After the sprint of twenty-four contests in fifteen days, this week’s four primaries represents a slowing of the pace.  After the March 17 contests, there will be only seven contests over the next three weeks concluding with the Wisconsin primary before there is a three-week break between Wisconsin and the Mid-Atlantic primary on April 28.  (EDIT:  Now six contests, with Georgia’s primary being postponed until May.)

In the last two weeks, in the states that vote by mail, we have seen the early results showing significant number of votes for candidates that are no longer in the race.  As counting has continued, however, the later arriving ballots have swung away from the candidates who have suspended their campaigns and toward Senator Sanders and Vice-President Biden.  There will have been some early voting in the states that are voting on March 17.  As such, the initial release of numbers will probably include some votes for these candidates, but that number should decline over the evening as election day returns are added in.

With the narrowing of the field, delegate math is now a state-by-state struggle.  And this state-by-state battle is different for the Democratic primaries than it is on the Republican side.  The media likes to focus on who wins a state.  And, in the general election (and in many states on the Republican side), the winner-take-all rule makes winning a state very important.  On the Democratic side, the proportional allocation of delegates means that it matters more whether somebody wins a state by a large margin than who wins the state.  As we have seen over the past seven days, a narrow in by Vice-President Biden is currently netting him around seven delegates in a large state, but his big win in Mississippi (less than half the size of Washington) is netting him over thirty delegates.

The four states on March 17 are Arizona, Florida, Illinois, and Ohio.   These four states have a combined seventy congressional districts (nine in Arizona, twenty-seven in Florida, eighteen in Illinois, and sixteen in Ohio) with between three and nine delegates each.

The three delegate districts are Arizona 3, Florida 1, Florida 25, Illinois 15, and Ohio 6,   The four delegate districts are Arizona 7, Florida 2, Florida 11, Florida 17, Illinois 16, Illinois 18, Ohio 4, Ohio 7, and Ohio 8,  The five delegate districts are Arizona 1, Arizona 3, Arizona 5, Arizona 6, Arizona 8, Florida 3, Florida 5, Florida 6, Florida 8, Florida 12, Florida 15, Florida 18, Florida 19, Florida 26, Florida 27, Illinois 4, Illinois 8, Illinois 10, Illinois 11, Illinois 12, Illinois 13, Illinois 14, Illinois 17, Ohio 2, and Ohio 5.   The six delegate districts are Arizona 2, Arizona 9, Florida 4, Florida 7, Florida 9, Florida 10, Florida 13, Florida 14, Florida 16, Florida 23, Florida 24, Illinois 3, Illinois 6, Ohio 1, Ohio 9, Ohio 10, Ohio 12, Ohio 13, Ohio 14, Ohio 15, and Ohio 16.   The seven delegate districts are Florida 20, Florida 21, Florida 22, Illinois 2, Illinois 5, and Ohio 3.  The eight delegate districts are Illinois 1, Illinois 7, and Illinois 9.  The nine delegate district is Ohio 11.

Arizona has nine party-leader delegates and fourteen at-large delegates.   Florida has twenty-nine party-leader delegates and forty-seven at-large delegates.  Illinois has twenty party-leader delegates and thirty-four at-large delegates.  Ohio has eighteen party-leader delegates and twenty-nine delegates.

With the field having narrowed, one key facet of delegate math with two viable candidates is how the math plays out in pools with an odd-number of delegates.  In those pools, a plurality of the vote guarantees a net gain of at least one delegate.  Thus, if one candidate won all of these pools, that would be a net gain of forty-two delegates.  Of course, in a state with a close contest, it is unlikely that the same candidate will win all of the close districts.  And, if a third candidate did become viable, that candidate would gain that “odd” delegate and the “even” districts would effectively become the “odd” districts.   (For the math below, I am assuming two viable candidates.  Representative Gabbard has, generally, not been competitive in the continental states.  If she were to achieve viability in any district, that would push up the below percentages slightly.)

For the three-delegate pools (Arizona 3, Florida 1, Florida 25, Illinois 15, and Ohio 6), the math is quite simple.  With two viable candidates, the winning candidate will get two delegates, and the other candidate will get one delegate.

For the four-delegate pools (Arizona 7, Florida 2, Florida 11, Florida 17, Illinois 16, Illinois 18, Ohio 4, Ohio 7, and Ohio 8), the key number is 37.5%.  If both candidates are over 37.5% of the “qualified” vote (the vote for the viable candidates), then they each get two delegates.  If the spread is greater than 62.5%-37.5%, the winning candidate gets three delegates, and the other candidate gets one delegate.

For the five-delegate pools (Arizona 1, Arizona 3, Arizona 5, Arizona 6, Arizona 8, Florida 3, Florida 5, Florida 6, Florida 8, Florida 12, Florida 15, Florida 18, Florida 19, Florida 26, Florida 27, Illinois 4, Illinois 8, Illinois 10, Illinois 11, Illinois 12, Illinois 13, Illinois 14, Illinois 17, Ohio 2, and Ohio 5), the breaks are on the odd tens.  It takes 30% of the qualified vote to get two delegates.  It takes 50% of the qualified vote to get three delegates.  Finally, it takes 70% of the qualified vote to get four delegates.

For the six-delegate pools (Arizona 2, Arizona 9, Florida 4, Florida 7, Florida 9, Florida 10, Florida 13, Florida 14, Florida 16, Florida 23, Florida 24, Illinois 3, Illinois 6, Ohio 1, Ohio 9, Ohio 10, Ohio 12, Ohio 13, Ohio 14, Ohio 15, and Ohio 16), it will take 25% of the qualified vote to get two delegates;  It will take 41.67% for a candidate to get three delegates.  It will take 58.34% for a candidate to receive four delegates.  Finally, it will take 75% for candidate to get five delegates.

