National League Playoff Race

The race for the final two playoffs spots in the National League has come down to the final day. Currently, the Giants lead the Padres by one game in the NL West, while the Padres and Braves are tied for the wild card. Tomorrow, the Padres and Giants face off for the NL West title, and possibly a wild card berth, while the Phillies and Braves square off with the Braves trying to get the last wild card spot. It will be an exciting day, with a possible three-team playoff (the first one in history) on Monday and Tuesday. In this post I want to determine the probability of each of the three teams (Giants, Padres, and Braves) making the playoffs and facing the Phillies and Reds.

There are four possible scenarios for tomorrow's games:

Scenario 1: Giants and Braves win, Padres lose
Scenario 2: Padres win, Giants and Braves lose
Scenario 3: Giants win, Padres and Braves lose
Scenario 4: Padres and Braves win, Giants lose

For the purpose of this exercise, I am going to assuming the probability of any team winning any game is .5 (a reasonable assumption, but probably not entirely accurate). So the probability of each scenario above happening is 0.25. In the first scenario, the Giants and Braves will make the playoffs, and San Diego will go home. This means that the probability of the Giants and Braves making the playoffs is 1.0, and the probability of the Padres making the playoffs is 0.0. The second scenario is similar, with the Padres and Giants both making the playoffs (prob. = 1.0) and the Braves going home (prob. of playoffs = 0.0).

The third scenario is where things start to get a little trickier. In this scenario, San Francisco wins, so they have a 1.0 probability of making the playoffs, while the Padres and Braves will face off in a one-game playoff on Monday. So the Padres and Braves will both have a probability of 0.5 of making the playoffs (in each case, 2 out of the 3 teams make the playoffs, so each scenario's probability should add up to 2.0).

The final scenario is the most difficult, as there is now a three-team playoff. The first playoff would be Monday, when the Giants and Padres play (winner goes to the playoffs), and then Tuesday the loser would play the Braves for the final spot. The easiest way to think about this is that in scenario 4, there are "four" possible scenarios given the two outcomes of each of the two playoff games. The four scenarios would work like this: a) Giants win, then Padres win, b) Giants win, then Braves win, c) Padres win, then Giants win, and finally d) Padres win, then Braves win. So in this final scenario, the probability of San Francisco and San Diego making the playoffs is 0.75 (they make the playoffs in 3 of the four cases), and the probability of Atlanta making the playoffs is 0.5 (they make the playoffs in 2 of the four cases).

The final step is to figure out the probability of each team making the playoffs. To do this, we multiply the probability of the team making the playoffs in each scenario with the probability of the scenario.

Probability(Giants making playoffs) = 1*.25 + 1*.25 + 1*.25 + .75*.25 = .9375 = 15/16
Probability(Padres making playoffs) = 1*.25 + .5*.25 + .75*.25 = .5625 = 9/16
Probability(Braves making playoffs) = 1*.25 + .5*.25 + .5*.25 = .50 = 8/16

So overall, there are 16 possible scenarios for the playoffs that will determine the two playoff teams in the next three days. In 15 of them, the Giants make the playoffs (the only way they will not make the playoffs is if they lose tomorrow and the Braves win tomorrow, then they lose consecutive one-game playoffs to the Padres and Braves, and the probability of this happening is 0.5⁴, or 1/16. In 9 scenarios, the Padres will make the playoffs, and in 8 scenarios the Braves will make the playoffs. We can see that the total probability of the teams making the playoffs is 32/16 = 2, so we can see that the probabilities are correct in that two of the teams will make the playoffs.

What does this mean? Basically, the race is a two-team race for the final spot, with one team all but clinched. The Giants are all but assured of a playoff birth, while the Padres and Braves are left fighting for the last spot (almost always the wild card, but potentially the Padres could win the NL West and the Braves could win the wild card, although the probability is only 1/16). The Padres do have a slight edge because they can potentially win the division, while the Phillies have already locked up the NL East, leaving the Braves with only the wild card possibility.

So keep yours eyes on the games tomorrow, the Braves and Phillies play at 1:30 and the Padres and Giants play at 4, so even by 4 pm tomorrow we will have a much clearer picture of the possible playoff spots. It will be an interesting day, and possibly an interesting 2 or 3 days, all to probably get beaten by the Phillies and Reds in the first round.