y = 2.0553X + 0.349 (trying to recreate results from FanGraphs.com article)

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danmath

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y = 2.0553X + 0.349

I am trying to recreate the results this article (which has this formula in it) got on Finding eSLG. In that section of the article there is an "UNLUCKIEST" SLUGGERS, 2015 graphic. I am trying to do the equation provided to come up with the .522 for Brandon Moss, .441 for Giovanny Ushela, etc. just to make sure I am doing things correctly. I can't seem to recreate these results.

It probably is human error. I take the B/PA data from the source referenced in the article (Statcast: https://baseballsavant.mlb.com/statcast_leaderboard?year=2015&abs=30&player_type=resp_batter_id ). I use that data for x.

So, Brandon Moss is ranked #38 on the list. His Brls/PA (same as B/PA as B and Brls stand for Barrels) is listed as 7.4.

I don't know what I do with the 2.0553 and also the 7.4 that is inputted into the equation as x. Am I supposed to multiply 2.0553 by the 7.4 (x)? Am I supposed to divide the 2.0553 by the 7.4 (x)? Am I supposed to do one of those things and then something else to the resulting number prior to adding in the .349 to get the y result?

Any help is appreciated. Thanks in advance!
 
danmath said:
y = 2.0553x + 0.349

… [x equals] 7.4 …

I don't know what I do with the 2.0553 and also the 7.4 that is inputted into the equation as x. Am I supposed to multiply 2.0553 by the 7.4 ?
Click to expand...
Yes. In mathematics, when a numerical value (2.0553) is placed next to a symbolic value (x), it means implied multiplication. We also do multiplication before addition:

y = (2.0553)(7.4) + 0.349

y = 15.209 + 0.349

y = 15.558

The article does assign symbol y to represent eSLG, and it seems to use symbol x for B/PA, but I admit to not studying the entire text.

Maybe they used a different value for B/PA.

We can set y to 0.522, and solve the equation for x:

0.522 = 2.0553x + 0.349

(0.522 - 0.349) = 2.0553x

0.173 = 2.0555x

x = 0.173/2.0553

x = 0.084 (rounded)
 
I read some more; I'm now thinking that the article does not contain the correct equation or the eSLG data is off.

Their slope value (2.0553) is close to my estimate of their other line (green), in the scatterplot showing HR-G versus B/PA.

The author might have mixed up some values.

Using the Statcast data for Moss and Jay, I solved a system of two linear equations (y=mx+b), and came up with this equation:

y = 0.02379x + 0.34597

It works for Moss and Jay, but it's off for Urshela. (I didn't check any others).

Next, I considered that maybe a typo showed 2.0553 instead of 0.020553.

Again, y = 0.020553x + 0.349 comes close to some, but not others.

You could request the correct equation from the author, or you could collect the same data and we could guide you through the least-squares regression process (or, perhaps, find an on-line site to do it for you). :cool:
 
Thank you so much

I VERY much appreciate your answers. It's good to know my initial thought of multiplying the 2.0553 by the x was correct. Looks like some of high school algebra way back when still stuck with me.

I think I have been viewing the 7.4 brls/pa (otherwise referred as well to as b/pa). It's impossible to barrel up the ball 7.4 times per plate appearance. The maximum is 1 barrel per plate appearance, which would be a 100% barrel percentage. So, in short, I think the decimal point needs to move two spots to the left. That would make it .074 (otherwise known as 7.4 percent).

Of course, using .074 as x doesn't get the desired y result for Moss. So I used the .084 you came up with and that worked perfectly.

In the end I'm left with the following assumptions:
1. I'm supposed to use the b/pa (brls/pa) number after o move the decimal point two spots to the left (7.4 becomes .074).
2. The data on the Statcast site has changed a bit. Maybe they slightly adjusted how the come up with the barrels stat.

The reason for assumption #2 is that last winter, when I found this article, I did the algebra (I multiplied back then...I shouldn't have second guessed myself this time lol), and I was able to reproduce things.

Basically, I need to identify 3 hitters that I feel had larger than expected SLG based on their other stats and see how they come out for eSLG in the equation. Find 3 hitters that I feel their SLG is totally believable and see if the eSLG is very close. Then find 3 hitters that I feel had lower than expected SLG. This should tell me how potentially reliable this equation still is.

Thanks again!
 
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