Super Tuesday is always a hard day for delegate math.  There are fifteen contests ranging from a territorial caucus in American Samoa (which given the time gaps will actually be taking while it is still Monday in most of the United States) to the massive primary in California in which a final count will not be available for several weeks.  Every candidate still running (and this post is going live while we are still waiting for the results in South Carolina) can point to some contest in which they might win delegates.  Super Tuesday is also the day on which we will see if Mayor Michael Bloomberg’s strategy of skipping the early caucuses and primaries worked.

As with the first four states in the “early” window,  these contests are complicated by the number of candidates running.  While the states differ from each other, in all of them, there is the question of how many candidates will reach the 15% threshold (either state-wide) or in a single district.  In Iowa (with the exception of the Second District in which only three candidates won delegates) every district and the state-wide results had four candidates break 15%.  In New Hampshire, in every district and state-wide, three candidates broke 15%.  In Nevada, one district had three viable candidates but the other districts and the state-wide results had only two viable candidates .  It seems likely that — in at least some districts and states — three or more candidates will reach that 15% threshold.  And multiple candidates reaching 15% will cause weird fractional issues.  Additionally, the possibility of some candidates getting between 10-13% could allow the viable candidates to gain more delegates than the minimum numbers discussed below.

Trying to do things chronologically, the first four contests to end (not necessarily the first four contests to report the results) are American Samoa, North Carolina, Virginia, and Vermont.  All of these contests close by 7:30 p.m. EST.  Part 2 will deal with the contests that close at 8 p.m. EST/7 p.m. CST,   Part 3 will deal with the states that close after 8 p.m. EST (excluding Texas and California).  Part 4 will deal with Texas and California.

American Samoa is the simplest of the four in today’s post.  It has a territorial caucus/convention that will elect six “at-large” delegates.  There are no district-level delegates or pledged delegates to consider.

Vermont is only a little bit more complicated.  As a single district state, there is no separate result from each congressional district to consider.  Instead, all three pools of delegates are allocated based on the state-wide result.  But there are still three separate pools to allocate — 11 “district” delegates; 2 party leader delegates; and three at-large delegates.  While, as the home state candidate, Senator Sanders will be expected to do well in Vermont, the main issue will be how many candidates reach 15%.  In 2016, Senator Sanders got the 85% needed to take all of the delegates.  If one other candidate reaches 15%, that candidate will take the other party leader delegate and one of the at-large delegates.  If two other candidates reach 15%, the second placed candidate gets the second party  leader delegate and each candidate gets one at-large delegate.

North Carolina and Virginia, however, have multiple districts.   Virginia has eleven districts and North Carolina has thirteen districts.  Those two states have more delegates combined than were awarded in the four early states.  The districts in these two states range from three delegates to nine delegates.  North Carolina has fourteen party leader and twenty-four at-large delegates.  Virginia has thirteen party leader delegates and twenty-one at-large delegates.

Going by district,  North Carolina’s Fifth and Thirteenth have three delegates each.  North Carolina’s Third and Tenth and Virginia’s Ninth have four delegates each.  North Carolina’s Seventh, Eighth, Ninth, and Eleventh and Virginia’s Second and Sixth have five delegates each.  North Carolina’s First and Virginia’s First, Fourth, Fifth, Seventh, and Tenth have six delegates each.  North Carolina’s Sixth and Virginia’s Third, Eighth, and Eleventh have seven delegates each.  North Carolina’s Second and Twelfth have eight delegates each. Finally, North Carolina’s Fourth has nine delegates.  (This wide variation says something about gerrymandering as delegates are allocated based on past Democratic performance.  The “average” non-gerrymandered district should have five or six district level delegates.)

As noted above, for Vermont’s two party-leader delegates, assuming that two or more candidates are viable, the top two candidates each get one delegate.  For Vermont’s at-large delegates and the district delegates from North Carolina’s Fifth and Thirteenth, if three or more candidates are viable, the top three candidates get one delegate each.  If only two are viable, the winner gets two delegates and the other viable candidate gets one delegate.  If only one candidate is viable, that candidate gets all three.

