# Napkin Math: Temporary Intellect and its value

Update: Spreadsheet had some really bad errors that I needed to correct. Numbers have been updated and look much more reasonable.

I wanted to do some brief napkin math today none of which is entirely new given my previous mathematical noodling. I wanted to look at on use intellect compared to static intellect as far as mana regen goes.

In the past we have shown that 1 raw unmodified point of intellect yields roughly 1.22 mana regen or .61 mp/5 factoring in intellect based regen only and distributed increased starting mana over the duration of the fight. When a burst intellect trinket is used I am going to make the assumption it is timed with Innervate as that yields the highest percentage return provided that is what it is being used for. When activated these benefits usually last for 15, 20, or 25 seconds so we can analyze each of these scenarios.

Over the duration of the buff you will gain mana return through Revitalize, Replenishment, and Innervate. The return for each scenario is the following:

Revitalize:

Procs- 15 seconds (1.25 procs, 2.5%), 20 seconds (1.67 procs, 3.33%), 25 seconds (2.08 procs, 4.17%)

Return per 1 raw intellect- 15 seconds [.025*19.28=.482], 20 seconds [.033*19.28=.636], 25 seconds [.0417*19.28=.804]

Replenishment:

Return per 1 raw intellect- 15 seconds [.015*19.28=.289], 20 seconds [.02*19.28=.386], 25 seconds [.025*19.28=.482]

Innervate:

Return per 1 raw intellect- 3.856 (only every 3 minutes)

Your total return per 1 raw intellect is then (using CD times that line up with innervate only):

15 seconds:

1.5 minute CD (2x over 3 minutes) – 5.398 mana total or 0.15 mp/5 [.3 mana regen]

3 minute CD – 4.627 mana total or .129 mp/5 [.26 mana regen]

20 seconds:

1.5 minute CD (2x over 3 minutes)  – 5.9 mana total or .164 mp/5 [.33 mana regen]

3 minute CD – 4.878 mana total or .136 mp/5 [.27 mana regen]

25 seconds:

1.5 minute CD (2x over 3 minutes)  – 6.428 mana total or .179 mp/5 [.357 mana regen]

3 minute CD – 5.142 mana total or .143 mp/5 [.286 mana regen]

Spirit regen is a little trickier. Generally speaking the linear approximation for spirit regen is the following:

SR = ((Modified_Intellect*.000125)+.55))*Spirit

1 Point on unmodified intellect gives us roughly .19 mp/5 [.38 mana regen] at 7000 buffed intellect and 2600 spirit (YMMV)

To evaluate things we’ll need to look at uptime.

15 second duration:

1.5 minute CD (16.7% uptime) – .063 mana regen or .031 mp/5

3 minute CD (8% uptime) – .032 mana regen or 0.016 mp/5

20 second duration:

1.5 minute CD (22.2% uptime) – .085 mana regen or .0425 mp/5

3 minute CD (11.1% uptime) – .0422 mana regen or 0.021 mp/5

25 second duration:

1.5 minute CD (27.8% uptime) – .106 mana regen or .053 mp/5

3 minute CD (13.9% uptime) – .053 mana regen or 0.027 mp/5

The handy spreadsheet of equivalency becomes, depending on buff duration and cooldown, the following:

15 second duration, 1.5 minute cooldown: 4.40 temporary int = 1 static int

15 second duration, cooldown between 1.5 and 3 minutes: 5.48 temporary int = 1 static int

20 second duration, 1.5 minute cooldown: 3.86 temporary int = 1 static int

20 second duration, cooldown between 1.5 and 3 minutes: 5.09 temporary int = 1 static int

25 second duration, 1.5 minute cooldown: 3.46 temporary int = 1 static int

25 second duration, cooldown between 1.5 and 3 minutes: 4.72 temporary int = 1 static int

Fiery quintessence for example gives 1149 temporary intellect for 25 seconds with a 1.5 minute cooldown. In a perfect world (not always the case as we know) it gives roughly the equivalent of 332 static intellect. You may only see a percentage of that as you may be forced to not start its rotation until your first innervate losing out on some time. There are some highly situational addition benefits such as: should mana tide be dropped at roughly the same time as your innervate/trinket activation then you will raise your maximum mana significantly and have the option to spend any mana returned over your normal maximum as it comes in. This would only be ideal during high damage moments.

There is something to be said for burst on demand though and the added spellpower granted by the on-use is not something I can put a value on as far as this study is concerned. I’m going to hold off going into a more in depth analysis of this trinket at this time as things get a lot more complicated when you try to compare it to other options such as Jaws of Defeat, Eye of Blazing Power, Alchemist Stone given the secondary benefits and individual player needs (spirit, haste, reforged secondary stats etc.).

Note: Please be aware that this analysis applies primarily to endgame 10 and 25 man raids. For people who are focusing more on 5 man content be aware that static intellect becomes significantly stronger as the duration over which the increased starting mana is distributed is smaller (as well as less chances for activating the item).

### 3 responses to “Napkin Math: Temporary Intellect and its value”

1. Ellannan

Good post, thanks for the numbers. My head has exploded on numerous occasions trying to map all that out. One minor correction: I believe the formula for converting Fiery Quintessence to a static average is (1149*25)/90 = 319 average intellect.

I’m still “stuck” with the Tsunami+Stone combo, and have been looking over the numbers for weeks now trying to figure out whether a switch to either of the rep trinkets would be an upgrade. I’m still not really certain, and I’ve seen lots of lovers and haters across the net. I suppose I should just give them a try and compare the logs, but I’ve grown really comfortable with not having to worry about trinket activation…

• Jar

That’s its average if you’re purely looking at it from a throughput standpoint. For regeneration it loses the initial mana “regen” portion of the int value, but fully retains the interaction with Innervate so the weighting won’t work out quite so simply.