I paid 100 Geek Gold so that you can read this! :-)
I keep getting questions about the meaning of some of the numbers in my opening statistics analysis, especially about "Margin".
So let me try to explain: Margin holds the key information, which is why I use Margin to determine the value of an opening. Margin is the delta between the average number of VPs reached in a given game and the number of VPs achieved by a particular faction.
If a 4p game between e.g. Darklings, Fakirs, Halflings and Witches ends 130:100:120:110, then the average score in that game is 115. Margin is what the faction achieved compared to this average score. I.e. in the example the Darklings have a margin of 15, the Fakirs of -15, the Halflings of 5 and the Witches of -5.
In a second game between these same factions, the result may be 100:70:90:80. The absolute VP thus are 30 less, but the Margin for each faction is exactly the same as in the first game.
Why doesn't the absolute VP score hold a lot of information? Some games yield lots of points (because there are plenty of bonus tiles and scoring tiles around which give VPs and no money shortage) while other games simply don't offer the potential of grabbing extra VPs left and right and/or are short on coins which restricts the speed of ramping up everybody's engine. You may win a game today with 110 points and only make 4th place in another tomorrow, also with 110 points. But the opening you used to win with 110VP is considered to be more successful (and has a positive Margin because the average VP score will be lower than 110VP) than the one you used when you lost with 110VP (which will have an average VP score higher than 110VP).
Why is the Margin of all factions not zero, but 6.91? The average of ALL players and ALL factions is indeed zero. However for my analysis I only consider games played by the upper 50% of ranked players. So every time one of these plays in a game with some from the lower half, the average is no longer zero. Presumably the upper half guy beats the lower half guy, so his/her positive margin goes into the analysis while the lower half person's negative margin doesn't. Which is why upper-half players come out with an average margin of 6.9. Which then also becomes the benchmark for factions and their openings.
Note: it may very well be that the Margins derived from a single game are misleading. E.g. an expert ends up in a game with three inexperienced players and uses the opportunity to try a funny opening. Still the game ends with him winning 130:100:90:80. The average score is 100, and the margins are 30, 0, -10 and -20. Let's assume the three inexperienced players hold ranks in the lower 50%, so only the expert opening will make it into my analysis. +30 Margin for a funny opening. That's why I warn to put too much value in the stats from low sample sizes. The assumption/hope is that with enough data points, such freak results will be dominated by the normal results.
Also keep in mind that experts weren't born as experts: Yet any opening they did in their initial games are considered as "used by a player with an above-average ranking", because the database uses the current rank and not the rank the player had when the game was played. This is also one explanation why in all the analysis the supposedly-upper-half-ranked players (who "should know better") still show significant numbers of strange / unsuccessful openings. And from my personal experience I can assure everybody that belonging to the upper half of ranked players doesn't mean I won't play quite bad at times.
- Last edited Tue Mar 10, 2015 5:41 pm (Total Number of Edits: 1)
- Posted Tue Mar 10, 2015 5:33 pm
Dist of Columbia
Wait, are my games counting towards the upper half? Someone made a mistake. I'm probably skewing your numbers.