League of Legends

Looking at Ryze’s build power curves and their interactions with recall frequency

LeagueofLegends12 - Looking at Ryze's build power curves and their interactions with recall frequency
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TLDR: I look at how build paths and back timings affect Ryze's rough power curves through 3 items. Conclusions at the bottom.

With the S11 item shifts, Ryze has new builds to explore. Here, I won't be looking at what is built, but rather when it is built. For a given 3-item core, there are many possible component routes/combinations to get the end result.

These combinations all have different "power curves", with peaks/troughs that strongly influence strength. On top of that, Ryze's recall timings have a huge impact. I will plot these out soon enough, but I need to explain some important things first!


Context

When doing build calculations, assumptions are extremely important. I have made many of them.

– I calculated this using a gold income of roughly 6 cs/min. This is quite low (I chose this because it was average for all ranks). If you assume a higher income, spikes will change and the timeline will be shortened.

– I made many adjustments to gold values. AP alone doesn't capture total "combat power", so I converted other stats into gold (and then an equivalent amount of AP) to get a better representation of how strong Ryze is at a particular point.

Health has a base value of 1.4 gold, and Armor has a base value of 20 gold. This means that 1 Armor is roughly interchangeable with 7.5 Health.

However, this isn't exactly true! If the stats were actually interchangeable, then 1 point of extra Armor and 7.5 points of Health should grant similar eHP. For Ryze, they don't. Here are the points where the relative gold values are accurate (compared to Ryze's base stat growth trajectory):

5zpl0x87plg61 - Looking at Ryze's build power curves and their interactions with recall frequency

https://preview.redd.it/5zpl0x87plg61.png?width=600&format=png&auto=webp&s=3cf050f9f90fb1473d8f55d4952b48cdf072e537

It might be more intuitive to view a graph of the marginal eHP difference itself. 7.5 HP starts losing out to Armor post-level 5 without other bonus health/resistances:

https://preview.redd.it/5t1n56u7plg61.png?width=600&format=png&auto=webp&s=ae0f18c790ade847351d6b6a547176b9eba420e4

I have accounted for this by shifting value between the stats. If Armor grants more eHP than Health, I place proportionally higher gold value on it at that particular time in the graph. If you don't want to accept this, keep in mind that the Ruby/Kindlegem spikes (and potentially Seeker's rushes too) are smaller than they would be under constant gold values.

I have given Omnivamp a value of 80 gold. I think that the "official" derived value of 40 gold doesn't make sense. I'm trying to derive a reasonable value, but I have to set an arbitrary one for now.

Magic Pen = 80 gold; same reason as Omnivamp. I don't think that 1 point of flat pen is worth only 2.17 AP. Is Luden's equally good if the Mythic passive is 11 AP per Legendary rather than 5 flat pen? Certainly not. I think 80 is closer to the actual power of flat pen rather than 40.

Luden's "Echo" passive (burst + movespeed) = 668 gold, based on assumptions from here.

I have avoided the Everfrost active entirely in gold calculations, since I wasn't confident in pricing it out. I'm using the current PBE build path.

Stopwatch gets 650 gold value; since I kept a static component order (Seeker's -> Fiendish -> Stopwatch), the low Zhonya's combine cost leads to both Stopwatch and the completed Zhonya's active coming in on the same recall. I give it 650 gold (stopwatch's value) on that base, and I add extra gold value to later spikes (assuming Zhonya's gets a useful activation, worth 650 gold, every 5 minutes).

I lowered the gold value of Ability Haste to 80% of its original amount. While it is valuable on Ryze, it is not efficient as a damage amp due to Ryze's prominent cast times. EQ has 0.5 seconds that Ability Haste doesn't affect, and this gets used frequently (along with W combos that have 0.75 seconds of casting). The actual % decrease is arbitrary; if I revisit this, I will calculate it so that it actually reflects the inefficiencies.

I didn't want to create 4x the work by swapping the different boots Ryze uses. Therefore, I came up with a "Generic Boots" item. This is 1100 gold, and it gives enough flat AP to be 140% gold-efficient overall.


Issues affecting accuracy:

Due to time constraints and the limits of my spreadsheet mechanics, there are flaws.

– As mentioned earlier, static component ordering doesn't fully reflect the versatility/options for specific build paths.

– There's always the potential for human error. I often make mistakes, and I expect that I will find something as soon as I submit.

– The gold values I use aren't infallible; I might be wrong about some assumptions, and stats like penetration change with opponent resistances. Stasis actives are skill-intensive, and I might overestimate how well the average player uses it by going with the default value.

