The Democratic Caucus process in Iowa is complicated and there are just 19 days left until February 1st to understand all the rules. The details are all well documented, but there are a large number of nuances. Microsoft is attempting to streamline the reporting process with a new cloud based reporting app which should hopefully prevent any delays similar to those which occurred in 2012. Microsoft's propaganda video is below and serves as a good introduction to some of the caucusing complexity. Pay attention to the segments where they hand wave around the "math":

To briefly summarize the video, each precinct will report their delegate allocations to a central server, where the results can be validated by each party and then disseminated for public consumption. On February 1st, we'll all be watching delegate allocations rather than raw votes. These delegates will be precinct level delegates who will in time elect county level delegates, then finally their state delegation to the national convention. The Republican Party uses a simpler process where raw votes correlate to delegates, but for the Democrats politicking and math collide. There are three distinct caucuses for the Democrats, but we'll focus on (a), from below, which will elect the vast majority of delegates:

7. Caucus participants will divide according to Presidential Preference.

a. For precinct caucuses, delegates will be apportioned by proportional representation based upon the number of Democratic votes during the most recent presidential and gubernatorial elections. In addition, the caucus participants will divide according to their presidential preference and delegates to be elected by each caucus will be apportioned and elected by presidential preference group. There may be an uncommitted group.

b. The total of satellite caucuses will be apportioned three state convention delegates by the State Central Committee. Each satellite caucus will divide according to presidential preference group, and report their presidential strength to the State Party.

c. The military tele-caucus will be allocated two delegates to state convention.

Source: Iowa Delegate Selection Plan [2]

The delegate allocations for each precinct have likely already been decided and published to each interested campaign. I can't find this data available publicly. The general idea of the delegate proportionment to each precinct is based on a historical metric of Democratic participation and outcomes in that given precinct. The formula for this changes between caucuses so it's not really possible to derive the formula; here is data from 2008 [3] and 2012 [4] in Johnson County Iowa for those curious.

The rules for proportioning delegates in a given precinct is easy and we'll go through some examples shortly. These are the official rules for determining candidacy viability which is often stated as a 15% threshold by the media, but its slightly more complicated:

8. For precinct caucuses, preference groups shall be required to have a minimum number of members within their group in order to be considered viable for the purposes of electing delegates to the county convention. The minimum number of members, or viability threshold, a group must have will be determined by the following factors: the total number of eligible caucus attendees at the particular caucus and the total number of delegates the particular caucus is to elect.

a. No viability threshold shall apply to any caucus that elects only one delegate. The delegate shall be elected by a majority vote of those eligible caucus attendees present and voting.

b. In caucuses that elect two delegates, a group must have at least 25% of the eligible caucus attendees in order to be considered viable.

c. In caucuses that elect three delegates, a group must have at least 16.66 repeating percent. (N.B.: Because of the repeating fraction in this case, the correct method to determine viability should be to divide the total attendees by six (6)).

d. In caucuses that elect four or more delegates, a group must have at least 15% of the eligible caucus attendees in order to be considered viable.

[...]

h. If more viable preference groups form than there are delegates to elect, the smallest groups must realign until there are no more groups than there are delegates to elect.

[...]

k. Due to rounding, it is possible to apportion more or less delegates than the caucus is required to elect. In these cases, a group or groups may gain or lose a delegate depending upon the fractions that result when determining their share of delegates. A group may never lose its only delegate.

Source: Iowa Delegate Selection Plan [2]

The intent of the entire process is to elect delegates from those in attendance. You become a delegate by literally filling out a simple form and saying "I want to be delegate." If there are fewer people who want to be delegates than there are delegates to apportion, then none of these procedures apply. Those who want to become delegates are delegates and that's it.

The rest of this article assumes that there are always enough people to self nominate for the delegate selection rules to apply. I have modeled the entire delegate selection procedure and can generate all possible group permutations if given the number of delegates to allocate and the number of supporters for a given candidate. I've chosen a few examples below to illustrate some of the peculiarities.

Let's start with a simple example of a precinct with 3 delegates. We'll assume that just 19 voters showed up to participate, and of those, lets say 10 people support Bernie Sanders and the remaining 9, another candidate. The table below illustrates all possible permutations of the different sub-caucus sizes. The table is presented from Sanders' perspective where positive numbers denote a positive outcome for Bernie:

There are four possible group permutations, and Bernie will end up wining 3 of the 5 delegates in three of the permutations. What the table doesn't illustrate is the multiple phases of sub-caucus selection. The viability threshold prescribed in 8(c) is 4 people; 19/6 rounds up to 4. This threshold would permit the creation of four groups; these are the possibilities {4, 5, 5, 5}, {4,4,5,6} and {4,4,4,7}. If four groups formed, the smallest groups would be required to dissolve and re-associate with another group per 8(k).

From Bernie's perspective, the ideal starting group size is {5,5}; this grouping ensures the most positive outcome while rendering the size of the other groups moot. The group selection of {5,5} is an offensive tactic that ensures an outcome above that which would be expected based on his local popular support. He had 10 of 19 supporters, just over 52%, while he would win 60% of the delegates.

Let's take a look at a bigger precinct with less ideal choices. Let's use averages from the 2008 Democratic Caucus in Johnson County; each precinct averaged exactly 6 delegates and slightly over 54 participants. Lets then assume Bernie has 26 supporters, which is about 48%. There are 48 possible permutations and all but three result in Bernie acquiring 3 delegates. The table below illustrates these three groupings:

Before we talk about grouping tactics, I want to explain why there are fractional delegates above. In two instances there are 3 groups (of either 13 or 14), but four delegates to apportion. In this case the tie-breaker is unclear; the tie may be broken by the gender of the delegate to create balance, but I suspect that in this instance the candidate with greater overall support may be given the benefit. In any case, Sanders' would be best off choosing group sizes which are not {13,13} or {12,14}.

Finally I used the model I created for the delegate selection process to create an optimized strategy for acquiring delegates based on some of the tactics covered above. The graph below depicts this optimization (the green line) and is derived against the 2008 delegate allotments from Johnson County:

My methodology was simple; I iterated through each precinct and calculated the permutations at each level of public support in increments of 1%. This increment creates some deviation with rounding; as an example, if there are 50 participants and a given candidate has 35%, the derived supports gets rounded from 17.5 to 18, which is an additional 1% increase. This deviation is largely rendered irrelevant when comparing the average to the optimization because both calculations use the same rounded input. The optimization ranks all the permutations by the delegates apportioned and averages the top 25%; the top 25% generally present feasible groups.

The optimization is greatest, with a 4.91% increase over the average, at the 49% support threshold. The other peaks then emanate from 49% in increments of 15% which correlates to the viability threshold for precincts with 4 or more delegates.

The current margin in Iowa based on our polling model is 6.48%, so optimizing delegate allocations could make a very real difference.