Like a lot of other commenters here, I think the OP didn't run an mobile app install ad which is meant exactly for this scenario - which would show up only on mobile inside newsfeed.
OP - would love to help out and dig in further. Can you email me (I'm firstname.lastname@example.org)?
Disclaimer: I work at Chartboost, now the largest mobile gaming ad network.
With a bigger budget, I might have been able to get more of a boost from Facebook, but I'm an indie developer and I really don't have the time or budget to spend hours and hundreds of $ tweaking a campaign.
Imagine taking a coin toss and trying to figure out whether heads or tails came up more often, but only tossing the coin three times. Imagine you get HHT, and conclude that head is a better bet than tails.
This is essentially what you're doing, by concluding that one option is better than the other, based on a single-digit install sample size.
Now, I'm not saying you should be spending massive ad budgets, and spending a lot of time tweaking your campaigns, I'm merely pointing out that you don't have enough raw data to make conclusive judgements about the effectiveness of these two networks.
Being a major player in this industry, I can tell you that the numbers I'm seeing seem to indicate that Facebook (and Chartboost) are in fact much more effective ways to buy installs for mobile games than AdMob, with a properly set up campaign. Feel free to contact me directly if you'd like more insight regarding this.
Also, your Google ad is significantly better looking than your Facebook ad, and is also much more likely to be seen while people are on their mobile phones.
Facebook supports conversion pixels as well, so conversions through his signup flow could have been measured. Instead we just get a vague disappointment in WoW signups
So I spent around the same time setting up the Facebook campaign as the AdMob one (about an hour each, including the time to make the graphic), and for the time/$ spend, the AdMob campaign trounced the FB one.
In terms of conversion tracking, it was quite unscientific, true. But basically, I can track the number of new players of the game per day. Normally I get a pretty steady flow just from the Play Store. With the FB campaign running, there was no significant uptick in signups, but with the AdMob one running, the uptick in signups was immediately clear.
I didn't actually know it's possible to target mobile only with FB campaigns, and so I'll definitely be giving that a go.
Anyway, my point with the post was just that for someone on a tight budget, with not a lot of mental bandwidth to spare for tracking ad conversions, AdMob was just way better value for me.
However what the OP did is sort of life-time-value (LTV) analysis which in the long run might give a better indicator on return-on-ad-spend. Post-install tracking is available now via various 3rd party tracking solutions.
It does involve more up-front work on an app developer - i.e. find all the important metrics in the app that is relevant (sign-ups, various activities like virtual good purchases etc...), and track these metrics over time.
There are quite a few flaws in the OP which most of the comments here have captured, and provided remedies to fix them, so I won't repeat them here. I look forward to the follow up here.
Disclaimer: an ex-Admob engineer + currently working in a mobile ad startup.
If I am correct (I can't be sure given the article), the results are not surprising. A properly run Mobile App Install Campaign can yield sub $2 installs depending on the app being advertised, but that assumes requires some experience running online ad campaigns.
Obviously ads that point to the appstore are going to convert at a higher rate.
$20 on each platform is by no means real test.
That said, the results are hardly surprising. I showed AdMob ads in a game once and they paid almost nothing compared to other networks. They have a huge glut of apps showing ads for almost nothing.
Your main problem is going to be that the game is sci-fi themed. They are very hard to marketing. If any perspective developers are reading this, don't make sci-fi themed mobile games.
There is no way to correlate a user who installed via FB with your revenue, if you have In App Purchases.
1: a better mobile specific Facebook ad
2: the same admob ad
3: a budget of $350 each to be spent over 7 days
That will provide a much more conclusive test.
But I'm definitely going to try a mobile-specific FB ad, I didn't even know those were possible!
Even if you had amazingly high conversion rates, with sample of that size, the total number of conversions could be just about anything. Simple variance.
Well done on releasing the game with good reviews though. That's a great achievement. Just spend a bit of time just thinking about advertising :)