I've been running a small monthly pinball tournament in Milwaukee using a format of: round-robin (each player gets one try on each game at the location), feeding into a top-4 player playoff game. I've been running this in an Excel spreadsheet (it works pretty well - the Scott Danesi tool doesn't really add much over Excel for this).
What I'm wondering about is: what are some guidelines around selecting a scoring scale to translate a player's individual game score into a point score? I'm talking about what's referred to as IFPA scoring (100-90-85-84-83-...-1-0-0-0-...) or linear scoring (1-2-3-4-5-6-...) in Scott Danesi's tool.
I've been using linear scoring (top qualifier on a game gets 1pt, 2nd -> 2pts, 3rd -> 3pts, etc), and then add up the player's points to get a total. This works, except it tends to generate ties, and can create complicated matchups if you are selecting more than top 4 for a playoff of some sort. I think the scale is frustrating as player, because it doesn't really do a good job at selecting who, on average, scores better than others by only have a single point spread between each score. Because of the granularity of the scale, it creates a lot of ties.
I talked about this with a friend who is well-versed in statistics, and he argued that I should try having the players points be computed by taking the natural logarithm [ln(x)] of the player's individual game score in Excel, and then adding up the players points at the end.
Individual machine points, then, would be dependent on how much better / worse your score is compared to the overall average player score on the machine. The higher your individual machine score is compared to the average machine score by all players, the higher your individual machine points will be. Which makes sense to me. Also, because its less granular (decimal places / floating point offer more opportunities for discrimination), it also has fewer ties. I also learned that natural logarithm scoring is used in some poker tournament systems for scoring, so there is *some* precedent to using it in competitive gaming.
To experiment, I used previous tournament data and tried re-running the qualifying order using ln(x) scoring, and it ended up with similar results to linear scoring when no ties were present, but clearly broke the ties when they were present in the linear scoring situations.
Does anyone here have experience in using natural log scoring in a pinball setting? If so, are there any caveats or things to watch out for?
I figure this is worth trying out - I've decided to use this scoring scheme for my tournament this upcoming Monday and get some feedback from players on it. I will report back results on Tuesday after its done.