Everyone loves the playoffs, and even more so, everyone loves math (right?). I’m here to combine these two fan favorites and talk about the probability of PTFC clinching a playoff berth this weekend.
Let’s talk about if the Timbers win. According to MLS, if the Timbers win, any of four results elsewhere in the league could clinch a PTFC playoff spot. Since only one of those things has to happen, we need to find the probability of none of those things happening, then find the inverse, to get the probability of any one of those things happening.
If we win, we clinch playoffs if any one of these things happen:
- Real Salt Lake tie (24%) or lose (38%) to LA Galaxy: 62% chance overall
- Houston tie (20%) or lose (16%) to Minnesota United: 36% chance overall
- FC Dallas lose to Orlando City: 45% chance
- Sporting Kansas City lose to Vancouver: 17% chance
- Sounders lose (39%) to Philadelphia AND Dallas tie (25%) Orlando: .39*.25=.097 (9.7%) chance
Now we find the odds that none of these things happen by taking the product of the probabilities of a negative result in each match (.48*.64*.55*.83*.903=.127). Since there’s a 12.7% chance of none of these things happening, there must be an 87.3% chance of at least one of these things happening.
The conclusion? If the Timbers win in San Jose, they have an 87.3% chance of clinching a playoff berth this week.
The Timbers can also clinch with a tie against San Jose, if RSL lose to the Galaxy (38%). This math is a lot easier. Essentially, if the Timbers tie, they have a 38% chance of clinching a playoff berth this week.
Those numbers seem pretty good, but the Timbers have to actually get a result first. FiveThirtyEight gives the Timbers a 44% chance to win, and a 24% chance to draw San Jose. This next math is pretty simple too. The probability of a win and a favorable other result is .44*.873=.384, or 38.4%, while the probability of a tie and a favorable other result is .24*.38=.091, or 9.1%.
The probability of neither of those things happening is .616*.909=.56, or 56%. Flip that, and we can easily say that the Timbers have a 44% chance of clinching a Playoff berth this weekend.
Disclaimer: I am not actually good at math and I could have easily gotten something horribly wrong. Take these numbers with a grain of salt and certainly don’t bet on them. Please also do not form an angry mob and storm my apartment if it turns out I was indeed incorrect.