– You can't swap Liandry's in seamlessly (there are a lot of complications with appraising the burn and the different build path). I have excluded it here. You can draw some rough comparisons between Zhonya's and Banshee's within a particular build path, since sitting on Seeker's vs. Verdant has a similar dynamic.

– As mentioned earlier, my gold income assumptions are on the lower side.

– The "Generic Boots" item doesn't fully reflect the situational power of all the actual choices.


The Builds

These are the builds I looked at. I chose Tear or Sapphire Crystal start based on what made sense for the specific build; this doesn't change very much.

Standard (Luden's)Full Luden's (Boots after LC)Full Seraph'sFull Zhonya's
Luden's Armguard Rush 1LC into Seeker's, Boots afterFull Seraph'sRest of Zhonya's
Luden's Armguard Rush 2T1 Boots into Seeker'sLost Chapter + Finished BootsFull Luden'sFull Seraph's + Rest of Zhonya's
Luden's Boots RushGeneric BootsFull Luden'sFull Seraph'sFull Zhonya's
Luden's Boots Rush + Seeker'sGeneric Boots into Seeker'sFull Luden'sFull Seraph'sRest of Zhonya's
Luden's LC Sit + Boots RushGeneric Boots into Lost ChapterFull Seraph'sRest of Luden'sFull Zhonya's
Luden's LC Sit + Armguard RushT1 Boots + Seeker'sLost Chapter + Generic BootsFull Seraph'sFull Luden's + Rest of Zhonya's
Luden's LC Sit + Quick Seraph'sT1 Boots + Lost ChapterFull Seraph'sGeneric Boots + Full Luden'sFull Zhonya's

Luden's + Zhonya's 2nd, Boots RushGeneric BootsFull Luden'sFull Zhonya'sFull Seraph's
Luden's + Zhonya's 2nd, Armguard RushT1 Boots + Seeker'sFull Luden'sRest of Zhonya'sFull Seraph's
Luden's LC Sit + Zhonya's RushT1 Boots + Seeker'sLost ChapterRest of Zhonya'sSeraph's + Rest of Luden's

Replace "Luden's" with "Everfrost" to get the other half.


Plotting Powerspikes

As mentioned before, I converted combat-related stats into flat AP to get a "combat power statistic". This is not some in-game value.

In the graphs below, I've plotted the distance from the average spike at the minute. For example, if a particular build hits 50 at 18 minutes, that means the build's "combat power" spike is 50 higher than the average. If a graph goes from -50 at 13 minutes to +50 at 18, that does not represent a +100 combat power increase. The values are all relative.

The builds are split into three sections (for legibility and convenient comparisons); however, the average spike values are taken across all builds. This means that each set of three graphs shares the Y axis, allowing for some rough comparisons (again, the flaws/uncertainties in my calculations make it difficult to compare exact spikes).

https://preview.redd.it/2ekms4b9olg61.png?width=1059&format=png&auto=webp&s=cc56f8cb00940828274563a06adac1e29d09f03c

3.008.0013.0018.0023.0028.0033.0038.00
Std L12.411.44-14.03-32.1546.2363.53-44.15-5.00
L A R 112.41-4.70-22.24-6.2263.81-29.1833.46-19.06
L A R 2-2.48-3.626.94-10.9054.44-10.7915.07-0.67
L B R-2.4810.73-7.12-38.0434.4461.28-44.15-5.00
L B R+ S-2.48-11.6124.55-32.3154.44-29.1833.46-19.06
L LC Sit + B R-2.4810.7318.78-18.04-8.1466.11-44.15-5.00
L LC Sit + A R-2.48-3.621.043.20-27.4610.1456.04-19.06
L LC Sit + Q S-2.4817.65-55.2767.17-26.2266.11-29.15-5.00​

qgmyvb3aolg61 - Looking at Ryze's build power curves and their interactions with recall frequency

https://preview.redd.it/qgmyvb3aolg61.png?width=1053&format=png&auto=webp&s=3914786cb1e789701e4ca7872cb86e5beb217fd3
3.008.0013.0018.0023.0028.0033.0038.00
Std E12.411.4416.26-8.31-59.3345.14-44.15-8.39
E A R 112.41-4.70-22.2422.87-16.70-29.1815.07-22.45
E A R 2-2.48-3.621.0425.54-39.33-29.1815.07-22.45
E B R 1-2.4810.7323.17-20.10-59.3345.14-44.15-8.39
E B R + S-2.48-11.6124.5510.03-39.33-29.1815.07-22.45
E LC Sit + B R-2.4810.7318.78-18.0416.25-28.10-44.15-8.39
E LC Sit + S R-2.48-3.621.043.20-27.4612.48-16.12-22.45
E LC Sit + Q S-2.4817.65-55.2767.17-1.82-28.10-44.15-8.39​

https://preview.redd.it/h165g1qaolg61.png?width=1044&format=png&auto=webp&s=eb8ddb3b715364a69b228dd7b1f6a7033a186c12

