Friday, January 20, 2012

Through the Ages - Part XII - Analyzing More Games

Many people requested I review more games than just 20.  So, out of consideration and a desire for completeness, I did.  I collected data on 100 games.  As we increase the sets of data, we increase our accuracy, or at least our confidence in the accuracy.

What Changed
After 100 games, the popularity race between Aristotle and Moses was finished.  Aristotle came out on top by just over 12 additional plays.  Julius Caesar made a comeback and it was neck in neck with Moses for some time.  As I loaded the last few games, Caesar passed Moses to achieve second place!  So, Hail Caesar (except for Aristotle)!
Game Final Score
The final score numbers shifted upwards by about 4% for all positions, except for the 4th which
increased 10%:
Final Score Breakdown
The additional 11 points earned by First position player was all gained in Age IV, except for 4 points which were earned in Age IV.

In the "Source of..." breakdown, there were changes in the decimals of the percentages, but the rounded percentages do not change.
Pyramids remains the top chosen wonder, being built nearly 98% of the time!  It no longer seems to have a negative correlation to player finishing order (possibly positive), but we will cover it in greater detail when its individual card comes up.
What Didn't Change
Almost all of the analysis to date!  Adding these new games to the sets essentially verified the numbers we already had, reinforcing most of the recommendations.
In short, except for the analysis of the Leader Julius Caesar and the potential leveling off of the Pyramids, nothing much has changed.  We have some slightly higher numbers, but nothing worth mentioning.  The big advantage is from now on I will have a larger number of games (100) to draw on, which should provide a higher level of confidence in any findings.
About the Data
All analysis should define the data drawn upon, and I want to clarify the conditions I put on the data and why.

First, all data comes from games played on BoardGaming-Online.  It is the only resource where I had access to the logs.

Second, I expanded the logs out to 100 games.  The games were chosen mostly at random, with a few conditions defined here:

  1. 4-Player games only
  2. Basic Set (no expansions)
  3. No "Solo" games
  4. No games with the same 4-players
  5. No games where a player resigned
4-Player games only
I wanted to analyze 4-player games, so only 4-player games are valid.
Basic Set
BGO has some custom created expansions.  Including these expansions messes with the odds as some cards randomly replace other cards.  The base set is a known set of cards, and is therefore easier to breakdown.
No Solo Games
It is possible to play the games solo on BGO.  I excluded these becuase solo games usually represent a player trying to grasp the rules, understand the interface, or try out some "experiment".
No Games of Same 4-players
I avoided loading games where the same 4 players were in two games.  I have found player's tend to play in a certain style or believe in a certain strategy and, after some time, "group think" occurs.  This exclusion is to help remove any "group think" from disturbing the statistics.
No Resignations
Resigning is a perfectly valid strategy.  However, I cannot easily tell why a player resigned.  The player may have had to resign due to time commitments, or basic frustration.  Removing these games also makes calculations easier, as it ensures all positions are adequately represented throughout the game.

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