How Unlikely Were the Pirates' Comeback Wins?

The Pirates had back-to-back walk-off nights against the Cardinals. How likely were their victories?

It was a series against the powerhouse -- the best team in baseball, the leader of the National League Central, and the perennial contender. To beat this team in this fashion can only be described as magical. Or resilient. Or maybe lucky.

But titles don't matter. All baseball fans know is that the last two nights in Pittsburgh have been out-of-this-world amazing.

The Pirates trailed the Cardinals 3-1 in the bottom of the eighth on Saturday. A Jung-Ho Kang single brought in a run, and then a Pedro Alvarez hit tallied another. Tie ball game.

We've seen this story plenty of times before, though -- tying a baseball game late and extending it to extras is no big deal. But the story is just getting started.

In the top of the 10th, St. Louis' Mark Reynolds hit a solo shot. At the end of that side of the inning, the Pirates, per FanGraphs, had just a 13.4% chance of winning the ball game.

But Kang tripled and Chris Stewart singled him in. The Pirates tied it up again.

Fast forward to the bottom of the 14th, and Pittsburgh's in another tough situation. Down 5-4 entering the inning thanks to a Jhonny Peralta RBI, the Pirates had roughly 15% odds of winning the game.

Then this happened.

The win -- off the bat of the player who isn't just the face of the team, but the player who can be largely credited for turning a once worthless franchise into a contender -- brought the Pirates one game closer to the division lead before the All-Star break.

They weren't done.

In last night's contest, the Pirates faced an even bigger deficit. It was another extra innings contest, but this time, the Cardinals scored twice in the top of the 10th to take a 5-3 lead. In the bottom of the 10th, though, Pittsburgh grinded out runs -- single by single -- to finally tie the game up at five. And with the inning still going, Gregory Polanco ended the thriller with a walk-off single of his own.

At their lowest point in Saturday's contest, the Pirates, as noted above, had a 13.4% chance of winning. In last night's game, they sat at a measly 4.2% shot after an Andrew McCutchen groundout in the 10th.

Math tells us that there was roughly a 0.56% chance of these two wins happening.

And then there's also this.

We'll wait and see if this magic continues after the All-Star break.