Thursday, March 22, 2012

Through the Ages - Part XXI - Strategy: Science

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The Leading Indicator

When looking for "Leading Indicators" to determine the good resources which increase the odds of predicting the outcome, the amount of science each player spends is a good place to look.  In fact, the following chart displays the relation between final position and ranking of science output quite clearly:
I have heard this theory several times, particularly when mentioning the importance of Alchemy as a key early technology, but the graph above is the first I know of which supports these suppositions.  The graph shows the relative amount of science spent correlates almost very well with the expected final position.

The first and second highest spender of science account for 89% of the wins. Similarly, those which spend the less in science appear lower in the final position.  To analyze more completely, there are two things to consider:

1) How much Science to spend?,
2) How to Generate the Science?

How Much Science is Needed

The real answer is "more than your opponents".  However, that is impractical and doesn't provide an objective to shoot for, so I offer the following chart which lists the science generated per player's final position:
From the chart above, we can see the lead player needs to spend 90 Science points on average.  This is roughly only 15 points higher than the second place player.  This 90 points provides a target we can use to analyze the various buildings, leaders, and Wonders: How much do they contribute to the Winning player?

Generating Science

Isaac Newton: A Great
Science really comes from two sources: buildings (Libraries and Labs) and Wonders.  Some Leaders enhance science output, but only with a Library or Lab previously.  Aristotle doesn't require a building, but he does require generating science by taking a tech card from the card row, thus requiring players to spend an action to gain a card.


Only 31 people who won the game built a science wonder: Universitas Carolina or Library of Alexandria.  In one game the winner managed to build both science wonders (In this game, the player scored 129 science total, but won by only 2 points).

For those games where Wonders are built, they account for roughly 10% to 21% of the player's total science.  Despite these Wonders, the total amount of science generated by the Winner was not significant (91.8 science on average compared to 89.8).

Science Leaders

Three Leaders in the game provide a science boost: Aristotle (Age A), Leonardo DaVinci (Age I) and Isaac Newton (Age II).  Bill Gates and Sid Meier provide a production and culture boost respectively, but neither increases the science output, so they are not considered in the Science Leader.

The Winning player chose at least one of the Science leader 57% of the time.  The distribution of these is such that there was no significant difference (24% Aristotle, 24% Leonardo, and 26% Isaac Newton).  In only 15% of the games did a player choose two or three science leaders.  Again, the distribution was roughly even among the combination of leaders.

Interestingly, when reviewing games were a science leader was chosen twice, the odds of success seem to drop significantly, from 57% to under 20%.  This leads to the conclusion that players are best off selecting a single science.  On average, Leaders will only generate from 5 to 10 science, but these 5 to 10 science are critical to improving the player's positioning overall.
Another Great Leader:
Just Don't Pair Them


Libraries and Labs generate science based on the number of workers assigned to them and the level of the building.  Many of these players build an upgrade for their building as well.  In only a single game (1%) did a player build neither a Library nor a Lab.  This indicates upgrading a lab or library is critical to success.

Which is better, however?  Most winners built Lab buildings (94%) over Libraries (78%), although 66% of winning players built some combination of both types.  In 8% of games the winning player upgraded to only a single Science building.  For this 8%, the distribution was roughly equal between Labs and Libraries, and they were fairly evenly distributed between Age I and Age II, though no Age III Science buildings appeared in this group.

The following Venn diagram displays the mixture of science building technologies discovered by the winning players:
Science Building Upgrade Breakdown
From the diagram we can see the general tendency of players to follow specific upgrade paths.  Many players build the Age I and Age II buildings, but by Age III the exorbitant science and production costs make them unfeasible.

The advantages of the two paths is not readily apparent.  Concentrating on Labs tends to yield no more additional science expenditure than those who choose to build just libraries.  However, fewer Age I libraries (Printing Press) are discovered than Age I Labs (Alchemy).  This indicates the preference to build Labs first, and Libraries second.
The conclusions are easy to draw.  The winning player generally out produces the other player's in science.  The winning player will spend roughly 90 points of science in the course of the game.

The two science Wonders: Universitas and Library of Alexandria, can provide a great boost in the odds of winning the game (roughly 30%).  However, the real boost comes from selecting a Science Leader: Aristotle, Leonardo Da Vinci, or Isaac Newton.  Counter intuitively, it seems better to only choose one science leader in the course of the game, and it doesn't matter which one is chosen!  After analyzing the losing positions against the winner, a player is better off choosing no science leader rather than choosing two or more science leaders, which is really quite surprising.

Like Culture, the majority of Science will come from buildings (roughly 60-75%).  The majority of the science will come from Labs, and the first lab built should be Alchemy.  Libraries are commonly built in conjunction with Labs, but normally later in the Ages.

Summarizing, the advice seems to be as follows:

  • Select only one of either Aristotle, Leonardo Da Vinci, or Isaac Newton
  • The Wonders Library of Alexandria or Universitas Carolina are nice, but not crucial to success.
  • Science Buildings should be discovered in this order:
    • Age I - Alchemy
    • Age II - Journalism
    • Age III - Computers and then Multimedia
  • Computers is often discovered, but rarely built.  Whereas Multimedia is less likely to be discovered, but is more often built.
So, the above four buildings make up 27 of the 90 Science points players will spend.  What technologies do you believe should form the other 63 points?  Let me know your ideas!
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