For the seven-delegate pools (Florida 20, Florida 21, Florida 22, Illinois 2, Illinois 5, and Ohio 3), it will take approximately 21.5% to get a second delegate.  To get three delegates, it will take 35.8%.  A candidate with 50% of the qualified vote will get four delegates.  It will take 64.3% to win five delegates.  Finally, a candidate with 78.6% will get six delegates.

For the eight-delegate pools  (Illinois 1, Illinois 7, and Illinois 9), a candidate needs 18.75% to get a second delegate.  A candidate needs 31.25% to get three delegates.  A candidate who gets 43.75% will win four delegates.  A candidate will win five delegates if he gets 56.25% of the qualified vote.   A candidate needs 68.75% to get six delegates.  A candidate will get seven delegates in he has at least 81.25% of the qualified vote.

For the nine-delegate pools (Ohio 11 and Arizona party-leader delegates), it takes 16.7% of the vote for a candidate to win a second delegate.  A candidate will get three delegates with 28.8% of the qualified vote.  To get four delegates, a candidate needs 38.9%.  For five delegates, a candidate needs 50% of the qualified vote.  A candidate needs 61.2% of the vote to get six delegates.  A candidate will win seven delegates with 71.3% of the vote.   It is possible to get eight delegates with 83.4% of the qualified vote.  However, because it takes 15% of the total vote to be viable, unless there is almost no vote for non-viable candidates, it is unlikely that a candidate who is viable will fail to win a second delegate.

For Arizona’s fourteen at-large delegates, each delegate is worth around 7.2% of the vote.  That means that any viable candidate will win at least two delegates.  It will take 17.9% to get a third delegate.  To get four delegates, a candidate will need 25% of the vote.  A candidate will get a fifth delegate with 32.2% of the vote.  A candidate will need 39.2% to get a sixth delegate.  With 46.5% of the vote, a candidate will get seven delegates.  A candidate will get eight delegates upon reaching 53.6%.  A candidate needs 60.8% to get a  ninth delegate.  If a candidate gets 67.9%, they will win ten delegates.  It takes 75% to with an eleventh delegate.  Finally, a candidate needs 82.2% to get twelve delegates.

For Ohio’s eighteen party-leader delegates, each delegate is worth approximately 5.56%.  That means that each viable candidate is guaranteed to get at least 3 delegates.  To get four delegates, a candidate needs 19.5%.  From that point, each additional 5.56% would equal an additional delegate.   Thus, 25% will get a candidate five delegates.  A candidate will get six delegates with 30.6% of the qualified vote.  It will take 36.2% to get seven delegates.  If a candidate gets 41.7% of the vote, they will get eight delegates.  It will take 47.3% to win nine delegates.  At 52.8%, a candidate is assured of ten delegates.  A candidate will get eleven delegates with 58.4% of the vote.  For twelve delegates, a candidate needs 63.9% of the qualified vote.  At 69.5% of the qualified vote, a candidate will get thirteen delegates.  A candidate gets fourteen delegates at 75%.  Finally, at 80.6%, a candidate will win fifteen delegates.  It is not possible for a candidate to get just sixteen or just seventeen delegates.

For Illinois’s twenty party leader delegates, the math is very simple.  Each delegate is worth 5%.  Thus, the key numbers where candidates gain an additional delegate are 2.5% and 7.5%  For example, a candidate with 27.49% wins five delegates, and a candidate with 27.51% wins six delegates.  Every viable candidate will get at least three delegates.

For the twenty-nine delegate pools (Ohio at-large delegates and Florida party-leader delegates), each delegate is worth approximately 3.45%.  Each viable candidate will win at least four (and probably five) delegates.  To win five delegates, a candidate needs 15.6% of the qualified vote.  (It takes around 3-4% of the vote going to non-viable candidates to bump 15% of the total vote up to 15.6% of the qualified vote.  Thus, there is a very narrow window in a viable candidate only gets four delegates.)  At 19.0%, a candidate will get six delegates.  From there, every 3.45% of the qualified vote will equal one additional delegate.

For Illinois’s thirty-four at-large delegates, each delegate is worth approximately 2.94%.  Each viable candidate will win at least five delegates.  To get six delegates, a candidate needs 16.18% of the qualified vote.  (it would take around 7.3% of the vote going to non-viable candidates to bump 15% of the total vote up to 16.18% of the qualified vote. Realistically, the runner-up in Illinois is going to have a lot more than 15% of the total vote.)  From there it will take around 19.12% to get seven delegates followed by an additional 2.94% for each additional delegate.

Finally, there are Florida’s forty-seven at-large delegates.  Each delegate is worth about 2.13% of the vote.  Thus, any viable candidate will get at-least seven delegates.    To get eight delegates requires 15.96% of the qualified vote.  (Again, if approximately 6.02% of the vote goes to non-viable candidates, that would be enough that any viable candidate would have 15.96% or more of the qualified vote.)  To get nine delegates requires approximately 18.09% of the qualified vote.  And for every 2.13% of the qualified vote above 18.09%, a candidate gets one more delegate.

As we have seen earlier this month, the logic of delegate math can bring an end to a once hopeful campaign.  However, the last two contested cycles on the Democratic side have seen the second-placed candidate continue to the end even though the odds of catching up were very long.  It remains to be seen how the rest of this campaign will play out.