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Digging Down into the Probabilities of the Houston Astros Earning a Playoff Berth

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Let's take a look at the statistical concept underlying the Houston Astros' high chance of earning a playoff berth at this very late stage of the season.

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Good morning everybody and happy National Houston Astros Have an Approximately 87.5% Chance of Making the Playoffs Day! Where did I get that number? Only from my brain*, but it's pretty consistent with the numbers being popped about by the algorithms fed into the gizmos created by the sexy, hirsute nerds over at Fangraphs.

Will the Houston Astros make the playoffs? It's an interesting and complex last-day scenario, but also amazingly satisfying given that the Astros' rebuild has worked better than anyone expected, with most baseball fans, including many Astros fans, assuming the team wouldn't have this chance for at least a few more seasons. It's nice to know that the Astros will get at the very least a 163rd game.

According to the below chart, provided by James Smyth, there are eight possible combinations of outcomes for the three games that count: NYY v Baltimore, Houston v Arizona, and LAA v Texas. Four of those outcomes lead to tiebreakers, which obviously have two possible outcomes each. Two involve Houston playing at Texas for the division title and the other two involve the Angels playing at Houston for the 2nd wildcard. Only the latter two matter when determining the Astros' odds of making the playoffs. On the surface, this is pretty complicated, right?

This is where it gets fun and easy for anyone familiar with the statistical multiplication rule of probability. I'll provide a brief explanation here because it is often (depending on the circumstances) incredibly useful and common is this exact type of situation: figuring out the odds of your team making the playoffs, in any sport. Briefly, it is used when figuring out the odds of multiple independent events *all* occurring and the formula is simple: you just multiple the odds of each individual event against each other. So, as an instructive example, let's try to figure out the odds of me sometime today eating a full bag of potato chips *and* proposing to Amy Schumer. For the former, I do like me some chips but I also want to maintain my svelte figure so let's put that at 50%. And my chances of proposing to Amy Schumer, despite my best intentions, are fairly low. Let's call that 1%. Multiple that together and we get 0.5%. Note that it wouldn't work for the odds of me meeting proposing to Amy Schumer and Amy Schumer accepting my proposal because A) those aren't independent events** and B) who am I kidding?

So how do we apply this to the Astros? Well, since the only way for the Astros to miss the playoffs is for the Angels to beat them in a tiebreaker game, we can calculate the odds of that happening and subtract it from 100%. The Angels have three independent events that have to occur: Houston has to lose, the Angels have to win, and the Angels have to then defeat the Astros in the tiebreaker. Everything else equal, that is 1/2 x 1/2 x 1/2 or 1/8, leaving the Astros with the other 7/8, or 87.5%.

Of course, not everything is all equal. For that one would need to factor in the odds of each individual game, which themselves involve many different factors. Fangraphs, for example, puts the Astros odds of beating Arizona at 56%.

OMG, you are all so very welcome!

Now go Astros!

* Because I may not be quite as knowledgeable as I have portrayed myself to be above and elsewhere, I welcome comments and corrections on my method and reasoning in the comments below.

**Why do the events need to be independent? Let's use another illustrative example to explain. Say we want to know the probability of two events both happening: A) me experimenting later today with peyote during an impromptu vision quest and B) me severely hallucinating like nobody's business. And, just so everybody understands that I'm not a complete hippy, let's put the independent probability of A at something rather low, like, say, 10% and the probability of me hallucinating at something also low, like 10%. Multiplying these two together we get 1%. But it's quite obvious that these two events are not dependent in a very important way -- my odds of hallucinating go way up, not down, once that peyote has been properly ingested.