## Let’s Get the Twins to the World Series

Imagine for a second that MLB Commissioner Rob Manfred has gone senile. I know that’s a ridiculous premise, and this is sure to be a ridiculous post, but bear with me. Commissioner Manfred, perhaps after a long night of choice MLB-sponsored adult beverages, has placed the Minnesota Twins in the playoffs. Yes, the same Twins of the .364 win percentage and facial hair promotional days. What is the probability that they make or win the World Series? For simplicity, let’s say they take the place of both AL Wild Card teams and are just inserted into the divisional playoffs.

We are going to look at a bunch of ways of estimating the probability the Twins win a five-game series or a seven-game series, then multiply our results accordingly to find an estimate for the team reaching each round. We’ll start simply, and gradually progress to more complicated methods of estimation. Let’s start as simply as possible, then, and use the Twins’ .364 win percentage.  The probability of the Twins winning a five-game series (at least three out of five games) is 25.7%. The same process gives them a 22.4% chance of winning a seven-game series. Multiplying these out gives the Twins a 5.8% chance of reaching the World Series (roughly 1 in 17) and a 1.3% chance of winning it. For reference, those are nearly the same odds FanGraphs gave the Mets of reaching/winning the World Series on October 2nd. Of course, those Mets also had to get through the Wild Card round (and the greatest frat boy to ever pitch a playoff game), but failed to do so.

Okay, so maybe you didn’t like that method because we included the Twins’ entire regular season, instead of just including games against playoff teams. Noted, but just understand that the Twins had basically the same win percentage against playoff teams (.365) as their overall percentage. Just to note, I defined playoff teams as the six division winners plus the four wild card teams. Using the Twins’ percentage against playoff teams yields identical probabilities as above.

How else can we attack this problem? Well, the Twins played 162 games this year, which means they have 158 different five-game stretches and 156 seven-game stretches. Over all those five-game rolling “series”, the Twins won at least three games 24.1% of the time, and they won at least four games in 25% of their seven-game tilts. Multiplying those figures out gives them a 6% chance of reaching the World Series and a 1.5% chance of becoming world champs.

Again, those numbers are unsatisfying because they include all teams, not just the playoff teams. However, removing the non-playoff teams leaves us with a bit of a sample issue because they played 52 games against playoff teams. So, let’s change the problem slightly: what is the probability that a last-place team can reach, and win, the World Series? The teams I’ll be considering all finished in last in their respective divisions: Twins, Athletics, Rays, Braves, Reds, and Padres. Cumulatively, these teams had a win percentage of .412, won 37.4% of their games against playoff teams, won at least three games in 30.6% of their five-game stretches, and won at least four out of seven 29.9% of the time. You can multiply these percentages out and get some answers.

I’m still not satisfied, so there is one more tool I’m gonna break out: a bootstrap simulation. Bootstrapping basically means sampling with replacement, which means every time I randomly choose a game from the sample, that game is thrown back in and has the same exact chance of getting picked again. This resampling with replacement process gives the bootstrap some pretty useful properties that I won’t get into here, but you can check here for more info.

I’m going to put all the games the last-place teams played against playoff teams into a pile. I’m going to randomly sample five games from that pile, with replacement, and count how many games were wins. I’m going to do this 100,000 times. I will then divide the number of samples that included at least three wins by the total number of samples, giving me an estimated probability of these last-place teams winning a five-game series against a playoff team. I will repeat this process for a seven-game series.

The bootstrap probability of a last-place team winning a five-game series against a playoff team was 27%. The probability of them winning a seven-game series was 24%. They have a 6.5% chance of reaching the World Series and 1.6% chance of winning it.

Honestly, these probabilities are lower than I expected. I have believed in and learned to embrace the randomness of the MLB postseason. I went into this post expecting the outcome to highlight just how random the postseason really is, even absurdly so. However, the randomness of the postseason really depends on the extremely small differences between all the teams at the top, so inserting teams from the very bottom of the league introduces a level of certainty that would be new to the playoffs. However, imagine repeating a similar exercise for the NFL or NBA. The 27% or so chance I’d give the Twins of advancing seems much higher than the probability of, say, the Cleveland Browns winning a playoff game if inserted into the postseason.

My methodology was clearly very simple, but intentionally so. I gave no acknowledgement to a home-field advantage adjustment, and I looked only at the team’s W-L record. A more complex method could have taken into consideration Pythagorean Expectation or BaseRuns.

This was a ridiculous post and ultimately a meaningless exercise. The Twins probably couldn’t reach the World Series if they were placed in the playoffs, but I’ll point out that as of this writing (October 10th during Game 3 of Nationals-Dodgers) the Cubs also probably won’t reach the World Series. Baseball is a weird and wonderful sport, and the postseason is the weirdest and most wonderful time of the year. If the Twins could conceivably reach the World Series as currently constructed, don’t think too hard about what’s happening and just enjoy.

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Beau played baseball at Williams College and is currently an MBA/MS Sport Management student at UMass Amherst

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