Poisson is a discrete distribution…what exactly are you showing with the red curve?

Data from fbref.com Made in Rstudio

Pls feel free to share as much criticism/critiques as you have. I’m trying to learn as much as possible.

I’m showing how 476 random outputs from a Poisson distribution with lambda=2.96 would look, however I can see how this may likely not the best way to go about it. Do you think it adds anything useful to this plot, or is there something similar that would be better?

I still don’t understand how this would yield a continuous curve as you’ve indicated here

I used geom_density to compute a KDE and show a smoothed histogram.

that makes more sense now

Another way to present this is to show the percentiles of the actual goals scored against the percentiles of the poisson distribution. If it's a straight line, then your eyeballs at least can be happy that the distribution you've selected matches the observations at least.

Instead of the curve, red horizontal lines in each column for the Poisson value for each number. That would be more accurate and indicate how close the real values are to it.

The Poisson distribution is exactly what we'd expect if goals were random occurrences and no extra time. So no surprise but a good example for anyone explaining Poisson.

Am I reading this right in thinking there's (slightly) more 3 goal games than we would expect?

Yes. 3 would be 22.4%.

5.2%, 15.3%, 22.7%, 22.4%, 16.6%, 9.8%, 4.5% for 0 to 6.