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The goal of baseball team is to make the playoffs.

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The A's approach was to get to the playoffs
by using analytics.

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We'll first show how we can predict whether
or not

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a team will make the playoffs by knowing how
many games they

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won in the regular season.

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We will then use linear regression
to predict how many games a team will

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win using the difference between runs scored
and runs allowed,

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or opponent runs.

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We will then use linear regression again
to predict the number of runs a team will

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score
using batting statistics, and the number of

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runs a team will allow using fielding and
pitching

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statistics.

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We'll start by figuring out how many games
a team needs

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to win to make the playoffs, and then
how many more runs a team needs to score than

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their opponent
to win that many games.

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So our first question is how many games does
a team

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need to win in the regular season
to make it to the playoffs.

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In Moneyball, Paul DePodesta reduced the regular
season

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to a math problem.

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He judged that it would take 95 wins for the
A's to make it

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to the playoffs.

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Let's see if we can verify this using data.

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This graph uses data from all teams and seasons,
from 1996 to 2001.

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There is a point on the graph for every team
and season pair.

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They are sorted on the x-axis by number of
regular season wins,

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and are ordered on the y-axis by team.

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The gray points correspond to the teams that
did not

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make the playoffs, and the red points
correspond to the teams that did make the

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playoffs.

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This graph shows us that if a team wins 95
or more games,

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or is on the right side of this line,
they almost certainly will make it to the

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playoffs.

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But if a team wins, say, 85 or more games
then they're likely to make it to the playoffs,

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but it's not as certain.

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And if a team wins, say, 100 or more games
then

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they definitely will make it to the playoffs.

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So this graph shows us that if a team wins
95 or more games then

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they have a strong chance of making it
to the playoffs, which confirms Paul DePodesta's

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claim.

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So we know that a team wants to win 95 or
more games.

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But how does a team win games?

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Well, they score more runs than their opponent
does.

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But how many more do they need to score?

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The A's calculated that they needed
to score 135 more runs than they allowed

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during the regular season to expect to win
95 games.

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Let's see if we can verify this using linear
regression in R.

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In our R console, let's start by loading our
data.

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We'll call it baseball, and use the read.csv
function

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to read in the data file, baseball.csv.

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We can look at the structure of our data
by using the str function.

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This data set includes an observation
for every team and year pair from 1962 to

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for all seasons with 162 games.

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We have 15 variables in our data set,
including runs scored, RS, runs allowed,

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RA, and Wins, W. We also have several other
variables

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that we'll use when building models later
on in the lecture.

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Since we are confirming the claims made in
Moneyball,

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we want to build models using data
Paul DePodesta had in 2002.

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So let's start by subsetting our data to only
include

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the years before 2002.

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We'll call our new data set, moneyball, and
use

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the subset function to only take the rows
of baseball

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for which year is less than 2002.

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We can look at this structure of the data
set, moneyball,

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by using the str function again.

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Now, we have 902 observations of the same
15 variables.

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So we want to build a linear regression equation
to predict wins using the difference between

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runs
scored and runs allowed.

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To make this a little easier, let's
start by creating a new variable called, RD,

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for run difference,
and set that equal to runs scored minus runs

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allowed.

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If we look at the structure of our data again,
we can see that we have a new variable called,

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RD.

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So let's build a linear regression equation
using the lm function to predict wins

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with RD as our independent variable,
and using the data set, moneyball.

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We can look at the summary of our linear regression
equation,

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and we can see that both the intercept
and our independent variable, RD, are highly

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significant.

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And our R-squared is 0.88.

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So we have a strong model to predict wins
using the difference between runs scored and

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runs allowed.

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Now, let's see if we can use this model
to confirm the claim made in Moneyball that

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a team needs
to score at least 135 more runs than they

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allow to win at least 95 games.

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Our regression equation is wins equals
80.8814, our intercept term, plus the coefficient

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for run
difference, 0.1058, times run difference,

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or RD.

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We want wins to be greater than or equal to
95.

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This will be true if and only if our regression
equation is also

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greater than or equal to 95.

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By manipulating this equation, we
can see that this will be true if

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and only if run difference, or RD,
is greater than or equal to 95 minus the intercept

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term,
88.8814, divided by 0.1058, which is equal

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to 133.4.

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So this tells us that if the run difference
of a team

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is greater than or equal to 133.4
then they will win at least 95 games,

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according to our regression equation.

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This is very close to the claim made in Moneyball
that a team needs to score at least 135 more

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runs than they
allow to win at least 95 games.

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So using linear regression and data,
we were able to verify the claim made

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by Paul DePodesta in Moneyball.