Why are models based on coded (-1,1 etc) and non-coded variables (as they are) very different? What should I use for publications? I am doing factorial experiments in R. I noticed when I use my variables as they are vs. coding them into -1,1, they are all very different. Here is my sample code. This dataset is adapted from the Experimentation for Improvement online course in Coursera.
#Example 1: Non-coded, as they are
runner1 <- data.frame(
  A = c(5, 10, 5, 10, 5, 10, 5, 10), 
  B = c(4, 4, 9, 9, 4, 4, 9, 9), 
  C = c(400, 400, 400, 400, 500, 500, 500, 500), 
  Y= c(39, 35, 40, 41, 40, 38, 41, 42))
runner1
runner1lm <- lm(runner1$Y ~ runner1$A*runner1$B*runner1$C)
runner1lm

#Example 2:Coded (-1, 1)

runner2 <- data.frame(
  A = c(-1, 1, -1, 1, -1, 1, -1, 1), 
  B = c(-1, -1, 1, 1, -1, -1, 1, 1),
  C = c(-1, -1, -1, -1, 1, 1, 1, 1), 
  Y= c(39, 35, 40, 41, 40, 38, 41, 42))
runner2
runner2lm <- lm(runner2$Y ~ runner2$A*runner2$B*runner2$C)
runner2lm

Which should I use? The coded or non-coded one? Also, how do I transform my entire dataset from coded to non-coded, if ever? Do I need a package for that? I was thinking about inputting coding parameters (like all 5 in column A will be -1, all 10 will be 1, so on and so forth like that) then letting R do its job and, boom!, I have a transformed data frame full of coded variables (except the dependent variable Y ofc). Basically I am asking if there's any code or package that can magically turn runner1 to runner2?

In the first model, you have a difference of 5 units between the two types of cases for predictors A and B, and 100 units for predictor C. In the second model, you've just scaled all the predictors to have a 2-unit difference between the types of cases.
The models aren't fundamentally different. They just use different scales for the predictor variables. It's like using distance as a predictor, but with one model measuring distance in millimeters and another in kilometers. The relative scales and coefficients are just inversely related.
If your predictor variables are fundamentally continuous, it's generally poor practice to convert them to categories as you seem to be doing in your question. That also removes the natural interpretation of regression coefficients as a change in outcome per unit change of a predictor value in its original scale. From that perspective, I see no need to transform data in a way needed to produce a model like runner2lm.
