If Rick Santorum wins in Michigan on Tuesday but loses Arizona, he may get the better spin out of the evening while winding up with fewer delegates. That is because Arizona is a winner-take-all state whereas Michigan is not.

It’s possible, in fact, that the candidate who wins the popular vote in Michigan will take away fewer delegates from the state. Most of the state’s delegates are appointed based on results at the Congressional district level, so a candidate who dominated in a few Congressional districts while narrowly losing most others would wind up disadvantaged.

If such an outcome occurs — say, Mitt Romney wins the popular vote by 2 percentage points, but Mr. Santorum wins more Congressional districts and more delegates — some analysts will be quick to describe Mr. Santorum as the “real winner” in Michigan, pointing out that the delegate count is what matters in the end.

Although there is some truth in this position, I am reluctant to embrace it fully. The reason is that the G.O.P.’s delegate-selection rules are exceptionally complicated and ambiguous. Many delegates could go to the convention in Tampa either loosely pledged or entirely unbound to any of the candidates.

That means there will be some wiggle room in the math. Doing things like winning key states, leading in the aggregate popular vote, leading in national polls and appearing to have the momentum at the end of the process may influence the behavior of these unbound delegates. If a candidate can make a credible claim to having a mandate from the voters, they might line up behind him. If his claim is poor, they could block his nomination.

There are 2,286 delegates to the Republican National Convention, of which 1,144 are required to clinch a majority. The Web site TheGreenPapers.com, which has extensive information on delegate-selection procedures in each state, divides them into two broad categories, what it calls “hard” and “soft.” Hard delegates are formally bound to a candidate on at least the first ballot at the convention, while soft delegates are not.

Although this is a useful conceptual framework, it probably simplifies things too much. Instead, Republican delegates exist along something of a spectrum between bound and unbound, pledged and unpledged, hard and soft.

Contributing to the confusion is that there are a series of three interrelated ideas about delegates which are often treated as interchangeable, even though they are not:

Bound vs. Unbound Delegates. Is the delegate officially bound to a particular candidate on at least the first ballot at the convention? Pledged vs. Unpledged Delegates. Whether or not she is formally bound to a candidate, will the delegate’s candidate preference be known in advance of the convention and reported upon by the news media? Elected vs. Selected Delegates. Was the delegate selected through some relatively direct means, such as based on the popular vote in the state’s primary? Or through some indirect means, like through the series of conventions that often take place in caucus states, and which may not correspond to the popular vote there?

There are delegates who will go to the convention technically unbound, but who will have pledged their support to a candidate and can probably be counted upon to vote for them. There are delegates who are selected through a complex, multistep caucus process that may bear little resemblance to the popular vote in those states, but who are formally bound to a candidate once that process has taken place.

The following represents an effort to sort the delegates into about a half-dozen categories. One could easily pick more categories or fewer. There are a number of states whose rules are ambiguous enough to qualify as borderline cases, and which could be placed into a different category than the one I have chosen. But this ought to give you some basic sense of how the math works.

Super Delegates

There are 126 delegates, about 6 percent of the total, who are complete free agents. These are party leaders and elected officials, three per state or territory, who will go to the convention unbound to any candidate. Formally, these are known as “automatic delegates”; the more common term is “super delegates.” A few states do bind their super delegates to the winner of the primary or caucus, but most do not.

Even though they are officially unbound, however, some of these delegates will indicate a candidate preference in advance of the convention. Some already have, in fact: 18 have said that they prefer Mitt Romney, while the other candidates have just 5 super delegates among them. However, these preferences are subject to change at any time.

Unbound Delegates Chosen through Party Conventions or Committees

In addition to the super delegates, there are 84 delegates who will be selected at state conventions, or appointed by a committee of Republican officials in the state, with no direct or indirect relationship to the popular vote in these states. States like Pennsylvania, Illinois and Louisiana select some of their delegates trough this method, for instance, even though they also pick some through their primaries.

