Above is a youtube video of the version of the game where these metrics were tracked.
Measuring Engagement
I use metrics in Bullet Time Ninja to see how many levels people play, and how many times people die in each level. In theory, if the game is extremely fun, most people will play the game all the way through. Otherwise, people will quit and play something else.
Thanks to free services like Playtomic, I can collect large amounts of player data, and organize it into pretty charts.
This chart shows how many people play each level:
Almost everyone plays the first level, but only about one-third of players make it all the way through to the end. Notice that the drop-off is pretty large in the early levels, but is a bit smaller in the later levels as players get more invested.