In my previous post, I explored whether playing as a strong civilization increased the likelihood of winning the game in Civ V multiplayer. Curiously, the data seemed to suggest that when FilthyRobot played with a strong civilization, he was no more likely to win than when he played as a weak civilization. This suggests that either there are other factors that have more of an effect on the outcome of the game, or that the effect of civilization bonuses are so small that we can’t detect them amongst all the other variation in the dataset.

In this post I want to explore some of the other factors that might help predict wins or losses. Many experienced Civ V players will tell you that the key to doing well in either single player or multiplayer is to get a strong start. However, “strong start” is a vague term, so I wanted to break it down and assess which specific elements of starting might be useful. So for each of the 180 games in the dataset, I recorded the following information about the starting location of the capital city:

Is the capital on a river? (yes/no)

Is the capital on the coast (yes/no)

Is the capital adjacent to a mountain? (yes/no)

Which minumum technology is needed to improve luxuries?*

*The reason I say minimum technology, is that most starts have multiple luxuries. For example, if the capital has both furs (requires trapping) and silver (requires mining), I encoded this as a mining requirement. The reason for this is that mining is a cheaper technology and so less likely to limit the start. Similarly citrus in jungle (requires bronze working & calendar) and pearls (requires sailing + work boat) are both considered more expensive than marble on grassland (requires masonry).

While non-capital cities are obviously still very important, the un-modded Civ V game is very capital-centric, and so the strength of the capital’s lands will have a big effect on the overall game. The only information I recorded about non-capital cities was:

Is there a natural wonder in the empire?

The above questions should reflect some of the key things that players look for when evaluating their starting terrain. Access to the coast has several benefits, such as fish tiles, better trade routes, and the option to build a large navy. However, it also comes with the caveat that it is much harder to defend, especially in multiplayer. So for coastal starts, it’s hard predict whether we expect an increased association with winning or losing. On the other hand, mountains only provide positives. They allow the player to build observatories for a big science boost, as well as providing nice defensive cover.

You may notice that there are other aspects of the start that I haven’t covered (such as how much food or production was available). Unfortunately this was too variable and complex to really calculate for each of 180 games. However, both river and coast access can be associated with more food, so there are some indirect links there.

Calculating the effect of start conditions on game outcome

So we have information on the starting conditions of 180 games, and we also know which of those games were won or lost. To see if any of the starting conditions predict the pattern of wins and losses in the dataset, I fit a logistic regression model (wikipedia has an in depth article on how this works). The logistic regression model can tell us the odds ratio (for example, how much more likely a win is with a coastal start versus a non-coastal start), as well as the probability that we would expect to see such a relationship by chance (the p-value).

Without going into all the mathematical details of how I did it (by all means comment if you’d like to know more!), the first thing I looked at was the p-value. This value tells us how likely it is that we would see the same pattern in a random dataset of the same size. In simple language, a low p-value indicates that certain start condition is likely associated with a win/loss ratio that is quite different compared to average. It’s a good way of flagging things for further interest and investigation (note: contrary to how it is often used, it does not tell us whether or not we have discovered the “truth”!). Looking at the p-values for the variables in our model (e.g. the different start conditions), the following things stood out:

Coastal capital: p = 0.03

Capital next to a mountain: p = 0.02

Mining tech luxuries: p =0.03

Trapping tech luxuries: p = 0.04

(a p-value of 0.03 means that we would expect to see such a relationship purely by chance in random data about 3% of the time)

So our model has identified 4 things that are likely to have a strong effect on the outcome of the game. However, what does this mean? On it’s own, the p-value doesn’t tell you much, but logistical regression also gives us the information required to calculate the odds ratio, e.g. how much more likely FilthyRobot was to win with condition A versus condition B. It is from this odds ratio that we can learn something!

Games with capital cities next to a mountain were 2.4 x more likely to have been won compared to games without a moutain start

to have been compared to games without a moutain start Games with coastal capital cities were 2 x more likely to have been won

to have been Games with mining luxuries were 1.7 x more likely to have been won

to have been Games with trapping luxuries were 3.6 x more likely to have been lost

It is interesting to note, that increased likelihood of losing is also associated with calendar luxuries (2.2 x more likely to have been lost), although this was associated with a weaker p-value (0.09) so may be due to chance.

Sea, mountains and mining. What does this mean?

The thing I like most about the results from the logistic regression, is that they intuitively make sense! Mountains are generally considered very strong for the start, because observatories give a colossal boost to science. It therefore makes great sense that this might increase the chances of winning. Similarly, despite the added risk of naval invasion, coast brings great advantages too. The trade routes provide much more gold/food/production, and sea resource tiles provide a lot of food.

As for the technologies required to improve luxuries, it is relatively widely acknowledged that mining luxuries are superior. They are quick to improve, only require one technology, and they provide a boost to production, which is much more useful in the early game than gold. On the other hand, trapping luxuries are not great. They provide gold, which is less useful than food and production, and unlike other luxuries they are not on the technology path to other useful things in the early game such as composite bowmen, or the National College. It therefore didn’t surprise me that they were associated with losing more than any other luxury type.

Interestingly, river starts seemed to have an equal outcome to games without a river. This was not what I expected, as rivers provide access to useful buildings the water mill, garden and hydro-plant. This doesn’t mean that there is no benefit to rivers at all, but perhaps the effect is too small to be visible in the data. Incidentally, I found that having natural wonder in the empire had no effect on the game outcome. This surprised me a little too!

In addition, to the results of the logistic regression, we can also observe the positive and negative effects of these factors when we look at the percentage of games won. Below, the % win rate of games with and without certain start conditions is shown as deviations from FilthyRobot’s overall % win rate, which is 59%. Positive deviations are shown in green, and negative deviations in blue.

This graph hopefully gives a nice visual summary of the effects we have found. They show that trapping based luxuries were associated with a much reduced win rate, whereas starting next to a mountain was associated with a high win rate. In fact, if FilthyRobot started next to a mountain, he won over 2 out of every 3 games!

Of course we don’t really know how well this will apply to all players and situations. If I could guess, I would say that coast might be even more beneficial in single player games as the AI is not very threatening at naval warfare. This is a nice benefit for the poorly-rated civilizations that have a coastal start bias (Japan, Ottomans, Byzantium, Denmark, Carthage). If the above trend is indeed true for all players, then it also suggests that while coast and mountains both improve the chances of winning, missing out either is not a huge handicap (no coast and no mountain are associated with only very small negative deviations from the win rate). However, having slow luxuries to improve is indeed a serious handicap.

So next time you start next to gold, silver, copper, salt or gems, count yourself lucky!