Sometimes, I get the feeling that people don't understand how bad the Ultimatum is. The thing is, since it behaves exactly like stock, it's easy to get very exact comparisons between the two. Which is what this is. A look at the Ultimatum, from a mathematical lens.
An important concept to understand going into this is opportunity cost. Google defines it as "the loss of potential gain from other alternatives when one alternative is chosen". In this context, opportunity cost will usually be referring to stock, as 1) it's stock and 2) the Ultimatum plays identically to stock, meaning there is no potential for easier gain; if a player hit a shot with the Ultimatum, they'd've hit it with stock and vice versa.
Pipes Only[]
Fun Fact: 6 stock pipes outdamage 7 Ultimatum pipes, assuming the first one didn't mini-crit.
First subject of discussion: only pipes. Here, the Ultimatum always loses. Every time a pipe hits, that's 35 potential damage lost, and every time a mini-crit pipe hits that's 12.25 potential damage lost. This doesn't really matter on light classes, as two pipes are required either way, but it definitely does matter on every other matchup. Troopers require three pipes instead of two, Brutes require four pipes instead of three (five instead of four if he's revved), and if Doctor regenerates at all between the first connection and the second connection then a third pipe is needed. Every shot just puts you further behind stock.
Other Weapons[]
This is the point at which the Ultimatum is believed to shine, when in reality, it doesn't. Look at this table showing the difference in damage between stock and the Ultimatum.
| Pipe # | Stock's damage | Ultimatum's damage | Damage difference | Alternate damage for 0 diff |
|---|---|---|---|---|
| 1 | 100 | 65 | 35 | 100 |
| 2 | 200 | 152.75 | 47.25 | 135 |
| 3 | 300 | 240.5 | 59.5 | 170 |
| 4 | 400 | 328.25 | 71.75 | 205 |
| 5 | 500 | 416 | 84 | 240 |
| 6 | 600 | 503.75 | 96.25 | 275 |
In particular, notice the last two columns. The first is the difference between stock's total damage and the Ultimatum's total damage. Obviously, it increases with every pipe. But the column I'd really like to bring notice to is the last one. It describes the total damage required from other sources in order to bring the difference to zero (as I feel attributing extra damage caused by the Ultimatum's mini-crits to the Ultimatum is fair). Now, one may realize that these values are quite high, relative to the health of most things in this game, which is in fact a point I would like to bring attention to. If one were to add up the total damage that the hypothetical target would be taking, they would find themselves with a table like this.
| Pipe # | Ultimatum's damage | Damage difference | Alternate damage for 0 diff | Total damage taken by target |
|---|---|---|---|---|
| 1 | 65 | 35 | 100 | 200 |
| 2 | 152.75 | 47.25 | 135 | 335 |
| 3 | 240.5 | 59.5 | 170 | 470 |
| 4 | 328.25 | 71.75 | 205 | 605 |
To put it simply, the target needs at least the health of the fifth column in order to "break-even", and column four is the damage that needs to come from other sources in order to hit that break-even point. This means the following:
- ...a target needs at least 200 total health in order for it to be possible for the Ultimatum to do more damage than stock, assuming that the player only bothers with a single pipe.
- ...the Ultimatum will never be able to break even on targets with a total health less than or equal to 200.
- ...using two or more Ultimatum pipes greatly increases the break even point.
- ...approximately half the damage output has to be from other sources in order to break even.
As a reminder, the break-even point is the point at which the Ultimatum's potential damage exceeds stock's potential damage.
Versus Healing[]
Over the course of the past section I've thrown around the term "total health". While this can just refer to the target's maximum health, what if they have overheal? What if they are healed during the fight? Total health is inclusive of this. Total health is the total damage ultimately required to defeat the target. An example; presume a Trooper is being pocketed and is at full overheal, and is defeated over the course of exactly 5 seconds (from when he first took damage). His health may have never exceeded 300, but given the Medigun's 24 HP/s, would have been healed 120 health throughout the fight. In this case, his total health would be calculated as 420.
The Ultimatum is able to capitalize off of this, being able to break even using a majority of the class's base health, then take advantage of the mini-crits for the remaining health. However, this does not solve the Ultimatum's problems. After breaking even, most classes will not have much health remaining. Consider the following table of classes' health in relation to the break even point.
| Class | Health w/ overheal | Health after break-even |
|---|---|---|
| Flanker | 187.5 | N/A |
| Trooper | 300 | 100 |
| Arsonist | 262.5 | 62.5 |
| Annihilator | 262.5 | 62.5 |
| Brute | 450 | 250 |
| Mechanic | 187.5 | N/A |
| Doctor | 225 | 25 |
| Marksman | 187.5 | N/A |
| Agent | 187.5 | N/A |
The only classes who have a significant amount of health remaining are Trooper and Brute, with the rest having so little that I'd argue it doesn't really matter whether or not they were Lemonade'd. This leads to active healing, such as pocketing, picking up a medkit mid-battle, milk, being the main contributor of extra health. The one which provides it excessively is pocketing. In this case, I think it's appropriate to assume that total health is the class's base health plus full overheal and 6 seconds of healing (144 HP), as the Ultimatum only lasts for 6 seconds (which is a whole other point that I haven't touched on— the Ultimatum doesn't last super long). From there, assuming this new total health, the previous table would now look like this.
| Class | Total health | Health after break-even |
|---|---|---|
| Flanker | 331.5 | 131.5 |
| Trooper | 444 | 244 |
| Arsonist | 406.5 | 206.5 |
| Annihilator | 406.5 | 206.5 |
| Brute | 594 | 394 |
| Mechanic | 331.5 | 131.5 |
| Doctor | 369 | 169 |
| Marksman | 331.5 | 131.5 |
| Agent | 331.5 | 131.5 |
These new health values are more significant, and represent what I believe to be the truth of the Ultimatum: the only point at which the Ultimatum is able to exceed stock is when there are players being pocketed, and only after breaking even (at approximately 100 damage, if only a single Ultimatum pipe has been hit). The issue lies in the fact that Doctor isn't very common, and that it's extraordinarily rare for it to be advantageous outside of that scenario.
Conclusion[]
I don't think highly of the Ultimatum. I believe I was fairly gracious to it, as I did not consider...
- ...where the hundreds of damage to take advantage of the mini-crits comes from.
- ...the fact users cannot use their primary to break even.
- ...the fact the Ultimatum only lasts 6 seconds, requiring all of the information in this blog to restart if it were to expire.
I was ungracious to it in the fact that I did not consider splashing multiple enemies, as I do not believe that to be a common enough situation to be included as a legitimate upside, and that mini-crits do not have fall-off, as I believe that it's too difficult to deal enough damage to reach the thresholds from afar, between bullet spread and slow projectile speeds.
A quick recap, to serve as a TL;DR of sorts:
- The Ultimatum deals less damage than stock with pipes only, with the more pipes that are used making it perform even worse comparatively.
- When using other sources of damage, the other sources must deal more than 100 damage (before the boost) in order for the Ultimatum to have been more effective than stock.
- When using other sources of damage, the target must have at least 200 health to break-even in damage with stock.
- Realistically, the only case in which the Ultimatum has the opportunity to be more effective than stock is against a pocketed player.
The core issue with it is that its opportunity cost is just too high. It requires just as much aim to hit a pipe as stock, and as a result directly competes with it, when it just isn't good enough to keep up.