For a $3 million prize sponsored by MLB.com, can you put together a 57-game hitting streak? Each day you get to pick one player, and if they get a hit, you live to play again tomorrow. If not, you start over and begin chasing DiMaggio from zero again.
Simple enough. The odds of winning are obviously very small, but it can’t be harder than picking a perfect bracket, right?
Let’s say you pick a different .250 hitter each day (wouldn’t be my first choice but it makes the math easier), and that they always get 4 at bats. In theory, you’ve got it made, if your guy just does average, goes 1-for-4, you’ll soon be collecting that cool $3 mill. But in real life, your guy is not a robot. Every 4th at bat doesn’t guarantee a hit; he could go 0-for-9, then get three hits in a row and still be .250.
So what are your odds of Beating the Streak?
First, we have to find a player’s odds of getting at least one hit in a game. Since the number of hits above 1 doesn’t matter, it is easier to work backwards and find his odds of going 0-fer. I’m kind of embarrassed to say how long it took me and Bryn to figure this out. If a player is hitting .250, that means he gets out 75% of the time. He’ll get out 75% in his first at bat, 75% in his second, 75% in his third, and so on. So the odds he’ll get out in all four at bats in the game is:
(1 – batting average)^(# of at bats) = Probability of going 0-fer
.750^4 = .3164
Conversely, his odds of getting at least one hit is 1 – .3164, or .6836.
A .250 hitter will hit safely in roughly 68% of his games. To calculate his odds of hitting safely for 57 games in a row, we raise .6836 to the 57th power.
.6836^57 = 0.00000000038
Put another way, a career .250 hitter has about a 1 in 2.6 billion chance of “beating the streak.”
But of course nobody picks the .250 hitters! Your odds improve dramatically the better hitters you choose:
- .300 hitters – 1 in 6.2 million
- .350 hitters – 1 in 73,715
- .400 hitters – 1 in 2,729
MLB.com tries to help by showing you the upcoming match-ups where batters have the highest career average against the scheduled opposing starter. These match-ups look great on paper, but as I learned in Baseball Between the Numbers, they almost always fall within the range of randomness, and given a larger sample size, the numbers will likely revert toward average. In other words, the career .300 hitter that is batting .500 against the upcoming pitcher is “due” to make some outs, and might not make a great pick to keep your streak alive.
Here’s my game plan: look at the top 10 hitters in the league, and see who has the weakest opponent the next day, taking into account both the opposing team and the pitcher. I’ll let you know how long I make it.
According to MLB.com, the longest streak ever in this contest is 49 games. Very impressive!