3.008.0013.0018.0023.0028.0033.0038.00
L + Z2, B R-2.4810.73-7.12-32.1544.852.652.2631.32
L + Z2, A R-2.48-3.621.04-16.8054.44-16.092.2631.32
L LC Sit + Z R-2.48-3.621.04-3.3515.30-38.4241.5857.30
E+ Z2, B R-2.4810.7332.98-29.91-48.9210.022.2612.93
E + Z2, A R-2.48-3.621.0425.54-39.33-8.732.2612.93
E LC Sit + Z R-2.48-3.621.047.4115.30-38.4254.6837.51​

a8mfuabcolg61 - Looking at Ryze's build power curves and their interactions with recall frequency

https://preview.redd.it/a8mfuabcolg61.png?width=1144&format=png&auto=webp&s=eb983aacfd75570514bd729403b30edfe6643497
Загрузка...
3.007.0011.0015.0019.0023.0027.0031.0035.0039.00
Std L12.4112.02-52.3134.13-58.2665.387.9420.92-2.90-13.71
L A R 112.4112.02-26.65-51.7758.2538.27-32.0650.51-12.27-23.08
L A R 2-2.48-13.93-0.8345.773.8111.51-32.0650.51-12.27-4.69
L B R-2.485.1137.95-38.9043.64-48.327.9418.67-2.90-13.71
L B R+ S-2.4821.42-42.9640.76-18.2633.58-32.0650.51-12.27-23.08
L LC Sit + B R-2.485.1137.95-53.001.7411.00-12.0643.51-2.90-13.71
L LC Sit + A R-2.48-13.93-0.8333.97-38.26-8.3267.2613.09-12.27-23.08
L LC Sit + Q S-2.482.52-0.70-13.0021.06-7.08-12.0658.51-2.90-13.71​

https://preview.redd.it/dmbxotgdolg61.png?width=1119&format=png&auto=webp&s=7e1f35f1f4a9979ae95231be614cf249db3a4449

3.007.0011.0015.0019.0023.0027.0031.0035.0039.00
Std E12.4112.02-52.3142.37-12.37-40.197.942.53-2.90-17.10
E A R 112.4112.02-26.65-51.7765.27-20.19-32.0632.12-12.27-26.47
E A R 2-2.48-13.93-0.8333.97-15.92-20.19-32.0632.12-12.27-26.47
E B R 1-2.485.1137.95-30.66-10.13-48.327.942.53-2.90-17.10
E B R + S-2.4821.42-42.9640.76-15.92-20.19-32.0632.12-12.27-26.47
E LC Sit + B R-2.485.1137.95-53.001.7435.405.88-68.65-2.90-17.10
E LC Sit + S R-2.48-13.93-0.8333.97-38.26-8.3269.60-59.07-12.27-26.47
E LC Sit + Q S-2.482.52-0.70-13.0021.0617.325.88-68.65-2.90-17.10​

grce8b4folg61 - Looking at Ryze's build power curves and their interactions with recall frequency

https://preview.redd.it/grce8b4folg61.png?width=1047&format=png&auto=webp&s=f18128c6fc371194f40380a9a6396dbb96888052
L + Z2, B R-2.485.1137.95-33.0043.64-37.902.12-33.7913.6852.11
L + Z2, A R-2.48-13.93-0.8333.97-18.2633.58-7.25-43.1713.6852.11
L LC Sit + Z R-2.48-13.93-0.83-7.27-3.5734.4418.69-32.12-6.3278.09
E+ Z2, B R-2.485.1137.95-30.66-10.13-37.902.12-26.4313.6833.72
E + Z2, A R-2.48-13.93-0.8333.97-15.92-20.19-7.25-35.8013.6833.72
E LC Sit + Z R-2.48-13.93-0.832.54-2.6234.4418.6912.8442.57-22.47​

https://preview.redd.it/5wm94pwfolg61.png?width=1153&format=png&auto=webp&s=0bccf68ff8813803801dbd09bd724bba9a9c7752

