# Cubs lose 5th straight 1-run game

On Sunday, they became just the second team in 100 years to get swept at home in a four game series and lose all four by a single run. They also became the first major league team since 2011 to lose five straight one-run games. It’s the first time it’s happened to the franchise since 1915.

There are three color coded assertions above.  Let’s look at all three starting with the assertion colored in blue. After hearing about this 5 game streak it occurred that a question like this is something this data model should easily handle.  This however required modifying a script that counts stuff in historical game logs since I hadn’t envisaged this use case.

First things first.  What is the probability of losing 5 one run games in a row?  Since we have no other information other than there are two outcomes to each event.   We can assume

P(lose) = 1/2 = P(win) , just like a flip of a coin.

The probability of a one run game is 0.30 using data from 1970 – 2018 , thus

P(one run game) = 3/10.

The probability of losing a one run game is P(L) * P(one run game) = 0.5 * 0.3 = 0.15.  This is the same as the probability of winning a one run game.  Thus, the probability of losing 5 one run games in a row would be 0.15^5 which is around 1/13169.

Since there are 157 * 30 / 2 = 2355 possible starts to a 5 game series that means we should expect one occurrence every 6 or 7 seasons.  Between May 8 and May 13 Arizona lost 5 straight 1 run games which is around what we would expect   Before that in September 1988, 23 seasons before 2011,  Atlanta lost 6 one run games in a row which is a larger gap than we would expect.  Distributions are never perfect — especially with small sample sizes.

Let’s look at the second assertion colored in brown. Each team plays around 11 four game home stands per season or a little over half of their 81 home games.  In 100 years that would be around 1000 events where a sweep like that can happen.

P(losing 4 one run games in a row) = [P(Lose) * P(one run game)]^4 = 0.15^4 = 1/1975

Probability of going so long without losing 4 one run games in a home stand after 1000 events or 100 years is around 60%.   The probability of it not happening next season is around 99.44%.  In other words, this assertion has nothing to do with the quality of the Cubs as a team and more how the pachinko ball bounces.

Update 10/1/2019:  In other words, had the Cubs lost a game by 2 runs in the middle of that losing streak noone would be talking about this.  Whether a team loses by 2 runs or 1 run is irrelevant but streaks make for click bait and give sportscasters something to pontificate about.

The Cubs went 2-7 in the last 10 days of the season losing 5 games.  How many a team loses in a row or how they lose those games is irrelevant.  Had they went 7-2 instead there would have been a 3 way scrum like last year for two playoff spots and who knows how that would have turned out.

Bottom line:  A baseball season is a marathon and the final record of a team encompasses 162 games played over 6 months — not a mere 5 in less than a week.  From all 10 parts to the Playoff Horse Race series of posts here it was clear very early Cubs didn’t have the horses to win an NL pennant let alone a World Series this year.  Cubs remained stagnant albeit above average all season so they ended the season about where they should have.

End of Update

And finally, for the assertion in green.  1915 is 104 years of baseball or around 16,000 games played.  We saw above that the probability of losing 5 one run games in a row is 1/13169.  The probability of going 16,000 games without losing 5 one run games in a row is

P’ = ( 1 – (1/131619 ) ) ^ 16000 =~ 30%

Thus it was a 70% possibility of it happening again in the time frame since 1915.

The probability of it not happening next season is 99.8%.  What does this have to do with the current Cubs team?  Nothing. Cubs simply couldn’t pull off wins at the end of this season and sometimes numbers align funny.

Wild Card handicapping and playoff coverage starting tomorrow.  Until then ….

DISCLAIMER: There are probably one or more errors in the math above.