Odds of being struck by lightning: 1 in 576,000 (source)
Odds of winning an olympic gold medal: 1 in 662,000 (source)
Odds of getting a royal flush in poker on first five cards dealt: 1 in 649,740 (source)
Odds of getting a hole in one: 1 in 5,000 (source)
Odds of a single player hitting 4 home runs in a single game: 1 in 1,440,000 (source)
Odds of a perfect game: 1 in 49,656 (source)
After yesterday’s post I totally nerded out and started to talk about statistics at work.
I thought there might be a little more to it, but wasn’t quite sure how to go about calculating it. This still isn’t 100% correct, but I think it’s closer than yesterday.
Ok, here goes. (This is definitely one of my longer posts, and it’s about baseball….if you stick with me, you’ll feel a little smarter, I promise. If you don’t want to stick it through, I understand.)
First lets start with some basic statistics.
What’s the probability of flipping heads 5 times in a row?
(1/2)^5
Each time you flip the coin you have 1 out of 2 chances of getting heads. Each flip is independent. Trust me on this one, I’m right.
Now, let’s think about this in terms of baseball.
We need the probability of hitting a home run for a given player. Ichiro gets about 1 HR for every 80 AB, Chris Gimenez gets about 1 HR for every 53 AB, and Babe Ruth averaged 1 HR for every 11 AB (he’s ranked #2 behind juicer Mark Mcguire…and we don’t like the ‘roids). Let’s say 1 HR for every 60 AB.
For simplicity, the probability of a player hitting a homerun 4 times in a row is:
(1/60)^4 = 7.7×10^-8 (or 1 in 12,960,000)
BUT there are 9 players per game, so there are 9 chances you could see a given player hit 4 homeruns. Odds go up a smidge:
9 in 12,960,000
1 in 1,440,000
Now, how likely is it for a pitcher to get 27 outs in a row. This is a bit trickier. What you really need is the probability that a player WON’T get on base. Turns out that baseball likes stats and every player has an “on base percentage.” This takes into account:
Hits
Base on Balls
Hit By Pitch
Errors (sort of….if you reach on an error you get an AB without the credit of a hit)
Career averages for:
Ichiro 0.369
Ted Wiliams 0.482 (best ever)
Nick says low 300s, so we’ll say the average player has an OBP of 0.330 (source)
That means that the probability of a pitcher getting a player out is 1 minus the OBP. If OBP is the chance a player will get on base, 1 minus OBP is the chance the player will not get on base….also known as an out.
So the odds of a pitcher throwing 27 outs in a row is:
(1-0.33)^27 = 6.57×10^-5 (or 1 in 49,656)
So in any given game there is (on average) a 1 in 1,440,000 chance of seeing 4 homeruns by a single player and 1 in 50,000 chance of seeing a perfect game.
We established yesterday that there have been 200,519 games as of yesterday.
16 games with 4 HRs means 1 in 12,532 (statistically requiring an average of 10.58 at bats per home run – staggering!)
21 perfect games means 1 in 9548 (statistically, pitching against players with an average OBP of 0.287)
I’m about to blow your mind. So the last perfect game was pitched against the Mariners a few weeks ago (and it totally sucked as a Mariner’s fan). Guess the average OBP for the Mariners – 0.289! (this actually has nothing to do with stats, but it’s super ironic that it turned out this way).
And if you looked at Josh Hamilton’s stats before his 4 HR night, he had 11 HR and 110 AB or 1 HR for every 10 AB.
What this doesn’t take into account is the extra stuff in baseball….the reason we all love it
I doubt the 4 HR games were hit against Cy Young winners and I doubt any team losing to a perfect pitcher went on to win the World Series (sorry M’s).
Did anyone stick with me? Happy math day! AKA, Friday
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