Let me start off by saying that no one should care about this. Like, I totally understand if you don’t have any interest in this, because you shouldn’t. I wouldn’t blame you if you stopped reading now – in fact, I encourage it. Thank you for your time.
Still reading? Ok. You probably still don’t care, but I’m going to write this post anyway. It’s about the only time I saw Mariano Rivera save a game.
I’ve been to 45 Yankee games. In those games, the Yankees are 24-21. I’ve seen four walk-offs, four shutouts, and, quite literally, the worst pitched game in the history of the organization.
Yes, I keep track of these things. What else did you expect?
Anyway, Mariano Rivera has pitched in 12 of those 45 games. But I’ve only seen one save. I was thinking about this the other day, because these are the things I think about, but based on the laws of probability and simple math, there is no way I should have seen just one save. I should have seen, like, at least ten.
I went back and did some calculations. It turns out that since 1999 (which was the year I went to my first Yankee game), Mariano Rivera has 267 saves at Yankee Stadium, which accounts for about 22% of all home games. The actual percentage of total saves at home is a bit higher, since other pitchers over the last 15 years have picked up a save here and there (and Rivera missed most of 2012).
So, let’s say that for any given Yankee home game, you have a 25% chance of seeing a save. That means, on average, you would expect to see about 11-12 saves for every 45 home games.
So, given this probability, what are the odds that you would see just one save? It’s low. Like, really low. And, yes, I calculated it (I had to recall some complicated permutation/combination and binomial distribution formulas from my pre-calculus days, and I got some help from the internet).
The answer: .00358%, or about 1 in 27,933*. So, if I lived 27,933 lives, I would expect see at least two home saves in 27,932 of those. This is assuming I went to 45 home Yankee games in each of those lives. So it goes.
*On the off chance you’re interested, here’s the formula I used
where p is the probability of success (25%), q is the probability of failure (75%), m is the number of successes (1), and n is the number of failures (44).
I am not 100% sure I did the math correctly, but I am fairly certain this was the correct formula to use.
Let’s talk about that one save. It was on June 13, 2006. I was nervous about going to the game because I had a final exam the following day. I also had to play hooky from my after-school job at the time. This was about as crazy as I ever got during high school.
Chien-Ming Wang threw seven and a third shutout innings, Robinson Cano hit a home run, and the game ended 1-0. It’s the only 1-0 game I’ve ever been to. Rivera threw a perfect ninth, minus an Andy Phillips error, and we were out of the Stadium by 9:30. It was Rivera’s 13th save of the year.
And … that’s it. 44 other games, 0 saves. I’ve seen Rivera pitch in tie games, in games with four-run leads, I’ve seen him blow saves, but there was only one real save on a cool spring night in 2006. What is the point of all of this? I don’t know. I guess I just have a bone to pick with the law of averages.