Equality of Opportunity is the Central Principle of Distributive Justice

I understand that I am supposed to be arguing the opposite from Will's position. This is in some sense impossible, because Will is a sophist who refuses to acknowledge his sophistry, and who therefore claims to embrace propositions that he in fact rejects. In the present case, Will might say that he agrees with the proposition if only you grant him his favored interpretation of “equal,” “opportunity,” “distribution,” and “justice.” And then we shall be astonished to see the Sun rising in the West.
That said, we do need to interpret these terms. What does it mean for opportunities to be equal?
Our interest in equality of opportunity rests on a shared moral intuition of general opportunities that must be open to us in order to have the prospects of a good and meaningul life. We don't mean equality of opportunity to join in ecstatic union with Jessica Alba. But we might mean equality of opportunity to join in ecstatic union with someone or other. In my way of thinking, the opportunities with moral weight are opportunities to realize basic human capacities, potentialities, or “capabilities.” This is an approach associated with Amartya Sen and Martha Nussbaum.
Before I say more, let me say that on most days I agree with Will that equality of opportunity to compete for the nth position in the income distribution is incoherent. It makes no more sense than does equality of opportunity to compete for a starting position on the US men's Olympic team. We all begin with different potentialities which are a function of our genetic endowments. Simply in virtue of my lineage I never had an opportunity to be competitive in basketball at a high level. No matter how many resources had been devoted to the development of my basketball capacities, my relative position in the distribution of basketball skill would never rise much above average. The Olympic team is reserved for people at a certain exalted level in the distribution of skill. And that level is closed to me due to the constraints of my physical constitution. There are opportunities that we do not have in virtue of what we are, and they cannot be equalized.
Likewise, the nth position in the income distribution might be closed to me due to irremediable aspects of the physical order. It therefore makes no sense to worry about equal opportunity to achieve the nth position. What makes sense is equal opportunity to develop the capacities that in large part account for your position. If the best I could do, if my capacities are fully realized, is position n-1,000,000, then that's the best I can do. This gets us close to our principle of equal opportunity.
To be precise and convincing, however, it is necessary to point out that it remains highly miseading to speak of competition for positions along various dimensions, especially the dimension of income. For our position in the income distribution is not much up to us. It is largely a function of demand in the labor market. (It is partly up to us insofar as our choices take the labor market into account. The choice between lawyer and professor is a choice, among other things, between different likely ranges of future income. Professors who complain that they do not make as much as lawyers are not complaining about their access to higher incomes–they could have been lawyers, but chose not to be. They are complaining about the tradeoffs defined by the interaction of their preferences and demand in the labor market.) In a society with our contingent history, in which Naismith happened to invent basketball, there exists a labor market which rewards some individuals who in every other possible labor market in which basketball did not exist would lack the capacity to reach the median position. That is to say, an individual's top possible position relative to their capacities can vary by orders of magnitude based on a single other individual's discoveries, inventions, or initiatives. This complicates matters a great deal. My relative position given ideally realized capacities may be a matter of whether others do or do not realize theirs, or a matter of the degree to which they do.
The interdepence of the utility of capacities pushes us to recognize the primacy of the most general and necessary capacities. I will not make a list here. But I have in mind those capacities the development of which is necessary to effectively pursue one's good, whatever that may be. Call these primary capacities.
We edge closer. We must all have the equal opportunity to realize our primary capacities. But realize to what extent? I think that the differential realization of capacities is not something subject to institutional manipulation. I don't think we can provide equal opportunity to maximally realize our capacities. The attempt to do so would hurt more than help, so we should be content with realization that is adequate. Adequate to what end? Adequate to enable each person to be a full participant in productive cooperation and to achieve their reasonable, meaningful ends.
So, here's our principle:

A just society will distribute opportunities so that each person has an equal opportunity to adequately realize their primary capacities.

Our society manifestly fails this principle. Now, my problem was not to lay out a set of policies that I believe will rectify this failure. Let me just say something brief about how we would justify the reallocation of wealth in order to ensure that our society satisfies the principle of equal opportunity.
As I mentioned earlier, the utility of capacities is radically interdependent. The economic value of one person's realized capacities may be a function of the realization of other person's capacities. Now, in a generally cooperative context, the development of one person's capacities enhances the asbolute value (but not necessarily the relative value) of other persons' capacities. Which is just to say, a person's realized capacities generally produces positive externalities. Whether they do in a specific case is a question of how a person's capacities are are expressed through their agency. But in a cooperative context, the incentives will create a general tendency for people to choose to express their capacities in productive ways.
Now, people who either would be participants, or would be more productive participants, in the network of cooperation if only their capacities were adequately realized, represent lost value to the network of cooperation. The realization of this pool of capacities is a classic public good. We would each be better off if they were realized, but we will individually underinvest in them. If there is an amount that we could reallocate to the development of primary capacities that is smaller than the value that would thereby be created by the productive expression of those capacities in the cooperative network, then we should reallocate it. Because the value of these adequately realized capacities is likely very high, we should be willing to reallocate a very large amount to the task. A subsidy that will produce benefits greater than the cost of the subsidy is smart and just, especially if the subsidy is funded, and its benefits are distributed, in a fair way, such that each person can see herself as a winner in the overall transaction.
In order to establish that equality of opportunity as I have characterized it is the central principle of distributive justice, I would need to say more about why a number of other principles are not. But I think I have said enough to indicate why I might think that equality of actual material holdings, or equality of opportunity to positions in the wealth distribution, or mere formal equality as citizens with regard to the laws, are unattractive alternatives.
I have gone on too long. I'm not comfortable in this format. However, I may be willing to address questions in the comments if they are well-framed, and politely addressed. And, since I've framed an argument that is designed to be appealing to Will, I wonder what he thinks is wrong with it, if anything. Perhaps some readers will wish to conjecture.