MLB 2021 Divisional Round Odds and Championship Probabilities

The baseball playoffs are finally here which, to me, means model time! I’ve spent the last week or two developing a model to compute the 2021 divisional rounds odds and to compute championship probabilities for each team that made the MLB playoffs this year. This model is built on ideas I’ve discussed in my mathematical modeling for baseball article and in my batting order analysis.

We’ll begin, actually, by presenting our divisional round odds and championship probabilities before spending the rest of the article explaining how we got to our answers. If you want to skip ahead to the model talk, click here.

2021 Divisional Round Odds and Probabilities

We began by simulating each of the first round series thousands of times in order to compute the most likely outcomes for each series. Here is what we computed for the divisional round odds for each series.

Dodgers-Giants Odds

Luckily for the Dodgers fans, they squeaked by St. Louis due to a rare walk off in a winner-take-all matchup. Unluckily for those same fans, they got matched up with the best (second best?) team in baseball. The winner of the Dodgers-Giants series is going to see a huge bump in their championship odds simply because they are likely each others’ biggest hurdle. Our model suggests that the Dodgers have a 56% chance of winning this series.

Brewers-Braves Odds

This game is a pretty big tossup. The Brewers starting pitchers are incredible which should help them in the playoffs with the shortened rotations. Our model gives the Brewers a 52% chance at beating the Braves to advance to the NLCS

Tampa Bay Rays-Boston Red Sox Odds

Tampa is one of the favorites to win the whole thing by the 538 baseball model and by Vegas odds. However, my model is significantly lower on the Rays and gives Boston a pretty good chance at taking this series. Interestingly, my model was also higher than Vegas was on Boston in their wild card Yankees match up which turned out to be correct. Our model gives the Rays a 53% chance of advancing to the ALCS.

Chicago White Sox-Houston Astros Odds

This series is also almost a perfect tossup. I try not to include rooting interests of my own in these articles too heavily, but I think as a society we all want the White Sox to be victorious. Our model gives the Astros a 51% chance to beat the White Sox in the divisional round.

Potential Matchups Past the Divisional Round

In addition to the 4 series above, we also simulated each possible matchup of teams currently in the playoffs. For the divisional round odds we simulated using a five game series. For each possible ALCS and NLCS matchup (green below), we used 7 game series. For each of the possible world series matchups (yellow below) we used 7 game series. The graphics below summarize these probabilities: the percentages in each cell are the probabilities that the team in the given column beats the team in the given row should they match-up in these playoffs.

2021 MLB Championship Probabilities

Simulating the entire playoffs thousands of times and counting the number of accrued championships lets us estimate each team’s 2021 championship probabilities. The results are summarized in the bullet points below. For the money line conversion, we rounded to the nearest 10:

• Dodgers Championship Odds: 22%,ML +360
• Giants Championship Odds: 16%, ML +530
• Brewers Championship Odds: 13.5%, ML +640
• Astros Championship Odds: 13%, ML +660
• Braves Championship Odds: 11%, ML +800
• White Sox Championship Odds: 10%, ML +870
• Rays Championship Odds: 8%, ML +1090
• Boston Championship Odds: 6%, ML +1530

Comparing these numbers to the Vegas odds here definitely shows some pretty big discrepancies. In particular, the biggest difference between my model and the Vegas consensus is in the valuation of the Tampa Bay Rays and the Houston Astros. The Vegas money line for the Astros implies championship probabilities about 4% higher than what my model suggests while the Rays implied championship probabilities are about 6% higher than my model.

There is certainly some room for making money here if you trust my model. [I am not saying whether you should or shouldn’t; the model is rooted in sound principles and takes into account every aspect of the matchup including injuries, pitchers, and hitting tendencies, the model simply hasn’t been validated yet]. Combining my 2021 MLB championship probabilities with the Vegas lines in the link shared, you can compute the expected profit for betting on each team to win the championship. For example, the Dodgers have an expected profit of +10%. This means that for every dollar spent you expect to profit 10 cents. However, it is important to note that this is on average in the same sense that putting a thousand dollars in the stock market will give you an expected profit of, say, 6% by the same time next year. It might happen, it might not.

