In our recent post, Predicting MLB Playoff Probabilities, we addressed a simple method for estimating the probabilities for each MLB team using a Markov Chain Monte Carlo using historical results from earlier in the season. We introduced the notion of continuity correction to help adjust for small sample sizes and a simple random number generator to simulate wins and losses from the remaining schedule.
What we did not show was the update to the future probabilities when a game is completed. For instance, earlier this week the Pittsburgh Pirates were gearing up for a trip to Los Angeles to take on the Dodgers in a three game series. From historical data, the Pirates were 3-0 against the Dodgers. Instead of using the 3/3 = 1.0000 probability, ensuring that the Pirates will sweep the Dodgers, continuity correction adjusted the probability to 5/7 = 0.7143. Here this says the Pirates have a 43.73% chance of winning two games, 36.45% chance of sweeping, 17.49% chance of winning one game, and a 2.33% chance of being swept. From this set-up, we see the Dodgers have over a 56% chance of winning a game this series.
So it comes as no surprise when Zack Greinke picked up his 18th win en route to the Dodger victory over the Pirates in game one of the three game series. So how do we adjust for this Dodger win? This is done in a simple manner. The Dodgers and Pirates had played in 4 games with the Pirates holding a 3-1 advantage. This adjusts the probability directly by counting (3 + 2) / (4 + 4) = 0.625. This adjusts the probabilities for the Pirates winning two games (39.06%), winning one game (46.88%), getting swept (14.06%) and getting a sweep (0.00%).
We can also make the adjustment by using the previous probability of a Pirates win, .7143, and noting that the Pirates did not win in their fourth game against the Dodgers. We take this probability and add (number of wins on new game / (number of games played before the new game + 4)) and multiply by ((number of games played before the new game +4) / (number of games played after the new game + 4)). In this case, we take .7143 and add 0 / (3+4) = 0. Then we multiply by ((3+4)/(4+4)) to get .7143*.875 = .625. This is the updated probability of a win for the Pirates against the Dodgers.
Performing this update across all games, we can obtain an updated simulation for the remaining MLB schedule.
Comparing to the previous set of probabilities from two days ago, we see the Minnesota Twins took a hard hit from a 32% chance of making the playoffs down to 10. This is in part due to the two-game drubbing the Los Angeles Angels doled out to the Twins for Saturday’s double header. This double-header sweep improved the Angels’ chances from 12% to 29% as they took a large portion of that probability from the Twins.
Things are looking bleaker from most teams as the Nationals, Indians, White Sox, and Giants’ probabilities all shrunk. Many other teams saw little to no change as they split the previous two games and were expected to split, such as Baltimore split with Tampa Bay, resulting in little changes as the Yankees split with the Mets and the Blue Jays split with the Red Sox. Baltimore’s slim 1.6% chance of making the playoffs will change dramatically in two ways over the remainder of the season. With only hopes for making the wild card, the Orioles are 4.5 games out but have four teams to leap over: Houston (current lead), Angels, Twins, and Indians.
Currently, the Angels, Rangers and Astros have to play six games against each other. If all teams go .500, the Orioles will have to sweep series against the Nationals and Red Sox, just to be two games out. That’s tough, considering the other seven Orioles games are against the division leading Blue Jays and the top wild card leading Yankees; both with strong holds on their respective positions.
This leaves the Twins and Indians to jump over. This is a curious finish as the Twins and Indians play each other 7 times to close out the remaining 16 games of the year. Hence the two ways the Orioles make the playoffs are by surging through the remaining schedule, a difficult task as 7 remaining games are against the Blue Jays and Yankees; or the remaining wild card teams go .500 and drop questionable games Red Sox (3 games), Tigers (3 games) and Athletics (9 games). As this next week unfolds, we will update the probabilities a couple times to show how quickly a few games change the probabilities.