## Friday, October 17, 2014

### Likelihood of a post season sweep

Question:   As of this writing, the Kansas City Royals are in the World Series.   They have not yet lost in the post season.   If they sweep the World Series they will be the first team to ever win a 13-game post season.   Their record was 89 wins and 73 losses in the regular season.

For each of the questions below assume that the outcome of each game is independent from all other games.

What was the likelihood that this team can win eight straight in the post season and get into the World Series without a single loss?

What is the likelihood that a team with this win-loss record will win 13 straight games?

Assume that the Royals record against left and right handed pitching is as follows below?

 Kansas City Royals Wins Losses Total 89 73 Righties 50 32 Lefties 39 41
Totals are actual numbers.   Righties and Lefties are hypothetical.

(Sorry I don’t have actual data but it is likely that they are better against one type of pitching than another.)

What is the likelihood of eight straight when four are against righties and four are against lefties?

What is the likelihood of a 13-game sweep if the Royals play 6 games against lefties and 7 games against righties?

Answer:   The win likelihood based in each game is 0.5494.

The likelihood of 8 straight wins is (0.5494)8  or 0.0083 around 83 out of 1000.

The likelihood of 13 straight wins is (0.5494)13 or 0.00042   (Around 42 out of 10,000.)

The win likelihoods against righties and lefties are 0.6098 and 0.4875 respectively.

The likelihood of eight straight with four against righties and four against lefties is 0.0078 ((0.6098)4  x (0.4875)4).

Note that the likelihood of a sweep is around 6 percentage points less after accounting for differences in win likelihoods for the two types of pitching.

The likelihood of 13 straight --  6  against lefties and 7 against righties – is 0.00042.   In this case the extra game against righties offsets the diversity effect.

If Royals played 7 games against lefties and 6 games against righties that answer would be 0.00034.

Concluding Remarks:

The Royals are hot.   Their win likelihood right now must be larger than it was in the regular season.

Typically statisticians assume the same random variable for each team.   In several of my posts I have agued this assumption is not valid.

The consecutive hitting streak problem for a batter with different leftie and righty averages was similar to this one

Hitting Streak Problem:

This issue also emerges when calculating the standard error of a polling sample combined from a landline and cell phone list.

Landline and cell phones:

#kansascityroyals
#Royals