(Bumped in honor of today's primary in Mississippi...because after today, Hillary Clinton's delegate math is just going to get tougher.)

We've all heard how tough Hillary Clinton's delegate math is.

For starters, in order to hit a majority of pledged delegates, she'll need to win 65% of the remaining delegates -- and she's only won more than 65% in one state, Arkansas. Even if you assume Michigan and Florida come up with an acceptable plan for a binding primary or caucus, she still must win 60% of the remaining delegates, a threshold she has only crossed three times -- in Arkanasas, Oklahoma, and Rhode Island.

But what if we change the goal posts and say that Hillary Clinton merely needs to "come close" to Barack Obama? The numbers must get much easier, right?

Well, you can say the numbers are easier -- anything is easier than the impossible. But there's not as much difference as you might think.

It's enough to make you wonder why she thinks she still has a path to victory -- and how far she'll go to accomplish her goal.

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I've divided this blog entry into two parts.

First, I answer the question: what percentage of the remaining pledged delegates will Clinton have to win to hit each of four possible goals: having bare majority; being within 50 pledged delegates; within 100 pledged delegates; and within 150 pledged delegates.

The answer to this question reveals how steep of a hill Clinton must climb in the final few primaries and causues.

Second, I answer the question: for each of these possible goals, what percentage of the uncommitted superdelegates must she win in order to get the nomination.

Thus, it's a two-tiered challenge that Hillary Clinton faces -- first she must win as many pledged delegates as possible, and second she must convince superdelegates to support her, even if that means overturning the results of primaries and caucuses.

It turns out that no matter how you slice, it both challenges look to be incredibly tough.

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Pledged delegates

Let's accept for a moment the concept that "closely trailing" actually means "essentially tied." (It doesn't, but we can fight that battle at another time.)

We'll look at the scenarios for whether or not Michigan and Florida are seated. (It turns out that it doesn't make much difference.)

First, numbers assuming that Michigan and Florida are NOT seated:

+ to gain a majority over Barack Obama, Clinton must win 65% of the remaining delegates. (She has done this once, in AR.)
+ to trail Barack Obama by 50 delegates, Clinton must win 59% of the remaining delegates. (She has done this 5 times in AR, OK, RI, NY, and MA.)
+ to trail Barack Obama by 100 delegates, Clinton must win 55% of the remaining delegates. (She has done this 8 times , adding TN, AZ, and NJ to the above list.)
+ to trail Barack Obama by 150 delegates, Clinton must win 51% of the remaining delegates. (She has done this 12 times, adding CA, NM, OH, and TX to the above list.)

By far the most likely scenario of these four is a 150 delegate spread. A 100 delegate spread is plausible, but very unlikely. Anything closer than 100 delegates is virtually impossible unless Obama completely collapses, and he shows no signs of doing that.

Okay, now let's include Florida and Michigan.

+ to gain a majority over Barack Obama, Clinton must win 60% of the remaining delegates. (She has done this 3 times, in AR, OK, and RI.)
+ to trail Barack Obama by 50 delegates, Clinton must win 56% of the remaining delegates. (She has done this 6 times, adding NY, MA, and TN to the above list.)
+ to trail Barack Obama by 100 delegates, Clinton must win 53% of the remaining delegates. (She has done this 11 times, adding AZ, NJ, CA, NM, and OH to the above list.)
+ to trail Barack Obama by 150 delegates, Clinton must win 50% of the remaining delegates. (She has done this 13 times, adding TX and MO to the above list.)

Assuming we include Florida and Michigan (which I think is likely), she'll have a better chance to get close to the 100 delegate spread, but even that would require a major shift in the campaign. Everything went right for her in Ohio and she barely got more than 53% of the delegates there; to expect her to do better than 53% overall down the stretch is just not realistic.

So still, the most realistic scenario is something closer to 150 delegates.

But let's see what would happen if she did do better than that in the next phase of winning the nomination: closing the deal with the superdelegates.

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Superdelegates

Currently according to politico.com, Obama has 206 "committed" super delegates and Clinton has 247, giving Clinton 54% of all "committed" superdelegates. I put committed in quotes because of course by their very definition, supers are never really committed, but for the sake of this analysis, I will assume that neither total changes.

Let's first look at the numbers if Florida and Michigan are not included.

+ If Clinton ends up with bare majority of pledged delegates, she would need 52% of the uncommitted superdelegates
+ If Clinton ends up trailing by 50, she would need 55% (more than the 54% of the already committed delegates she now has).
+ If Clinton ends up trailing by 100, she would need 63%
+ If Clinton ends up trailing by 150, she would need 70%

It is highly improbable that Clinton would be able to convince 63% of superdelegates to overturn the results of primaries and caucuses if she trailed by 100 pledged delegates -- and as I showed above, it is highly improbable that Clinton could get to within 100 pledged delegates.

You can do the math -- she's not winning under this scenario.

Let's take a look at what things would be like with Florida and Michigan included. One of the interesting things about including these two states is that it will increase the total number of superdelegates by 54. This seems to benefit Clinton much more than Obama as Clinton has significantly more support from Florida and Michigan superdelegates than does Obama. According to Democratic Convention Watch, Clinton would gain 15 superdelegates and Obama 5. That leaves 34 uncommitted.

+ If Clinton ends up with bare majority of pledged delegates, she would need 50% of the uncommitted superdelegates
+ If Clinton ends up trailing by 50, she would need 53%.
+ If Clinton ends up trailing by 100, she would need 60%.
+ If Clinton ends up trailing by 150, she would need 67%.

Once again, I've shown above it's almost certain that Clinton will not get within 100 delegates, even if we include Michigan and Florida. If she could get the gap down to 50 -- which would be nearly impossible -- she might be able to convince the superdelegates to overturn the results of primaries and caucuses, but even that is questionable.

Certainly at a spread of 100 delegates, especially after changing the process to include Michigan and Florida, I don't see Clinton being able to win over 60% of the super delegates, which is a significantly higher share of the superdelegates than she now enjoys.

Anything beyond that is a fantasy. Moreover, as I've already shown, the idea that she'll end up with in 100 pledged delegates of Obama is also likely a fantasy.

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After running through these numbers, I've now got an even harder time understanding what Clinton's path to victory is. To put it in poker terms, Hillary Clinton isn't drawing to an inside straight -- she's trying to make a bigger full house. That's tough to do, even in Texas.

Of course, some card players look at it differently. Where you see impossible odds, they see an opportunity to "massage the outcome," to put it euphemistically.