does not imply that all have the same μέτρον. The thought is parallel to that in 1 Cor 12:7 (each has been given some measure of faith), as is clear from v 6a and indeed v 3a itself (cf. also the very Pauline 1 Pet 4:10); see also on 12:4–5. 
  (3) Cranfield’s concern lest Paul be understood to commend a reliance on “fluctuating subjective feelings” is understandable, but it rather misses the point. The sober self-assessment just called for has in view the rich diversity of the expressions of faith (and grace): by recognizing that each is graced in some measure and each expression is indispensable to the community of faith a false sense of superiority will be effectively avoided (as Paul argued at length in the parallel passage, 1 Cor 12:14–26). Cf. particularly Schlatter.
    (4) All this confirms what we would have had to deduce anyway from the use of πίστις, since throughout the letter Paul uses this key word of the human act and attitude of believing, as the means through which God effects his saving work (δικαιοσύνη), in contrast to a more objectively or externally ascertained pattern of conduct (ἔργανόμου).

This trust, which is the common denominator of all Christians (= believers), Paul clearly sees as variable in different believers (4:19–20; 14:1; Leenhardt compares the concept of maturity, as in 1 Cor 2:6; 3:1; and Phil 3:15). Here there is no sharp distinction in fact between “saving faith” and “miracle-working faith” (as in 1 Cor 12:9). Both indicate that measure of reliance on God which enables χάρις to come to expression in χάρισμα. It is the confident trust in God which recognizes that all faith and grace is from God which prevents the misjudgment of ὑπερφρονεῖν. Paul’s vision is that such reliance needs to be strengthened since it is the basis of Christian conduct and relationship (see further on 14:23). Black’s suggestion that πίστις here should have the sense “responsibility” is really a variation on πιστις = “faithfulness” and does not fit with Paul’s whole train of thought in the letter.

Dunn, J. D. G. (1998). Romans 9–16 (Vol. 38B, pp. 721–722). Dallas: Word, Incorporated.

What living sacrifices do have is a measure of faith God has given. This corresponds to the grace that Paul himself received from God. Paul said in Ephesians 4:7 that “to each one of us grace has been given as Christ apportioned it.” Peter said that, “Each one should use whatever gift [of grace] he has received to serve” (1 Pet. 4:10). God’s gifts of grace—the measure of faith God has given each believer—levels the playing field. No one is better than another, so no one should think more highly of himself than he ought.

Boa, K., & Kruidenier, W. (2000). Romans (Vol. 6, p. 368). Nashville, TN: Broadman & Holman Publishers.

Controversy arises over what is meant precisely by the phrase μέτρον πίστεως, which Cranfield (1961–62) has discussed at some length, and he illustrates how a number of different readings are possible. Here I shall concentrate on the main interpretations that have been proposed. The word μέτρον may be defined as “standard.” Those who defend this interpretation typically understand πίστεως as appositional, and identify the standard of faith either as Jesus Christ (Cranfield 1961–62; Ziesler 1989: 296; Fitzmyer 1993c: 646; cf. Moo 1996: 761) or as the gospel (Stuhlmacher 1994: 192).  According to this view, believers are called on to estimate themselves either in accord with the objective standard of the gospel or with reference to the standard of their faith, Jesus Christ himself.  Despite the attractiveness of this interpretation, another one is preferable. The use of the verb ἐμέρισεν with the noun μέτρον suggests that the latter does not refer to a “standard” but to a “measure” or “quantity” of something (cf. 1 Cor. 7:17; 2 Cor. 10:13). It seems more likely that the phrase relates to the apportioning of an amount of faith instead of apportioning “the standard of faith.” That is, the very word “apportion” is such that the idea of “quantity” is more fitting than “standard.” The “faith” in view could be miracle-working faith (Barrett 1991: 217), but elsewhere Paul limits the special gift of faith to only some believers (1 Cor. 12:9; cf. 13:2). This sense sits awkwardly with the present context, for Paul emphasizes that he addresses every believer. It is unlikely that the measure of faith refers to the special gift of faith that is given to only some believers (1 Cor. 12:9), since the admonition is addressed to all believers (rightly Wilckens 1982: 11). I conclude, then, that Paul is speaking of the quantity of faith or trust that each believer possesses

Schreiner, T. R. (1998). Romans (Vol. 6, pp. 652–653). Grand Rapids, MI: Baker Books.

Paul proceeds to the thought that this is to be done in accordance with the measure of faith God has given. NIV omits “to each” with which this clause starts, but it is important. Paul is not speaking only about great leaders, but about all the Romans. “To each” God has given faith as the measure.31 Without faith none of the gifts can be exercised, and faith is the standard whereby they are to be estimated. If we take this with full seriousness, seeing God as the sole author of the gifts and ourselves as totally dependent on him for them all, it is unlikely that we will be arrogant. Humility proceeds from genuine faith. There is another thought here. When we see that God is the giver of all the gifts and that faith is the measure, we will not deny our own gifts either. Being sober-minded means recognizing what God has given us and being zealous in its use as well as humble.

Morris, L. (1988). The Epistle to the Romans (p. 438). Grand Rapids, MI; Leicester, England: W.B. Eerdmans; Inter-Varsity Press.

The measure of faith. ‘Faith’ here has a rather different sense from that which it bears in the earlier part of the letter; here it denotes the spiritual power given to each Christian for the discharge of his or her special responsibility (cf. verse 6, ‘in proportion to our faith’).

Bruce, F. F. (1985). Romans: an introduction and commentary (Vol. 6, p. 226). Downers Grove, IL: InterVarsity Press.

These special abilities or gifts are correctly understood as a measure or “quantity” (1 Cor 7:17; 2 Cor 10:13; not “standard” of faith as if it were Jesus Christ or the gospel; cf., Moo, Romans, 761) of faith possessed by each believer (Schreiner, Romans, 652–53) to serve the Church a concept that is more fully developed in vv 6–8.

Lopez, R. A. (2005). Romans Unlocked Power to Deliver (p. 244). Springfield, MO: 21st Century.

The measure of faith] Cp. Eph. 4:7, where (see ver. 11) the context is similar to this. There, however, the word “grace” is used where “faith” is used here; and “faith” here is not quite easy of explanation. In this Epistle the special aspect of faith (trust in God and His word) as justifying has been consistently in view, rather than its aspect (Heb. 11:1) as laying hold upon invisible realities in general. Here, therefore, it seems best to seek for a reference as consistent as possible with that of the rest of the Epistle, and one also which shall harmonize with the phrase in ver. 6 below; q.v. We explain the present passage then as follows:—“Faith” here means specially acceptance of Christ, revealed as the Propitiation: but that acceptance is also, ipso facto, the entrance on bondservice to God, (see e.g. 6:18:) therefore the gift of faith is here mentioned as involving the idea of the allotment of consequent duties and functions also to the various believers with their various capacities. Faith, in the Divine plan, is the grand qualification for service, (because it is the appointed instrument of reconciliation;) and it is therefore the sphere, so to speak, in which all true service is to be done.
In this view, we may paraphrase the passage before us: “even as God distributed the sovereign gift of faith, (Eph. 2:7, 8,) the gift of the power to ‘believe unto justification,’ to each of you, with a view in each case to the various tasks and services of the life of faith.”

Moule, H. C. G. (1891). The Epistle of Paul the Apostle to the Romans, with Introduction and Notes (pp. 207–208). Cambridge: Cambridge University Press.