Converting Levels Into XP & Vice Versa

The Problem

Many games (such as my own Pixel Blacksmith and Blacksmith Slots) contain an XP / level system, where performing actions will reward experience, and eventually new levels. These new levels often unlock new content, or provide currency, so keeping players incentivised without feeling like a “grind” is a tricky balance.

The Solution

First, come up with a basic formula to use for calculating the XP required for a level. The most common by far is (level/x)^y, with x affecting the amount of XP (lower values = more XP required per level), and y being how quickly the required xp per level should increase (higher values = larger gaps between levels).

Next, make a spreadsheet where x and y can be quickly and easily modified, and the XP per level seen. Here is my spreadsheet, feel free to make a copy.

As an example, here’s a comparison of the XP required for levels using varying values of x and y. Note that using 2/3 for y is recommended, so that built in squaring / cubing functions can be used.

Example 1: X: 0.07, Y: 2

This has a fairly quickly increasing amount of XP per level (y) and a large amount of XP (x), and is good for games where XP is relatively easy to gain.

Level XP Difference
0 0 0
1 204.0816327 204
2 816.3265306 612
3 1836.734694 1020
4 3265.306122 1429
5 5102.040816 1837
6 7346.938776 2245
7 10000 2653
8 13061.22449 3061
9 16530.61224 3469
10 20408.16327 3878

Example 2: X: 0.3, Y: 2

This has a high value for x, so the amounts of XP required for a level up are very small. This would be good for a game where XP is relatively hard to obtain (e.g. requires collecting items). Note that the % increase in XP between levels 1 and 2 is the same as Example 1 (3x higher).

Level XP Difference
0 0 0
1 11.11111111 11
2 44.44444444 33
3 100 56
4 177.7777778 78
5 277.7777778 100
6 400 122
7 544.4444444 144
8 711.1111111 167
9 900 189
10 1111.111111 211

Example 3: X: 0.07, Y: 3

This uses a different value for y than the other 2 examples, and as such the XP required rapidly increases. This would be used in a game where higher levels have significantly higher XP gaining potential (e.g. an incremental game).

Level XP Difference
0 0 0
1 2915.451895 2915
2 23323.61516 20408
3 78717.20117 55394
4 186588.9213 107872
5 364431.4869 177843
6 629737.6093 265306
7 1000000 370262
8 1492711.37 492711
9 2125364.431 632653
10 2915451.895 790087

Using The Formula

Now that we have a formula for XP required for any level (using Example 1: XP = (level/0.07)^2), we also need to know the current level based on XP. Inverting the formula gives us level = 0.07 * √XP.  The second formula can be harder to implement due to requiring “nth root of”, hence why using a value of 2/3 is recommended.

XP and levels can now be converted easily and efficiently, without requiring any lengthy formulas. However, how useful the formula will be depends entirely on how well the x and y values are tuned for the specific use case. Get it wrong, and players will power through content or complain about being too grindy, get it right and they’ll never mention it!

The Conclusion

Levels are an extremely common way of rewarding consistent players, and providing an incentive to continue playing the game, or to replay older content. Balancing the formula is extremely important, and the simplicity of the formula described in this post means that consistent complaints of level ups being too frequent or too infrequent can be fixed by changing a single variable.

It is applicable to pretty much any game on any platform, but is especially useful in mobile applications, where processing power can be more limited, and player attention harder to keep.

A gist of a Java implementation of converting between XP & levels, as well as calculating current % progress towards next level is available here.

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