September 30, 2006

Kissing Your Sister

Breaking Ties

by Clay Davenport

I've received a number of e-mails over the last few days regarding the way the Postseason Odds Report handles ties. The program that runs the report, of whichever flavor, has no code to settle any ties and no knowledge of major-league tie-breaking procedures. Any two-way tie, for a division or wild card, results in each team getting credit for one-half of the prize; a three-way tie means that all teams get a one-third credit, and so on. That is the reason why this million-season model actually extends to five decimal places, instead of only four; it needs to be able to account for the ties.

Since the code doesn't handle it, I will. These numbers are through Friday's games, and are based on the regular Postseason Odds Report only.

In the American League Central, the model left the Tigers and Twins tied in 377,115 of the million runs. Since this is a tie for both the division title and for the wild card, league rules say that there will be no playoff game, but that whichever team won the most games in head-to-head play will be called the division champion. The Tigers won the season series, 11 games to eight, so they should be called the champions in all of those tied series, not half of them. Net result: the Tigers chances of winning the division increase from 59.90315 to 78.7589, and the Twins chances fall from 40.09685 to 21.2411.

The National League is a lot more complicated. Let's start with the Central, because there are no wild-card possibilities to distract us.

Because there are no wild-card chances, any ties in this division will have to be resolved by a playoff. The model saw that happen 127,472 times, so we're looking at about a one-in-eight chance of baseball on Monday. Actually, any playoff would be on Tuesday, because the Cardinals would need Monday to play a make-up game against the Giants. I neglected to print out the relevant numbers for calculating the likelihood of that, but it has to be at least as high as the number of times the teams finish in a tie, along with some portion of the time that that final game results in either St. Louis or Houston winning outright. The breakdown in the Central went like this:

• St. Louis won the division outright 85.164 percent of the time.

• Houston won the division outright 2.0888 percent of the time.

• St. Louis and Houston finished in a tie, necessitating a playoff game, 10.7621 percent of the time. When MLB did their coin tosses earlier this month, they did not flip for a possible St. Louis/Houston playoff, only a St. Louis/Cincinnati playoff. When they did finally make the toss it came up in Houston's favor, so this game would be played in Houston.

• In 2.6431 percent of the cases, there was a tie between St. Louis, Houston and Cincinnati, one which would require two playoff games. These games would not be played before Tuesday, since we have to get through the Cardinals' Monday makeup game in St. Louis. If I understand correctly, a three-way tie would first have the teams designated as A, B and C, with A playing at B, and then the winner hosting C the next day; the winner of that game is the champ. Frankly, I'm not certain how those labels get assigned.

• Finally, there was a 0.734 percent chance of a St. Louis/Cincinnati tie, without the Astros. That game would be played in St. Louis.

The National League West race is tied into the wild card, with six possible outcomes:

• The most common outcome is that the Dodgers and Padres finish in a tie, and that they will be ahead of the Phillies. In this case, the Padres would be declared the division champs, while the Dodgers would be the wild card, because the Padres won the season series. This was the result in 34.8954% of this morning's runs, a little more than a third of all cases. Since the report splits these games between the Padres and Dodgers instead of giving all of them to San Diego, we need to adjust the numbers. San Diego's chances of winning the division championship are 67.464, not 50.01625, and their WC chance reduces to 27.09067. The Dodgers' championship chances drop to 32.536, while their WC chance increases to 65.4912.

• The second-most common outcome was that the Padres would finish ahead of the Dodgers, and the Dodgers would finish ahead of the Phillies, giving the same net result as scenario number one. This one happened 28.1173% of the time.

• Third-most was the case where the Dodgers won the division and the Padres won the wild card, coming in at 23.7242% of all cases.

• That covers more than 86% of the cases, and none of them require a playoff game. The only way to get a playoff games is to get the Phillies involved, and the most common way for that to happen was a San Diego/Philadelphia tie, with LA winning the division, which happened 7.5645% of the time. The similar "SD wins, LA and Philadelphia tie" situation only happened half as often, 3.2039% of the time. Either way, such a game would be played in Philadelphia.

• A three-way tie happened 2.4947% of the time. If this happened, then the Padres would play the Dodgers in Los Angeles to settle the championship of the NL West. The loser would then fly cross-country to Philadelphia for the right to be the wild card.

So, add all that up, and we have about a 5% chance of seeing a situation that requires two playoff games, and a 25% chance of getting at least one.