I have a Mean and Standard Deviation. If I multiply the Mean by a number (non-constant), do I have to multiply the Standard Deviation by that number?

#1
Hello!

I'm making an MLB Model and I'm at a point where I'm stuck.

I have the AVG Runs Scored for each team, and the Standard Deviation of Runs Scored for each team for the season as well. If I know that one team is facing a pitcher who is superb, let's say 15% better than the league average, I will multiply the AVG Runs Scored by .85 to try and get a better indication of how many runs I can expect the team to put up.

My question is, do I have to multiply the Standard Deviation by .85 too? Or do I leave it be? and why?

I've been very confused on this and any input is appreciated!
 
#3
Yes

Do an experiment in Excel. Type some random numbers. Find the mean and SD. Multiply the numbers by 0.85. Find the mean and SD. Compare the means and SDs
If I multiply the STD Deviation by .85, the STD Deviation of course decreases. But I want to make sure that makes sense.

My plan is to run a Monte Carlo simulation. If I increase or lower my variability, it's going to widely change my predicted Runs Score over a simulation of 10,000 times. Does it make sense affecting the SD? I don't want to falsify my numbers.
 

katxt

Active Member
#4
If I multiply the STD Deviation by .85, the STD Deviation of course decreases.
I think we are talking at cross purposes here. The short answer, in my opinion, is that you can decrease the numbers to 85% and the variability will automatically decrease to 85% without you doing anything, or you can use the untouched numbers and decrease the mean and SD at the end.
If this doesn't make sense in your context, then perhaps you could explain the actual project more fully.
 

noetsi

No cake for spunky
#5
This makes an assumption that the variance won't change but in fact the variance might well be different for elite pitchers than non elite pitchers. That is if you look at the mean and standard deviation for regular pitchers and elite ones you might not find the distribution is the same. So the automatic method you suggested might not work.

But I have never heard this raised, you normally would calculate the SD from the data not adjust it the way you have. So I am just speculating,
 
#6
I think we are talking at cross purposes here. The short answer, in my opinion, is that you can decrease the numbers to 85% and the variability will automatically decrease to 85% without you doing anything, or you can use the untouched numbers and decrease the mean and SD at the end.
If this doesn't make sense in your context, then perhaps you could explain the actual project more fully.
Let me explain the project more fully.

The model I made is a Monte Carlo Simulation (10,000 times) and is used to show two teams playing each other and the probability of either one winning. Winner is determined by who has a higher final score for each simulation

Here’s what I do: I collect each teams AVG Runs Scored (Offense), AVG Runs Against (Defense), and the Standard Deviation of these numbers as well. I pull this information from finding every single game each team has played thus far into the season.

Now, I will find the average of a teams AVG Runs Scored and the other teams AVG Runs Against. This gives me an understanding of Offense vs Defense and now I have a consolidated value. I also do this for the STD DEV Runs Scored and STD DEV Runs Against, I find an average of the two.

At this point I have an AVG Predicted Runs and STD DEV Predicted Runs for each time.

My next step, and this is where I get confused, is I now look into the starting pitcher each team is facing. I will find the league average ERA, and divide the starting pitchers stats by league average ERA. If the team is facing a pitcher with an above average ERA, that pitcher’s value relative to league average will be above 1, let’s use an example and say 1.15

I will then multiply the AVG Predicted Runs for team that’s facing this pitcher by 1.15. I expect their Predicted Runs to go up because the pitcher they are facing isn’t very good. My question is, do I multiply the STD DEV Predicted Runs for this team by 1.15 too? Or not? And why? I just don’t see why I would but I’d like to confirm that so I can be more accurate.

Does this help clarify a little more? I can also send you the Excel file!