Whenever analysts mention that bonus stats accrued from items (such as movement speed) fall victim to diminishing marginal returns, I always wondered why and how. For movement speed, I assumed it was solely because during team fights, movement speed is a stat only useful for map rotations, dodging skill shots, and gap closing—in the end, its value diminishes as the game drags onward when soaking or dealing damage in team fights becomes progressively essential. However, as I researched more about the game, I found out that movement speed is calculated via a formula, and is subject to two soft caps. In this article, by assessing how movement speed is calculated via several tables and graphs, I want to not only want to visualize the timeline of bonus movement speed in multiple facets, but understand how movement speed breakpoints are affected when taking into account Cloud Drakes, items with movement speed bonuses, and champion abilities.

Methodology

For this article’s sake, I will not be going over the formula for a champion’s movement speed (this information can however be found on sites such as the League of Legends Wiki). Instead, I will be examining the movement speed soft caps and its implications as movement speed is accrued. The soft caps operate through the following:

Raw speed less than 415 is multiplied by 100%.
Raw speed between 415 and 490 is multiplied by 80%
Raw speed over 490 is multiplied by 50%

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Example: raw movement speed = 520.
(415 x 1.0) + [(490-415) x 0.8] + [(520-490) x 0.5]
415 + 60 + 15 = 490 = capped movement speed.

Visualizations

Knowing how to solve capped movement speed, let’s visualize the timeline of a champion’s bonus movement speed.

After calculating our outputs, let’s put them in several graphs. This will be key in projecting the effects of percentage bonuses and champion abilities. For this blog post, I will only limit myself to tier 2 boots and Cloud Drakes. Additional bonuses via items and abilities can be estimated easily on your own. Furthermore, I will only use Pantheon’s base movement speed for continuity when making projections for tier 2 boots and Cloud Drakes. What is interesting to note is that Pantheon (along with Master Yi) has the highest base movement speed of 355, excluding Cassiopeia at level 18. Therefore, with any additional bonuses via items or champion abilities, Pantheon and Master Yi will inevitably hit the second soft cap if they have both tier 2 boots and three Cloud Drakes.

Figure 1. Marginal Product Graph

The Marginal Product Graph is essentially an illustration of how the soft caps are applied. As we continue to add bonus movement speed, the additional movement speed will eventually decrease. A soft cap of 80% is applied to movement speed above 415. Similarly, a soft cap of 50% is applied to movement speed above 490. Both soft caps are shown with the parallel dips on the graph, as well as the dotted vertical lines. Note that the dotted lines are also shown in the following two graphs.

Marginal product for raw movement speed

[(capped 2) – (capped 1)] / [(raw 2) – (raw 1)]
Example: marginal product of 500 raw movement speed
(480 - 477.5) / (500 - 495) = 2.5 / 5 = 0.5

Figure 2. Input vs. Output Movement Speed Graph

The Input vs. Output Movement Speed Graph shows us how the soft caps affect the accrual of raw movement speed. For example, once raw movement speed exceeds 490 with bonuses, we can visualize how the secondary soft cap cuts additional bonuses significantly. What is interesting to note is that this graph is the best out of the three in showing us movement speed conversions when taking into account multiple movement speed bonuses. Once we identify our raw movement speed given base numbers, items, champion abilities, and dragons, we can use this graph to predict our resulting capped movement speed.

Figure 3. Percentage of Bonus Movement Speed Lost Graph

The Percentage of Bonus Movement Speed Lost Graph gives us a better understanding on how much of a champion’s raw movement speed is lost when bonuses are accumulated. By calculating the area, we are able to solve the exact amount of lost movement speed through the two soft caps. For example, when a champion’s raw movement speed is 575, it will lose 10% of that number (57.5), ending up with 517.5 capped movement speed. As such, any additional bonus movement speed translates into a greater percentage loss of total raw movement speed.

Percent reduction of raw movement speed

[(raw) - (capped)] / (raw)
Example: raw speed of 500 is reduced by...
[(500) - (480)] / (500)
20 / 500 = 0.04 = 4%

Implications

While we can use this knowledge to better predict (and even time) map rotations given multiple movement speed bonuses, as well as assess movement speed efficiency, we have to remember that marginal returns of movement speed are applicable for both macro and micro play. In terms of macro, understanding champion timelines can help us optimize build paths, as well as in-game choices. For example, capturing that third Cloud Drake now becomes more situational, especially if you hypothetically have a Sivir-Karma composition. If that third Drake means you will lose tempo or a mid tower, definitely consider prioritizing the latter.

In terms of micro, we can easily say that during chases between two champions, the one with higher movement speed will ultimately escape or find its prey-- given no gap closing abilities, summoners, or item actives. However, we must also understand (as I mentioned before) that movement speed becomes irrelevant as teams approach late game. When team fighting becomes more critical, individual mechanics and combat stats become more essential for a team’s overall success. Unless movement speed can be utilized in a pick or map rotation, mechanical skill such as kiting becomes less reliant on bloated bonus movement speed. Gap-closing abilities and crowd control will invariably negate all the bonus movement speed you accrue.

Hence, the diminishing marginal return of movement speed isn’t just a product of calculations and soft caps, but a product of in-game variables. Superior movement speed can become easily negated through combat stats or even champion abilities, a variable that costs zero gold. Just as the saying goes, sometimes the best things [in-game] are free.

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