Baseball Team Rankings

Part $1$: A small example

In this question, you will estimate the "rankings" of baseball teams using their past game performance. We will first do a tiny example to show how one might try to rank four teams, A$,$B$,$C$,$D who all played against one another in a season.

Game $1$: Team A vs Team B: $1-4$

Game $2$: Team C vs Team D: $4-3$

Game $3$: Team A vs Team C: $9-5$

Game $4$: Team B vs Team D: $6-8$

Game $5$: Team A vs Team D: $9-0$

Game $6$: Team B vs Team C: $3-8$

Now, let us suppose that the object of our ranking system is that the difference in the rankings between Team I and Team J should correspond to the point difference in a game where Team I plays Team J$.$

This gives us$,$ for each pair of teams, a linear equation

$$r$\_$I $-$ r$\_$J $=$ y$\_\{$IJ$\}$$$

where $r$\_$I$ is the ranking of Team $I$$,$ and $y$\_\{$IJ$\}$$ is the score difference between Team $I$ and Team $J$$.$