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Undefined or Infinity ERA?

SmokeySmokey500+ posts
Earned Run Average, ERA, is calculated by multiplying the number earned runs allowed by nine and divide by the number of innings pitched, represented by the equation;

ERA = 9 (ER/IP)

What happens if a pitcher gives up earned runs and is pulled before getting an out?

How would you calculate the ERA for a pitcher who started an inning, gave up five earned runs, and was pulled before getting an out? His ERA, given this equation would be, ERA = 9 (5/0) or ERA = “undefined”. That’s not right???? I have heard that some would say his ERA would be “infinity”. That doesn’t sound right either
Father Luke, my high school algebra teacher, would say... there is no answer! That is why mathematicians refer to numbers that are divided by 0 as "undefined." Some people tend to think of them as being infinite, but this isn't exactly true. There simply is no answer.
This actually happened. How would you treat this pitcher’s ERA if this was his only outing?
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L LOW337100+ posts
When calcualting an ERA:

1 inning = 3 outs
2/3 of an inning or .6 = 2 outs (it may be .66666...) irrelevent to the question.
1/3 of an inning or .3 = 1 out ( it may be .33333...) irrelevent to the question.
0 innings = 0 outs

In your total stats:

If you have given up 1 earned run or 1,000 earned runs and have yet to record an out, your ERA would be infinity.
SmokeySmokey500+ posts
Thanks.

Makes sense to statistically carry his ERA in this situation as 99.99 until he gets an inning or an out under his belt and can properly quantify his ERA. We didn't know how to represent his ERA until this happened so we posted it as "undefined". 99.99 is a better representation. BTW he ended up with a ERA of 4.02, respectable.
F fvb10100+ posts
quote:
Originally posted by Smokey:
Earned Run Average, ERA, is calculated by multiplying the number earned runs allowed by nine and divide by the number of innings pitched, represented by the equation;

ERA = 9 (ER/IP)


this is true only if your regulation game is 9 innings in duration. If your league plays a different numbr of innings (7 or 6 innings for younger guys) then the multiplier is however many innings you play. So if the regular game is scheduled for 7 innings, the his ERA would be 7(ER/IP). This confusion on the part of coaches parents, and statisticians is why HS statistics are so meaningless.


quote:
Originally posted by Smokey:
What happens if a pitcher gives up earned runs and is pulled before getting an out?

How would you calculate the ERA for a pitcher who started an inning, gave up five earned runs, and was pulled before getting an out? His ERA, given this equation would be, ERA = 9 (5/0). . . How would you treat this pitcher’s ERA if this was his only outing?


As the denominator of a fraction decreases to 0 the decimal representation of the whole fraction increases to infinity. Therefore, any ERA in which the pitcher never recorded an out is infinity.

Your algebra teacher was correct as far as algebra is concerned, but if he'd been teaching calculus or even advanced Trig he would have been more careful about how he explained dividing by zero.
Last edited by fvb10
F fvb10100+ posts
as long as we are playing with math, here's another fun question, what if he'd give up no earned runs and after walking the first batter he hurt himself and had to be removed (and the runner didn't score)? now what is his era? is it 9? or 0? or infinite? or nothing (you don't even put him on the list of pitchers)? or undefined?

Remember that x/x=1 so when you divide 0 runs by 0 innings pitched you get 1, which is then multiplied by the number of innings in a regulation game (9 in your example), so his era is 9, right?
Last edited by fvb10
SmokeySmokey500+ posts
fvb10,

No doubt that we can have a lot of fun with zero. I was looking for a practical answer. I like the idea of carrying the ERA value as 99.99 or “undefined” until it can be accurately quantified.

That being said, this is an algebraic expression and not calculus. A discussion on non-standard analysis and abstract algebra could get a bit heavy. Therefore, in an effort to keep this simple, using the algebraic properties (identity, associative, commutative, and distributive), your scenario could not be 1, or 9, because of the following mathematical proof.

For argument sake, say that 0/0 followed that algebraic rule that anything divided by itself is 1, i.e. 5/5=1, etc…

Sooooo, we're given that:

0/0 = 1

Now multiply both sides by any number n.

n * (0/0) = n * 1

Simplify both sides:

(n*0)/0 = n
(0/0) = n

Again, use the assumption that 0/0 = 1:

1 = n

This proved that all other numbers n are equal to 1! Soooooo, 0/0 can't be equal to 1.

BTW… My apologies for posting this in this forum. I see we opened one for Stats and scorekeeping.
F fvb10100+ posts
quote:
Originally posted by Smokey:
fvb10,

No doubt that we can have a lot of fun with zero. I was looking for a practical answer. I like the idea of carrying the ERA value as 99.99 or “undefined” until it can be accurately quantified.

That being said, this is an algebraic expression and not calculus. A discussion on non-standard analysis and abstract algebra could get a bit heavy. Therefore, in an effort to keep this simple, using the algebraic properties (identity, associative, commutative, and distributive), your scenario could not be 1, or 9, because of the following mathematical proof.

For argument sake, say that 0/0 followed that algebraic rule that anything divided by itself is 1, i.e. 5/5=1, etc…

Sooooo, we're given that:

0/0 = 1

Now multiply both sides by any number n.

n * (0/0) = n * 1

Simplify both sides:

(n*0)/0 = n
(0/0) = n

Again, use the assumption that 0/0 = 1:

1 = n

This proved that all other numbers n are equal to 1! Soooooo, 0/0 can't be equal to 1.

BTW… My apologies for posting this in this forum. I see we opened one for Stats and scorekeeping.



lol, you got my point

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