Flat vs. scaling runes

There are many interesting trade-offs to consider when choosing your runes. Today I'm going to look at just one, flat vs. scaling. Not every rune comes in both varieties, but today I'll consider every one that does.

Flat runes give you a bonus to a statistic equal to their value from the start of the game, and the bonus they give you is constant throughout the game. Scaling runes give you a smaller bonus to the relevant statistic, but the bonus increases linearly with each experience level your champion earns in game. So, scaling runes give you less benefit at level 1, but more benefit at level 18.

Since the scaling is linear, its easy to calculate the level at which the scaling runes start to give a bigger bonus than the flat runes.

I looked at each tier three rune which is available as a scaling rune. Then I looked at the bonus values for it and its corresponding flat version, and then calculated the first level at which the scaling rune gives a bigger bonus than the flat rune (the crossover level).

Here's the table for marks:

The AP and Mana marks are not efficient (when compared to equivalent glyphs) but they do have a low crossover level. If you're creating some gimmicky rune page that isn't optimized for level 1 cheese, you might consider going with the scaling versions of these runes.

With a crossover level of 8, the choice between flat and scaling AD marks might seem like a genuine one. However, as we saw in the article about actual rune use the scaling AD marks are never used by challenger solo-queue players. I suspect this is because the bonus of about 9 AD from the flat marks at level one, which helps with early farming, is a lot more valuable than the 21 AD at level 18 one could get from the scaling runes.

On to the table for seals:

The most used seals are health and armor. The flat versions are used more than the scaling, but with a crossover level of only 7, it may be wise to switch over to scaling runes if you think the game will go late. The scaling health regeneration seals have a low crossover level, which makes them attractive. In the analysis of silver vs. challenger player the challenger players used the scaling health regeneration seals much more frequently. This is likely because they give a significant bonus at level 18.

Here's the table for glyphs:

With a crossover level of only 5, the scaling health glyphs are the quickest in the game to overtake their flat counterparts. Of course, health glyphs are so inefficient, that there is almost no reason to ever take them. The effective health one gains from taking magic resist glyphs instead is much more valuable, if the opposing team has at least one magic damage dealer.

The scaling ability power glyphs are taken more frequently by challenger players than the flat ability power ones. The crossover level is only 7. But, perhaps more importantly, later in the game when you buy Rabadon's Deathcap the extra 30% bonus from that will benefit the scaling ability power glyphs more.

Finally, here's the table for quintessences:

It's interesting to note that the crossover levels here seem higher. This is because the bonuses from the flat quintessences are significant. They can be used to gain advantage in the early game. Taking ability power or attack damage quints makes farming a lot easier for the first few minutes when their bonus values are relatively high compared to minion hit points.

The other quintessences are used relatively rarely, but have their place in certain types pages. When you're deciding to use these, take the crossover level into account when you're considering whether the game will go late or not. It's all about how much time you expect to spend at each level.

Well, that's about it for scaling runes. I hope you had fun, I know I did. Personally, all my runes are flat, but after doing this analysis I might pick up some scaling health regen seals. 8) Take care of yourselves; I'll be back soon with more league fun and math fun here at LeagueMath.com.

No quintessences were harmed in the making of this article. Flat or scaling, I love you all. I appreciate the opportunity to share this math with you.

Peace.