3.006.009.0012.015.018.021.024.027.030.033.036.0
Std L12.4-24.414.74.78-1.21-38.372.2-49.330.455.1-44.0-6.80
L A R 112.4-24.48.60-3.43-47.133.5-16.877.2-29.5-27.964.0-20.8
L A R 2-2.48-8.15-6.6325.720.0-38.20.5950.5-29.5-9.6045.6-2.47
L B R-2.4816.78.69-14.2-7.11-38.260.4-49.330.452.8-44.0-6.80
L B R+ S-2.4816.7-13.6-13.129.2-38.2-21.472.5-29.5-27.964.0-20.8
L LC Sit + B R-2.4816.78.69-14.2-21.221.717.8-9.31-29.577.7-44.0-6.80
L LC Sit + A R-2.48-8.15-6.6319.814.1-18.2-1.4830.010.4-87.986.5-20.8
L LC Sit + Q S-2.4814.2-7.71-36.418.741.0-0.24-9.31-29.592.7-44.0-6.80​

uqrbcergolg61 - Looking at Ryze's build power curves and their interactions with recall frequency

https://preview.redd.it/uqrbcergolg61.png?width=1166&format=png&auto=webp&s=150b9425c0ede5dc471dee54ec841ae4f255e488
3.006.009.0012.015.018.021.024.027.030.033.036.0
Std E12.4-24.414.74.787.037.61-33.3-49.330.436.7-44.0-10.1
E A R 112.4-24.48.60-3.43-47.162.61.15-21.1-29.5-27.945.6-24.2
E A R 2-2.48-8.15-6.6319.814.14.06-21.4-21.1-29.5-27.945.6-24.2
E B R 1-2.4816.78.69-14.21.131.71-33.3-49.330.436.7-44.0-10.1
E B R + S-2.4816.7-13.6-13.129.24.06-21.4-21.1-29.5-27.945.6-24.2
E LC Sit + B R-2.4816.78.69-14.2-21.221.717.8-6.9710.4-34.4-44.0-10.1
E LC Sit + S R-2.48-8.15-6.6319.814.1-18.2-1.4830.012.7-47.9-25.5-24.2
E LC Sit + Q S-2.4814.2-7.71-36.418.741.0-0.24-6.9710.4-34.4-44.0-10.1​

https://preview.redd.it/cm65gcdholg61.png?width=1111&format=png&auto=webp&s=81d5236e6dd7db2c3e8b97b9e4a6eb11e7bddb8e

3.006.009.0012.015.018.021.024.027.030.033.036.0
L + Z2, B R-2.4816.78.69-14.2-1.21-38.250.8-4.62-0.070.422.0629.5
L + Z2, A R-2.48-8.15-6.6319.814.1-38.2-21.472.5-4.76-8.952.0629.5
L LC Sit + Z R-2.48-8.15-6.6319.8-27.116.410.5-18.541.12.09-17.955.5
E+ Z2, B R-2.4816.78.69-14.21.131.71-42.95.19-9.887.792.0611.1
E + Z2, A R-2.48-8.15-6.6319.814.14.06-21.4-11.3-14.5-1.592.0611.1
E LC Sit + Z R-2.48-8.15-6.6319.8-17.317.310.5-18.541.12.09-4.8435.7​

Conclusions

After staring at the graphs, you might be wondering: what the hell are you supposed to take away from this? Based on my assumptions, there are some main results to consider:

– Luden's builds have significantly more volatile peaks/troughs. This is to be expected given the smoother Everfrost build path.

– With 4 or 3 minutes in between recalls), rushing boots or boots + seeker's respectively will invert the standard Luden's power curve. If this holds for higher income assumptions, players could use this to plan spikes for objective fights in coordinated games.

– Rushing into Seraph's after Lost Chapter is suboptimal if you are recalling frequently. The powerspike isn't attractive enough to deal with troughs that the other paths don't always have. With infrequent recalls, the relatively large powerspike is worth considering.

– If you build Zhonya's second after Luden's, it seems like completing Luden's (rather than sitting on Lost Chapter) tends to be better. On the other hand, for Everfrost, sitting on Lost Chapter (especially with more frequent recalls) spikes more consistently than building the full Mythic to start. Factoring in the Everfrost active could switch this up, but if you are unable to hit it then this is how it is.

– Everfrost's Armguard Rush 2 more consistently approximates the standard power curve, while Armguard Rush 1 starts to diverge and get more volatile with more frequent recalls.

– Etc., considering specific timeframes you are interested in

Source: Original link


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