# Score multiplier based on lowest time

I'm making a score system that will be based on several factors, how many collectibles you have obtained, how few hits you have taken, etc. I want to add in a multiplier based on how quickly the player manages to finish the game.

So far the only thing I've thought of is to have a maximum time, and to subtract the final time from that number. So as an example, say I set the maximum number to 300 seconds and somebody beat the game in 220 seconds, that would leave 80. This could be divided into a smaller number and then used as a multiplier on the total score.

It works but feels a little limited. What would be a better way to achieve this?

• Can you describe the specific way in which this feels "limited" to you? In what way would you like to see this improved? – DMGregory Nov 24 '18 at 8:21
• Well I'm just not a huge fan of this dependency on another arbitrary number really. It feels like there's a more clever way to mathematically achieve this. I suppose I may be wrong but I just wanted to hear some other thoughts on it. – Danny Santos Nov 24 '18 at 8:34

$$\frac{9}{100 ^ {t/300}} + 1$$