Metrics
This can be a contentious issue for some creatives, it's seen as Science vs Craft, but for me anything that can better inform the design and decision making process is a good thing. The key with any data gathering is how you interpret that data. The gathering and analysis is the science, the application is the craft.
There are 2 benefits for me that are linked but also separate. One is the commercial aspect, how you attract players to your game, and how you convert them into a paying player, and how you optimise that process minimising barriers to entry. The second is retention, keeping the player interested, creating a fun and engaging experience that will keep them coming back for more.
Conversion funnel metrics are well established used by sales and marketing on websites to optimise the conversion of prospective customer to actual customer. It is used to analyse the stages of the process a customer goes through minimising their exit before a sale can be completed. If you've been involved in website design then this will be very familiar. This just doesn't apply to an initial purchase, it can be for in game purchases and micro transactions if you're free to play, so there can be lots of funnels.
The second is in understanding what kind of experience you are creating, and whether people actually like what you're doing. Now this is a lot more familiar to game developers as focus testing and QA have been a big part of games development for some time. There's nothing really better than watching someone first hand playing your game, but what metrics can provide is this on a much larger scale.
First thing you need to decide is what you want to measure, and this will depend on what type of game you are developing, and design a system that will gather this data. There are some basic things for trying to measure fun, do players play the game for extended periods, do they finish gameplay segments, do they unlock achievements or earn trophies, do they frequently fail or win, do they quit out and if so at what point, and do they come back to the game and at what frequency.
If players are consistently failing or quitting the game at a certain point there is obviously an issue there and will need analysis. For online games there are two terms used to analyse player usage patterns, Monthly Active Users and Daily Active Users. This is a key metric, and giving players a reason to continually return to your game needs to be core to the design and vision. So it's not just about making the game fun, it's about giving the player the incentive to keep returning on a regular basis which has significant commercial importance also.