Yesterday, Shohei Ohtani had a game for the ages.
The baseball particulars speak for themselves. Let’s look at the one-day change in his batting average.
We know his preceding average:
We know he went 6 for 6 during the game $\framebox{G} = 1.000$
What is his succeeding batting average, $\framebox{S}$ ?
$\fbox{P} = \text{preceding average (before the game)}$
$\fbox{S} = \text{succeeding average (after the game)}$
In one line, we can easily calculate: $\framebox{S} = \fbox{P} + \displaystyle\frac{{\Large6}\cdot(\fbox{G}-\fbox{P})}{({\Large593}+{\Large6})}$
See my hand calculations below for a step by step approach.
How much did his average jump?
Again, in one line: $\framebox{JUMP} = \displaystyle\frac{{\Large6}\cdot(\fbox{G}-\fbox{P})}{({\Large593}+{\Large6})} = 0.007145 \approx\textbf{ 7 points}$
Rather, the student would recognize:
- at-bats are approximately 600
- 6 for 6 is batting 1000
- $(1000-\fbox{P}) = (1000- 287) \approx \textbf{700}$
- $\displaystyle \frac{\Large6}{\Large600} = \textbf{1 %}$
Therefore, the jump would be $700 \cdot \text{1 %} = \textbf{ 7 points}$
In the last 9 days, Ohtani has had 24 hits in 34 at bats — a 0.706 average!
He has raised his batting average to 0.309 — an increase of 22 points !!
He now has 54 homers and 57 stolen bases, with 2 games left in the regular season.
Enjoy!
