This post is an extension of the main Model v2.1 article. Here we analyze in more detail the impact that placing expansions has on the Spire squad size calculation. I assume that you’ve read the main post (and have done so recently 😉 ). So if you haven’t read it, please go and read it before continuing. Without that, this post will make little sense 😉

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#### Model v2.1 – Expansions

##### Data

Here is a snapshot of data relevant for expansion impact analysis. You may want to click on the image to see a higher-resolution version. Don’t worry, I’ll explain what it all means 😉

OK, let’s unpack this. On all these charts, X axis is a number of expansions, while Y axis is *incremental *increase to the base Spire SS. You will see some red and blue dots here. Blue ones are relatively clean datapoints; red ones, on the other hand, are not. Basically, red ones are deduced from datapoints where several other things other than expansions changed, and some of the assumptions used are pretty questionable. Basically, red ones should generally be ignored as long as we have enough blue ones.

So the top row of charts have both red (questionable) and blue (reasonable) ones included, while the bottom row is the same, but with blue dots only.

##### Classification

Now the letters on top of the charts – T, P, M, R and V – designate different kinds of expansions:

**T**– all expansions (total)**P**– premium expansions**M**– map negotiation expansions (I include initial 6 here as well)**R**– research expansions**V**– regular (vanilla) expansions, meaning M+R expansions

So far, we only looked at total number of expansions (so T class). And last time around it looked like there is a nice exponential curve there. If you try, you can still see it in the T chart above. And while we can ignore the red dots, there are a couple of blue points that do not quite line up there now. And both seem to be fairly reliable (one of them is my own).

###### So why classes?

Worse still, one of the players reported 20 points per expansion for T#126, and then 28 points for T#127. That’s a massive jump, and while there could be other explanations if these observation would have come from different cities, the same city results are puzzling. However, it turns out that T#126 was a premium expansion, and T#127 was a map expansion. So it may not really be a jump if we consider these to be in different classes. And that idea may line up better with some of the other observations, where I’ve seen 28 points for T#120 (which also was a map expansion).

So if we look again at charts for individual expansion classes, it is quite possible that premium expansions gradually increase their contribution to Spire SS the more you have them (the chart looks almost linear, even though we clearly don’t have enough datapoints). We can say the same about M and V classes (there is really not much on R just yet). On these charts we see that points that are close to each other on X, are close to each other on Y. That’s a good thing, and it is not quite true for T.

##### Insights

So what does this data tells us so far? Well, here are the things that we’re pretty certain about:

- Placed expansions impact Spire SS positively
- i.e. the more expansions you have, the higher your Spire squad size will be

- Available but not placed expansions do not impact Spire squad size
- I have tested it with a map expansion

- The more expansions you have, the more each additional expansion contributes to your Spire squad size
- Observed increments were within 4-45 range, so quite wide

###### So why different contributions?..

Now, the point about varying contributions is interesting. While it is quite obvious that this is the case, the reasons for that are not clear yet. There could be several explanations for that.

The easy option would be that expansions simply have different contribution values for each additional expansion in each class. E.g. P#2 adds 4 points, P#12 adds 20 points, P#35 adds 45 points, M#64 adds 28 points etc. It would be easy as these contributions won’t depend on anything except the expansion number.

Another reason could be that number of expansions is a multiplier on some other value that grows with the city. As you can imagine, the lowest numbers in the chart (e.g. 4-10 point increments) come from early chapter cities. We’re talking chapters 3-9. And 20-45 increments all came from chapter 15 cities, but even there the span of base Spire SS was pretty wide (3K-8K).

###### …and how can we tell which is which?

It’s not easy to distinguish between these two cases. It is practically impossible to find low level cities with high numbers for M or R expansions; ditto for high level cities with low numbers for M or R expansions. That’s just how the game works. The closest we can hope for is to find a high level city (e.g. high number of AW levels leading to relatively high base Spire SS) with low number of premium expansions, and see if these add a little (corroborating dependency on just expansion number), or they add a lot (corroborating hypothesis of dependency on something else level-dependent).

And even that would work only if premium expansions are indeed treated separately. If somehow it is all about total expansions, then it is practically impossible to find high level city with really low number of expansions. Realistically, we would be talking about a difference between 120 expansions and 150 expansions. That would be quite a bit harder to distinguish.

##### Possible Experiments

So, to summarize some possible experiments here. I know that premium expansion #2 in chapter 4 with no AWs (we’re talking ~150 base Spire SS) added just 4 points. If someone with much higher base Spire SS is to add the same premium expansion #2 (P#2, or close enough), will we see ~4 points, or something much higher?

Alternatively, if someone with base Spire SS much lower than 3K can place P#11+, are we going to see 20+ points increments (as we’ve seen so far), or lower numbers? Low level cities with significant number of premium expansions are probably very hard to find though…

In any case, if you have a city (or know someone 😉 ) like that, I’d like to hear from you! Either in comments, PM, or on US forums. It’s for science! 😉

#### Conclusion

And that’s it for now. We’ll need to wait for additional datapoints, and see if they can shed some additional light on what is going on. So if you have an expansion of any kind – premium, map or research – consider freezing your city for a week (in terms of unlocking research and placing/upgrading AWs) to record data for this expansion. Let me know if you need any assistance with that.

I am certain we will revisit this when we’ll get more data.