Surely many developers whose applications have not been in high places in the App Store ratings for a long time will be interested to know how many downloads you need to get to get there. I will try to answer this question to the best of my ability. Recently, I managed to promote my game in the TOP-10 free games of the Russian App Store, and I want to tell you about how many installations it took.
Unfortunately, I do not promise a very exact answer. It so happened that because of the annoying bug, the analyst was not working in the game. But even without this, one can estimate approximately how many downloads were needed for the TOP-10 in early August.
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As can be seen from the screenshot above, for the first 3 days, the game received 11,000 installs, but 6,500 of them fell on the 3rd day. In this case, the game hit the 7th place in the ranking of free games on the iPhone at 17:00 on August 1. After that, there was no PR anymore, and considering that the given statistics of downloads is considered Pacific time, at least half, and most likely even more downloads can be considered organic. It is also worth considering that for the 7th place you need more installs than for the 10th. With all this in mind, we can conclude that at the beginning of August, for the TOP-10 free games, about 6-7 thousand downloads were needed in 3 days.

The second screenshot shows how many organic installations can be obtained from the TOP-10. I repeat that after reaching the 7th place there was no advertising. At the same time, the next day the game rose to the 6th place, after which it lasted in the TOP-10 and the next day. Then began a slow drop in the rating, and 3 days after departure from the TOP-20, the drop was already dramatic. In total, in five days after getting into the TOP, it turned out about 14 thousand organic loads, plus 3-4 thousand per day hit the 7th place.
The cost of PR amounted to about 500 bucks, and all of them have already got out due to advertising. Interestingly, another game with approximately the same budget and at about the same time reached only the 11th place in the games and quickly lost its positions.
I also have more accurate statistics. But it dates back to February. At this time, getting to the tops is more difficult than in the summer. And then it was like that. The release date of the game was set for February 5th. On the same day came the main PR strike. At the same time, in Russia the game was already visible on February 4 at 10:00 pm, and after 5 minutes an advertising campaign began. On the graph with Tapjoy, I bring only one (main) day with an hourly number of new users, of which there were about 7,000.
On the 4th, there were a little less than 800 users, and on the 6th of February from 00:00 to 6:00 (namely, at this point, the game hit the TOP-10, as can be seen on the chart with AppAnnie below) - a little less than 2000 thousand. Total in February, it took about 10 thousand installations to get into the TOP-10 free games in Russia.
Then, by the way, the effect of advertising was very good, and I continued PR for some time, keeping the game first in the TOP-10, and then in the TOP-20. In this case, the cost of support for some time more than covered by the profit from advertising. When the profit was not enough to support, I stopped the PR.
So, to sum up the above, it can be argued that when releasing a free game, a PR campaign should be planned with an eye on 6-10 downloads in the next 2-3 days, and preferably even one day. And if, depending on the season and the situation in the ratings, you manage to get into the TOP-10, then you will receive at least 2-3 times more organic installations.