For the four-delegate districts (NC-3, NC-10, and VA-9), there is a chance that four or more candidates will get 15%.  If that happens, the top four candidates get 1 delegate each.  In turn, that means that a candidate needs to get 55% to assure two delegates, 70% to assure three delegates, and 85% to sweep.

For the five-delegate districts (NC-7, NC-8, NC-9, NC-11, VA-2, VA 6), again there is the chance of five candidates being viable which would mean that everyone would get one delegate.  Thus, it will take 40% to guarantee two delegates, 55% to guarantee three delegates, 70% to guarantee four delegates, and 85% to get all five.

For the six -delegate district (NC-1, VA-1, VA-4, VA-5, VA-7, VA-10, American Samoa), again there is the chance that six candidates are viable which would mean that each candidate gets one delegate.  To assure a second delegate, a candidate would need more than 27.5% of the vote.  A candidate will need 42% to get a third delegate.  A candidate will need approximately 60% to get 4 delegates.  It will take 75% to be certain of five delegates.  Finally, any candidate who tops 85% will get all six delegates.

For the seven-delegate districts (NC-6, VA-3, VA-8, VA-11), at most six candidates can be viable, so whomever finishes first will get two delegates (even if first is only 20%).  Additionally, because each delegate is worth about 14.3% of the vote, each whole delegate eliminates a viable candidate.  Of course, there is still the complicating factor of multiple high fractions.  My best guess is that 35% will guarantee a third delegate (a 3-2-1-1 split with four viable and either 3-3-1 or 3-2-2 with three viable candidates).   Given that 15% is slightly more than one delegate, a candidate who gets to 50% should get the fourth delegates.  In turn, 64.3% should get five delegates; 78.6% should get 6 delegates, and 85% gets all delegates.

For the eight-delegate districts (NC-2, NC-12), again, only six candidates can reach 15% and that is slightly higher that one delegate.  It will take 21.5% to assure a second delegate (by assuring a top four finish and that — if fourth — no more than four candidates qualified for delegates.)  (Practically, the number will be  a little bit less as the odds of four candidates finishing within a handful of votes of tied for first is highly unlikely.)  A candidate with 34% should get three delegates.  A candidate with 44% should get four delegates.  A candidate with 59% should get five delegates.  A candidate with 69% should get six delegates.  Finally, 81.5% will get seven delegates and 85% will get all eight delegates.

For the nine-delegate district (NC-14), at most six candidates will be viable which is about 1.3 delegates.  It will take about 20% to assure a second delegate (a top four finish with only five viable candidates).  It will take about 28.5% to assure a third delegate.  It will take around 41% to get a fourth delegate.  It will take around 53% to assure a fifth delegate.  It will take around 63% to assure a sixth delegate.  It will take around 73% to assure a seventh delegate.  It will take 83.3% to get eight delegates (with 85% getting all nine delegates).  So it is theoretically possible for a candidate to get eight delegates from this district, but highly unlikely.

For Vermont’s eleven district delegates, it is almost certain that every candidate who reaches 15% will get at least two delegates.  It is possible that six candidates could reach 15% in which case the sixth-placed candidate would only get one delegate while the other five would get two each.  To get to three delegates, a candidate will need 25%.  To get to four delegates, a candidate will need 34%.  To get five delegates, a candidate will need 43%.  A candidate with 53% will get six delegates.  A candidate with 62% will get seven delegates.  A candidate with 70% will get eight delegates.  A candidate with 77% will get nine delegates.  It is not possible for a candidate to get ten delegates.  A candidate with 85% or more will get eleven delegates.

For Virginia’s thirteen party leader delegates, the formula works out to 1 delegate for every 7.7%  With a maximum of 6 candidates being viable, any candidate who is viable should get 2 delegates each.  A candidate with 21.3% should get a third delegate.   A candidate with 28% should get a fourth delegate.  A candidate with 36% should get five delegates.  A candidate with 43% should get six delegates.  A candidate with 50% should get seven delegates.  A candidate with 58% should get eight delegates.  A candidate with 67% should get nine delegates.   A candidate with 74% should get ten delegates.  A candidate with 81 percent should get eleven delegates.  It is not possible for a candidate to get twelve delegates.  A candidate with 85% or more will get all thirteen delegates.

