Statistics and Baseball

Today we looked at the number of wins for American League teams for the 2004 and 2005 seasons.

• We saw that there was a positive relationship in the scatterplot. Teams that win a lot of games in 2004 tended to win many games in 2005. Also, losers in 2004 tend also to lose in 2005.
• We can measure the strength of the relationship by means of a correlation r. We talked about how to compute r based on the standardized scores. For these data, r was close to .8 which indicates a strong positive relationship between a team's 2004 win total and its 2005 win total.
• Once we have r and values of the mean and standard deviation for both variables, we can compute the equation of the least-squares line.
• We used this least-squares line to make predictions. Suprisingly, we saw that a bad team that wins 60 games in 2004 is predicted to win 65 games in 2005.
• This observation motivates a discussion of the regression effect. We graphed a team's improvement (Wins_2005 - Wins_2004) against Wins_2004 and saw a negative relationship. This means that a great team in 2004 will tend to get worse in 2005, and likewise a bad team in 2004 will tend to get better in 2005.
• So there is hope for the Kansas City Royals who is currently the worst team in baseball. Things are bad this year, but I predict they will win more games next season.

To get you thinking about the test on Thursday, here are some terms that we've used so far:

dotplot, stemplot, histogram, bar chart, 5-number summary, mean, standard deviation, mode, boxplot, rule of thumb for outliers, comparing batches, z-score, scatterplot, correlation, relationship, least-squares line, predicted value, residual, sum of squared residuals, regression effect,68-95-99.7 rule