# Quick Baseball Series Simulations With Julia

Listening to game three of the National League Divisional Series
between the Washington Nationals and Los Angeles Dodgers today on
the way to the airport, I heard a startingly weighty statistic: The
team that wins game three of a five-game series wins 77% of series!
That's one pivotal game!

After mulling over that for a second, I thought to myself, "Hmm, I
wonder if that's significantly different from what you'd expect even
with each game being a coin flip. After all, it's not like the winner
of any game in a series is only 50% to win the whole best-of-five."
And with Gogo internet on the flight in typical fine form, I had
plenty of extra time to jump into a quick Julia REPL and find out.

We can simulate a 5-game series between teams 1 and 0 like:

julia> (round(Int, rand(1,5)))
1x5 Array{Int64,2}:
1  1  1  1  0


In real life they don't play games 4 and 5, but there's less effort
making the machine calculate those dead rubber games than real
major league playoff games.

Here's a function to see whether the winner of game three won
the series:

julia> function gameThreeWonSeries(series)
winner = sum(series) > 2 ? 1 : 0
series[3] == winner
end


So now let's just run that simulation 100,000 times and see what happens.

julia> wonGameThree = Array{Int}(10000)
100000-element Array{Int64,1}:
...

julia> for i = 1:100000
wonGameThree[i] = gameThreeWonSeries(round(Int, rand(1,5))) ? 1 : 0
end

julia> mean(wonGameThree)
0.68857


So even if every game were a simple coin flip, the team that won
game three would win about 69% of series. And of course, the games
aren't exactly coin flips — one of the teams is probably a
little bit better than the other, skewing that number even higher.

A nice thought experiment realized while flying without internet.
What I failed to figure out is how my laptop could chat with a
ground-based customer service rep to troubleshoot the broken
airborne Wi-Fi.