Category: R

Jelte Hoekstra has a fun post applying the Bayesian average to board game ratings:

Maybe you want to explore the best boardgames but instead you find the top 100 filled with 10/10 scores. Experience many such false positives and you will lose faith in the rating system. Let’s be clear this isn’t exactly incidental either: most games have relatively few votes and suffer from this phenomenon.

The Bayesian average

Fortunately, there are ways to deal with this. BoardGameGeek’s solution is to replace the average by the Bayesian average. In Bayesian statistics we start out with a prior that represents our a priori assumptions. When evidence comes in we can update this prior, computing a so called posterior that reflects our updated belief.

Applied to boardgames this means: if we have an unrated game we might as well assume it’s average. If not, the ratings will have to convince us otherwise. This certainly removes outliers as we will see below!

This is a rather interesting article and you can easily apply it to other rating systems as well.

John Mount has an informative post on how you can trick yourself when running linear regression models in R and forcing the y intercept to be 0:

So far so good. Let’s now remove the “intercept term” by adding the “0+” from the fitting command.

m2 <- lm(y~0+x, data=d)
t(broom::glance(m2))

##                        [,1]
## r.squared      7.524811e-01
## adj.r.squared  7.474297e-01
## sigma          3.028515e-01
## statistic      1.489647e+02
## p.value        1.935559e-30
## df             2.000000e+00
## logLik        -2.143244e+01
## AIC            4.886488e+01
## BIC            5.668039e+01
## deviance       8.988464e+00
## df.residual    9.800000e+01

d$pred2 <- predict(m2, newdata = d)

Uh oh. That appeared to vastly improve the reported R-squared and the significance (“p.value“)!

Read on to learn why this happens and how you can prevent this from tricking you in the future.