Like the super delegates, these 84 delegates are officially unbound. However, influential Republicans within each state will have some say about just who they are and about which candidate they are most likely to prefer.

Unbound Delegates Chosen through Caucuses

I distinguish this group of 84 delegates from another, larger group of 188 who are picked through a caucus process but are officially unbound to any candidate. In addition to being unbound, these delegates are usually also picked in a way that is separate from the straw poll or popular vote that is held in each state.

All 28 of Iowa’s delegates, for instance, fall into this category. When the state held its caucuses in January, voters there held a straw poll to indicate their presidential preference; these are the results that were widely reported on in the news media and that eventually showed Rick Santorum winning a small victory. Caucus-goers took a separate vote, however, on which delegates should be appointed to county conventions that the state will hold in March. These county conventions will then pick delegates to district conventions, who will then pick delegates to the state convention, who will in turn appoint delegates to the Republican National Convention.

As confusing as this sounds, this process is fairly typical in most Republican caucus states. There are only a couple of exceptions, like Nevada and Idaho, where delegate selection is directly related to the presidential preference vote at the caucuses.

Although the delegates in this group are officially unbound, most can be expected to be supporters of one of the candidates. Delegates who are known to be favorably disposed toward Ron Paul, for instance, are more likely to be voted for by caucus-goers who like Mr. Paul.

Still, the eventual delegate allocation will not always match the straw poll results in the state. For example, if one candidate’s supporters tend to stick around for the delegate-selection part of the caucus, while the rest take off after casting their straw-poll vote, that candidate could benefit. In Maine, for instance, it looks like Mr. Paul may get the plurality of delegates even though he narrowly lost the state’s straw poll.

Unbound Delegates Chosen through “Loophole” Primaries

Three large states, Illinois, Ohio and Pennsylvania, conduct so-called “loophole” primaries, in which voters at the primary cast one ballot for their presidential preference and another for a slate of delegates who are known to be supporters of one or another candidate. In essence, this mirrors the process in caucus states like Iowa, where there is a beauty contest vote for presidential preference coupled with a separate vote for delegate allocation.

Most of the delegates in these states are chosen at the Congressional district level. Sometimes candidates, like Rick Santorum in three districts in Ohio, may fail to post a full delegate slate in those districts, costing themselves the opportunity to win delegates even if they win the popular vote there.

Even though these delegates will have their names officially associated with one of the candidates on the ballot, they are not legally bound to them and are free to change their minds.

Bound Delegates Chosen through Party Conventions

Every case we have listed so far concerns delegates who are officially unbound on the first ballot at the convention, even though they may be unofficially pledged to a candidate. But not all bound delegates are chosen in the same way.

Nebraska, for instance, chooses its 32 delegates through a party convention. The delegates are not required to match the preferences of voters in the “beauty contest” primary that Nebraska will conduct on May 15. Nebraska’s delegates are bound on the first two ballots at the national convention, however, once the state convention picks them.

Bound Delegates Chosen Through Caucus Process But Not Bound by Popular Vote

Finally, there are two states, Missouri and Washington, that pick their delegates through a multistage caucus process, as Iowa or Maine do. As in Iowa and Maine, these delegates are not bound by the results of the straw poll in each state and are instead chosen through a separate process. However, unlike in Iowa or Maine, these delegates are officially bound at the national convention once they are chosen in this way.

All told, about 25 percent of delegates to the Republican National Convention will be officially unbound, although many of these will be informally pledged to a candidate. Another 5 percent — those in Nebraska, Missouri and Washington — are bound by the time they get to the convention but are chosen in a circuitous way.

That leaves 70 percent of delegates who are both bound and chosen through relatively straightforward means. Even within this group, however, there exists some ambiguity.