Team	Profit Ratio
Dodgers	+10%
Giants	+12%
Brewers	+21%
Astros	-25%
Braves	+43%
White Sox	-10%
Rays	-44%
Red Sox	-46%

In this way, perhaps the two best teams to bet on are the Braves and Brewers. This doesn’t mean the Braves and the Brewers have the best championship probabilities, it just means I think betting on them is the best bang for your buck. You couldn’t pay me to bet on the Rays or Red Sox at their current money line. Well, maybe you could.

Baseball Model

Our model is nothing more than Monte Carlo simulation with some domain knowledge applied to correctly choose the probabilities of all the events. The simplest explanation is this: if a batter hits .300, then a reasonable way to simulate their at-bats is to flip a coin that comes up ‘hit’ 30% of the time and ‘out’ the other 70% of the time. In order to properly simulate the outcome of an at-bat, we need to know the probability that a given hitter walks, gets a single, gets a double, hits a triple, hits a home run, is hit by the pitch, or records an out.

For example, suppose that our hitter walks 10% of the time, gets a single 15% of the time, a double 8% of the time, a triple 1% of the time, a home run 5% of the time, is hit by a pitch 2% of the time, and gets out otherwise. Then, to simulate that player’s at-bat we simply roll a 7-sided dice that says ‘Walk’ 10% of the time, that says ‘Single’ 15% of the time, etc. Even though no such dice exists in real life, they are easy to fake inside a computer. We then have a special ‘dice’ coded in our computer that is able to simulate the outcome of each hitter’s at bats.

After being able to simulate the outcome of an at bat using our 7-sided die, it is relatively easy to simulate innings, games, and series.

There are two intricacies in all this. First, players will likely hit well below their season long averages against very good pitchers and well above their season long averages against very bad pitchers. For instance, a .300 hitter probably isn’t going to record a hit 30% of the time against Max Scherzer. We used the techniques introduced in our prior article about mathematical modeling and baseball in order to combine a hitter’s probabilities with a pitcher’s probabilities to adjust a hitter’s dice to respond appropriately to the pitcher’s quality.

The second intricacy is that teams often use shortened rotations during the playoffs. For instance, they might only use three different starting pitchers throughout the entire playoffs in order to give themselves the best shot at winning. Our model lets us take this into account by specifying who is pitching in which innings and which games. In this way, we can also capture the effects of bad bullpens, rotations with a stronger front-end, etc.

With all this machinery, we simply use thousands of simulations to compute the probabilities of individual teams accomplishing various tasks. For example, to compute the 2021 MLB divisional round odds for each series, we simply simulate 5 games between the two teams while rotating the starting pitchers over the course of the 5 game series. To compute the championship probabilities, we do the same thing except that we simulate all rounds of the playoffs instead of just the divisional round and count how often each team wins the championship. Doing these simulations thousands upon thousands of times should lead us to a good guess for divisional round odds and championship probabilities.

Caveats

There are certainly a few things that this style of analysis relies upon in order to be accurate. If these assumptions are satisfied, then the numbers we present for divisional round odds and championship odds are as accurate as you can get. As these assumptions become less and less accurate, so too do our estimates of the championship probabilities and divisional round probabilities. My gut instinct says that these assumptions are quite accurate and so our numbers should describe reality very well.

First, we assume that each player’s performance this season is indicative of how they will perform in the future. That is, if a player hit .300 this year, then we have to assume that the player will continue to hit .300 into the immediate future. This assumption is fairly accurate especially as players accrue hundreds of at bats throughout the season. In order to improve upon this data, one could perhaps use Bayesian priors involving league average hitters and each player’s past performance.

Second, we assume that the outcomes of consecutive at bats are independent. Certainly this is not the case in the real world. If a pitcher gives up a few hits in a row, maybe that is an indication that the pitcher isn’t at his best and will be more likely to give up more hits for the rest of the game. The opposite could also be true. However, there is no good way to quantify this effect and test its significance, so we ignore it. However, there is some evidence in past analyses we’ve done that indicate that streaks aren’t anything more than statistical anomalies. That is, I am not convinced that a player being on a hot hitting streak or a pitcher being on a cold streak should be incorporated into a model because it may not allow for any increased predictive ability.

Please stay tuned as we continue to post updates throughout the 2021 MLB playoffs and as we updated our championship probabilities as more data comes in.

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