Guild Wars 2

The Guardian Virtue line increases +5% recharge rate of your virtues for each 5points spend.
However this is not true, the +% recharge rate is not calculated correctly.

Note: Table values are rounded up for simplicity

Lets look at 10% intervals what the cooldown actually indicates:

• Recharge Rate……: |Base|10%|20%|30%|
• Virtue of Justice….: | 30 | 27 | 24 | 22-23 |
• Virtue of Resolve..: | 60 | 54 | 49 | 45-46 |
• Virtue of Courage: | 90 | 81 | 74 | 68-69 |

Let’s look at the actual second reductions for each 10% intervals:

• Recharge Rate……: |Base|10%|20%|30%|
• Virtue of Justice….: | 0 | 3 | 3 | 1-2 |
• Virtue of Resolve..: | 0 | 6 | 5 | 3-4 |
• Virtue of Courage: | 0 | 9 | 7 | 5-6 |

The correct values should be instead:

• Recharge Rate……: |Base|10%|20%|30%|
• Virtue of Justice….: | 30 | 27 | 24 | 21 |
• Virtue of Resolve..: | 60 | 54 | 48 | 42 |
• Virtue of Courage: | 90 | 81 | 72 | 63 |

We can clearly see that beyond the first 10%,the recharge rate is absolutely wrong. More noticeable with the virtue of courage at 30% instead of being 63 seconds of cooldown we get 69, which is incorrect and 6seconds of difference is a lot in a fight.

Are there diminishing returns or something we are not aware of?

Have you timed the “real” recharge time?
Maybe that, as said in the wiki, the reduction is not properly reflected in the tooltip.

These are the “real” recharge times, I’m aware that the reduction is not reflected in the tooltip…

Math is then correct, but not in an intuitive way.

The traits add to the Recharge rate. But they don’ REDUCE THE CD.

So, you have to reverse the numbers.
Let’s try with Virtue of Courage.

With no traits, you get your virtue back in 90 seconds, i.e. Recharge Rates is:
1/90 = 0.011111 per second

Then you add 10 traits, and that is added to the RECHARGE RATE:
0.011111 * 1.1 = 0.01222 per second
That means you need (1/0.01222) seconds = 81s
If you add 20 traits:
0.011111 * 1.2 = 0.01333 per sec
You need (1/0.01333) = 75s
If you add 30 traits:
0.011111 * 1.3 = 0.01444 per sec
You need (1/0.01444) = 69s

I guess the difference is due to them adding each increment AFTER the previous one:
10 traits, RECHARGE RATE:
0.011111 * 1.1 = 0.01222 per second
20 traits, the previous +10%:
0.01222 * 1.1 = 0.013444
1/0.013444 = 74s
30 traits, the previous + 10%
0.013444 * 1.1 = 0.147888
1/0.014788 = 67.8s (this one doesn’t fit well)

With this second formula, however, all other virtues are correct, while this one differs in 1s in the last trait (maybe an inexact misuration).

I suspected it was something like that but went with recharge rate as cooldown reduction.
Your first formula makes sense.Thanks for pointing that out.

I don’t think it’s the second formula because if they are adding each increment after the previous one then a new calculation should be made for each 1%,because you can add points one by one in the trait trees.