For North Carolina’s fourteen party leader delegates, the formula works out to 1 delegate for every 7.15%.  With a maximum of six viable candidates, every candidate who is viable will get at least two delegates.  A candidate who gets 20% will get at least three delegates.  A candidate who gets 27% will get at least four delegates.  A candidate who gets 34% will get at least five delegates.  A candidate who gets 41% will get at least six delegates.  A candidate who gets 48% should get seven delegates.  A candidate who gets 55% should get at least 8 delegates.  A candidate who gets 62% should get at least nine delegates.  A candidate who gets 68% should get at least ten delegates.  A candidate who gets 75% should get at least eleven delegates.  A candidate who gets 83% should get at least twelve delegates.  It is not possible for  a candidate to get thirteen delegates.  A candidate with 85% or more will get all fourteen delegates.

For the last two pools, the key numbers to remember are 4.8% for Virginia’s at-large delegates and 4.2% for North Carolina’s at-large delegates.  Again, any candidate who reaches the 15% viability threshold in either state will win multiple delegates (three in Virginia and probably four in North Carolina).  At this point, with the possibility that these states could have four or more viable candidates, the exact break for each delegate bump-up is difficult to calculate.  My rough rule of thumb would be to start with 3.0% as the major fraction that should get an extra delegate and work every whole delegate from there (e.g., four delegates in North Carolina is like at 15.6%), but the possibility for weird math remains when dealing with fractional delegates for more than two candidates.

Before leaving this part, one explanation of the above math.  There are two calculations used for delegate allocation.  The first calculation is the raw vote — a candidate needs 15% in the raw vote.  The second is the qualified vote (the total vote for all candidates who are viable).  In the qualified vote, the vote for candidates who are not viable is excluded.  Delegates are allocated proportionately based on the qualified vote.  When we are down to two candidates, the qualified vote will probably exceed 90% of the total vote.  In New Hampshire, the qualified vote was only 70% of the qualified vote.  For the leading candidates, it is nice if you have a lot of candidates getting around 10% of the vote.  If the qualified vote is 70% then a candidate who gets over 35% of the raw vote can get the majority of the delegates.  If you are a leading candidate, your fear if candidates getting 16% or 17% of the vote because the vote for those candidates is part of the qualified vote dragging your delegate count down.

To calculate delegates in a multi-candidate field, I have had to magically assume that a candidate is either at 15% (and thus gets delegates) or at 0% (so that only the viable candidates are getting votes).  The breaks occur when the candidate is assured of having a higher fractional remainder than all remaining viable candidates to allow that candidate to round-up.  Effectively, the calculation is based on the qualified vote with the caveat that all viable candidates get at least one delegate (so, at least at the district level, part of the calculation is what raw vote is needed to reduce the number of viable candidate and free up a delegate to the leading candidates).

While these are the first states to close, there is, of course, no guarantee that these are the states that will get their returns in quickly.  All three states are primary states and closing time is just when a voter has to be in line.  In some locations, the line might be very long such that the last vote might not be cast for thirty or sixty minutes.  And then those ballot boxes need to be transferred to the local counting center.  When we will have enough votes from these states to get a good handle on the delegate allocation is an open question.  And some of the states in the next part may have something resembling final results a lot sooner than these states.  (Additionally, while American Samoa should have final results before any of the polls close in any of the states voting on Super Tuesday, those results may not be widely reported.  It might take a day or two before any local news reports from the territory about the caucus results are picked up by the AP or any major media outlet.)

The big thing about Super Tuesday is that we are going to fast move from the question of whom is doing well to the question of what is the delegate count.  Every candidate would like to win several states.  If one candidate can win ten or more of the states that candidate would have a significant boost going forward even if some of those victories are narrow.  But if you have three or more candidates winning multiple states, then the picture on March 4 is going to be very murky.  And if there is no clear front runner, delegate count will become very crucial.  And as 2008 showed, the candidate that is prepared for what comes after Super Tuesday could gain control of the race for delegates and never look back.