In case you missed the previous installment of Breakdown, we are defining three basic baseball statistics in terms of singles, double, triples, and home runs. Then using those three equations, we will determine a player’s hit distribution for the season! Unfortunately, we looked at four equations, but found only two that were independent. Luckily, thanks in part to you all, we have found our missing link.
Adrian Beltre’s Stats, 2016:
Here are the two equations we have so far, with 1B = x, 2B = y, and 3B = z, derived from hits and slugging percentage:
The two most popular statistics recommended to us that incorporated our missing variables were On-Base Percentage (OBP) and Extra Base Hits (XBH).
On-Base Percentage is defined as follows:
Extra Base Hits is defined as follow:
Adhering to the principle of Occam’s Razor, we selected XBH, and swapped out BA. Also, we personally love XBH as a description of offensive prowess because not only does the player get on base, but they also at the very least put themselves into scoring position, if not score other runners or even themselves in the instance of a home run!
Now here are our three equations:
We will solve these in two ways, by manipulating the equations and by solving the matrix of coefficients into its reduced echelon form.
First, since we know y + z = 32, we can substitute that into the first equation and solve for x:
Now we will substitute x into equation 2 and subtract it from the constant:
Then we will multiple equation 3 by 2 and subtract it from equation 2 to solve for z:
Finally we substitute z into the third equation and solve for y:
So by this method, Adrian Beltre hit 111 singles, 31 doubles, and 1 triple in 2016!
Here is the matrix method:
So also by this method, Adrian Beltre hit 111 singles, 31 doubles, and 1 triple in 2016! This hit distribution matches exactly to Beltre’s stats on Baseball-Reference.
To conclude, we can now confidently describe the relationship between solely a player’s hit distribution and all of the following stats: batting average, hits, slugging, extra base hits, and isolated power!
The SaberSmart Team