Patch 5.13: AP item changes

tl;dr Luden's Echo was a bigger change for magic damage than then 5.13 ap items rework. Neither made mages significantly more rich.

In patch 5.13 some super-interesting changes were made to many of the core ability power items in League of Legends. The overall effect of these changes will take a long time to shake itself out, I think, but now might be a good time to look at some basic statistics.

This week I focused on the ap items that were changed in patch 5.13. Namely, Blasting Wand, Needlessly Large Rod, Rabadon's Deathcap, Zhonya's Hourglass, Luden's Echo, Rylai's Crystal Scepter, Archangel's Staff/Seraph's Embrace, Rod of Ages, Haunting Guise, Liandry's Torment, Void Staff, Morellonomicon, and Athene's Unholy Grail.

I started with my dataset of 2,446,074 ranked NA solo-queue matches played on patches 5.3-5.13. I looked at any player from those matches who finished the match with one of the above items. There were 7,123,320 such players. For each of those, I measured their total magic damage dealt per game, and their total gold earned per game. Investigating how these stats change over time (per patch) can elucidate shifts in game balance.

Here is a table full of numbers summarizing average magic damage dealt per game by buyers of the recently changed items:

What we ostensibly came to see is the difference between the last two rows of this table. I did not know what to expect; would the changes result in more, less, or the same magic damage being done? It appears that, if anything, the changes are resulting in slightly less magic damage per game, but nothing drastic. At these sample sizes there may be statistical significance, but a difference of a few hundred points of magic damage over an entire game is nothing to get too excited about.

More interesting in this table is the jump between patches 5.4 and 5.5. Patch 5.5 was the introduction of Luden's Echo, and there we see a much more sizable jump in magic damage per game. The introduction of Luden's Echo appears to have had much more impact on this particular statistic than all the changes in patch 5.13. That is neat to see.

The differences in sample size come from the way I am pulling games from Riot's public data API. There is no trivial way to say 'give me a nice random sample of n solo queue games from patch x'. The data must be walked as a graph from each match to its players and from them to their matches, recursively. I have developed significant tech to try and get good, large sample sets from the API, but there is still more work to do in this area.

Here is a similar table for gold earned per game by buyers of recently changed ap items:

Looking at the last row of this table, we see that typical buyers of these items are not seeing significant changes to their income over a typical match. To me, this is a first indication that the recent changes have not drastically shifted the balance of champions that use these items. I assume that was a goal of these design changes, and it appears to have been met. With many of the build paths smoothed out, it is likely less frustrating to play with these items, and the changes do not appear to be obviously game-breaking by the two metrics I chose.

The change in patch 5.5 to introduce Luden's Echo did not affect gold earned as much as it did magic damage dealt. I might have expected to see a parallel uptake in gold earned, but it is not there. Interesting to consider. Overall, gold earned by users of these items has not changed significantly throughout season 5, it seems.

These tables of numbers are a bit nerdy, and tough to glean much from. In cases like this it is often better to visualize the data in some other way to see more of it at once, and to make more comparisons. Plotting over seven million points is a bit of a task, but I have been working on a tool called ScatterPlotBot to address precisely this challenge.

Using ScatterPlotBot I was able to generate this plot of magic damage dealt per game for all 7,123,320 players in the dataset who bought at least one of the ap items changed in patch 5.13:

(click the image or here for a huge version)

Mmm, now we are talking. A few things I saw right away:

• Patch 5.7 was half-again as long as other patches in season 5 (three weeks instead of two).
• The high-frequency vertical stripes, which come from more games being played during the day than during the night.
• The changes in brightness per-patch that come from the uneven sampling as discussed above.
• The gap on the far right that corresponds to the recent ranked downtime due to the instant-recall bug.
• And perhaps an overall upward trend.

The upward trend is a bit tough to tease apart from the uneven sampling, but looking again at the table for magic damage above, it does seem that the changes wrought in season 5 have lead to more magic damage per game over time. Very neat.

There is also a slight gradient within each patch going from left-to-right. This could be either players playing more ranked matches right after a patch is released, or it could be an effect of the way I am sampling the population of matches. Tough to say from this vantage, but it is probably a combination of both.

Here is a similar plot for gold earned per game by users of these items:

(click the image or here for a huge version)

The analysis here is very similar to the magic damage plot above. The most interesting features of these plots are likely obscured by the poor sampling over time. However, I am encouraged by the progress of ScatterPlotBot for visualizing these big data sets.

I also love how these images being to resemble spectrograms. There is a music to these datasets.

You and I find ourselves at the end of this post, but there is so much more to say about the changes to ap items in patch 5.13. What statistics could be pulled that would show drastic changes? How would normalizing the data above by damage/min and gold/min change things? That would depend on how game-length is changing over time. If damage/game is staying the same, but game lengths are getting significantly shorter, then damage is actually going up. Moreover, how can the sampling be improved to draw out the salient features of these multi-million point scatter plots? Guacamolly, so many unanswered questions, so much interesting work left to do.

So yes, for now we quit (you can go back to the index if you want). Not to worry, I will be back next week (subscribe to the rss feed). If you need anything before then, or ever, we can tweet.

The pizza theorem is by far the most deliciously named theorem, but one cannot subsist on eating mathematical results. Perhaps, if we are lucky, then we are sated for the moment with regards to league and math. If we are unlucky, then there is always more LeagueMath.com.

No one-shot/one-kill Luden's + Runeglaive Trueshot Barrage Ezreal nonsense was harmed in the making of this article.

Peace.