Ambiguous Circumstances Among Bound Delegates

First, even if delegates are initially bound by the results of a primary or caucus, they enter a gray area if their candidate subsequently drops out and releases them. So far, this has not been a material issue, although Jon M. Huntsman Jr. won two delegates in New Hampshire. But it could become more pertinent if a candidate like Newt Gingrich, who has more delegates, were later to drop out. State laws differ on how delegates are obliged to behave once this occurs.

Second, there is the possibility of legal or rules challenges to delegate slates. Florida and Arizona, for instance, plan to apportion their delegates on a winner-take-all basis, but this is technically in violation of Republican National Committee rules since their primaries were held prior to April 1. Other states have delegate selection rules that are confusingly written, perhaps making them fodder for legal challenges. Finally, even where the rules are relatively clear, the delegates at the convention have broad latitude to change them if they don’t like the result that they are producing.

Another complication is that all of the delegates are human beings, and human beings can be fickle. A legal complication could arise if a delegate who was officially bound to a candidate decided later on to change his mind. How such a case would be handled is hard to predict; some delegates are bound to a candidate by the rules of the state party, but not by state law.

The substantial amount of ambiguity in delegate selection rules presents both risks and opportunities to the Republican Party. On the one hand, in a case where one candidate had a fairly clear plurality of delegates, but not an outright majority, uncommitted delegates (especially super delegates) could align behind them to give them their majority.

In the scenario outlined below, for instance, Mitt Romney would still be 3 delegates shy of the 1,144 that he needs for a majority after the final state (Utah) holds its primary. However, there are 170 unpledged delegates. Some of them would almost certainly declare their support for Mr. Romney in advance of the convention. This is the scenario that resulted in Walter Mondale’s nomination in 1984, for instance; he did not have quite enough delegates after the last set of primaries, but super delegates put him over the top.

There are also cases, however, in which the substantial number of unpledged delegates could work against the convention’s ability to reach a majority. In the scenario outlined below, for instance, Rick Santorum has a narrow plurality of delegates, but is still 319 votes shy of the number that he would need for a majority, considerably more than the number of unpledged delegates. Such a deadlock would probably require several ballots to resolve.

The most interesting scenario, however, is the case where the unpledged delegates would be sufficient to give a candidate a majority, but his claim to the nomination was somewhat tenuous. Suppose, for instance, that Mr. Romney had 43 percent of the delegates, Mr. Santorum 37 percent, and about 8 percent of delegates had not yet pledged to a candidate. Incidentally, if you assume that the Republican contest will continue to go back-and-forth and make some guesses about how each state will vote, you wind up with a lot of scenarios like this one.

If all of these unpledged delegates aligned themselves with Mr. Romney in this case, he could win on the first ballot. But whether they would do so is an open question.

If Mr. Romney’s plurality lead seemed to be built upon structural advantages in the delegate selection process rather than popular support — say, for instance, that Mr. Romney had the most delegates, but Mr. Santorum was 10 points ahead in national polls at he time — some delegates might conclude that it was not in the best interest of the party to give him a helping hand.

There has not been a case in the recent past when the candidate who was ahead in delegates once the last primaries were held trailed in popular support — even George McGovern led in national polls by the time states like Michigan and California voted in May and June 1972. Such a scenario seems plausible this year, however.

The aesthetics of how a candidate performs could be important in a case like this. If in addition to trailing in national polls, Mr. Romney had lost key states like Michigan and Ohio, it would be harder for him to claim that his nomination reflected the collective will of the Republican electorate. He would have a more credible argument, however, if he had won these primaries, which would add to his other impressive results like in Florida.

In short, the notion that the Republican nomination process is simply a delegate-counting contest is correct on technical grounds, but somewhat misses the forest for the trees. Quite a lot of delegates to the Republican convention may go there unpledged to any candidate, or will have the wherewithal and the legal standing to change their minds. If one candidate holds a lead in the delegate count, but another seems to have the clearest mandate from Republican voters, the delegate math could change quickly.