# Hammer of Math: Riptide Arithmetic

Last week we looked over a few considerations for T’au forces including the efficacy of Drones and Saviour Protocols, what scenarios it was preferable to use the Automated Targeting System, which weapon was preferable for the XV88 Broadside, and which main gun was preferable for the XV104 Riptide. This week we’re going to examine when it’s in the best interest of the T’au player to allocate a wound to a Riptide or apply Saviour Protocols.

This is also the start of a slightly different approach for Hammer of Math. Rather than put together comprehensive articles, we’re going to drill down on specific questions and maintain a more concise format. If you have any ideas or questions that we should answer, we’d love to hear about them! We’ve put together a form for you to submit your ideas and requests. Thank you so much for reading!

For a full overview of the Riptide, the rules regarding Savior Protocols, and the impact of this ability on damaging a vehicle we highly recommend you check out the Start Competing: T’au Empire article as well as last week’s Hammer of Math. When fielding a Riptide protected by Shield Drones, there are two major questions that must be addressed when it’s being shot at, typically in this order:

1. Should the T’au player activate Nova Shield for a 3+ invulnerable save at the expense of a mortal wound?
2. Assuming the Riptide was targeted, does the T’au player activate Saviour Protocols or take the wound on the Riptide?

We’ll tackle these in reverse order since the final outcome dictates the other answers.

### Risk

Not the board game (which is fun), but the concept. In the vast majority of real world situations, particularly ones dealing with safety or expenses, there is rarely an absolutely correct answer. Often the possible outcomes exist on a spectrum. Risk management is the process of understanding, analyzing, and mitigating risk so that the spectrum of possible outcomes is as favorable as possible while balancing the benefits and consequences. Risk itself is the function of probability and consequence, and generally focuses on negative outcomes. A high-risk outcome is one with a high probability of occurring and producing a highly negative result. A low-risk outcome is one that has a low probability of occurring and a minor outcome. Working around high-risk and low-risk outcomes is relatively easy; the tricky part is in the middle, balancing the medium-risk options. Things with really bad consequences but low likelihood, or minor consequences but high likelihood. You apply risk management when you understand the risks and either accept the risk or mitigate it through some kind of action intended to reduce the probability of occurrence or the impact of the consequence.

You make risk management decisions every time you play Warhammer 40K. It starts off with your choice of army list; you look at the meta and the probability of what you might face and tailor the list to mitigate the impact. Perhaps you bring two or three of a critical unit, or leave out a unit that’s vulnerable to something prevalent, or create an entire list built around countering a popular force you might see a lot of. You also make risk management decisions with every decision you make in the game. Is the benefit of exposing a unit and getting a better shot worth the increased chance of it being destroyed if you fail to kill something? Is it worth taking a wound on the improved save of a Riptide instead of sacrificing a Shield Drone?

The reason I bring this up is because the kinds of questions we’ll be answering in Hammer of Math are not always going to have obvious answers or even singularly correct ones. It’s up to you as the player to manage your own risk and balance the probabilities and consequences. The goal of these articles is to provide you with the information needed to make that decision.

### When Should You Use Saviour Protocols?

In order to answer this question we need to first establish our desired outcome. For the purpose of this exercise our goal is to minimize the amount of damage dealt to any unit. The Riptide has a 2+ armour save complemented by either a 5+ or 3+ invulnerable save. Because Saviour Protocols occurs after the wound roll is made the only values that matter at that point are AP and damage. We address this question as an expected value problem; look at the distribution of wounds as the product of the weapon damage, the probability of the wound being transferred to the Drone (if appropriate), and the probability of the wound being disregarded through a save or FNP.

The chart above compares the expected wounds for a Riptide that is not under Nova Shield. The columns are armour penetration; the Riptide has a 5++ so any value of -4 or lower is irrelevant. If the Riptide is in cover then simply shift the AP value to the left. The rows are for potential damage values; against weapons with variable damage (1d6, 1d3, etc) use the expected value based on the die roll. The expected value for 1d3 roll is 2, and the expected value for a 1d6 roll is 3.5. The colored chart on the right indicates which result is optimal; since Shield Drones are less valuable than Riptides in the event of an even (white) reading the optimal solution is to apply Protocols and risk killing a drone. For 1 damage weapons the Riptide save is preferable up until the result is a 5+. Things get more interesting on multiple-damage weapons with no AP (either because they’re AP 0 or AP -1 against cover). From a raw mathematical perspective the improved save of the Riptide makes it an optimal choice even against weapons that deal 2 or 3 damage. According to the math, by using Saviour Protocols you will eventually take more wounds in the form of dead drones than you would take wounds on the Riptide.

Of course the math is without context, and here the risk tolerance of the player becomes key. A three damage, no AP shot only has a 1/6 chance of getting through the armor on a Riptide but the consequence of failure is still three damage. If that hit causes the Riptide to become bracketed, or puts the Riptide in a position to be degraded should the T’au player choose to activate the Nova Reactor and receive a mortal wound, then the risk may be unacceptable high.

It’s important to consider what happens if the Riptide has a better save; would applying Nova Shield change anything?

The AP -2 and AP -3 columns are superfluous thanks to the 3+ invulnerable save, but they’re included for the sake of consistency (and because I already had the chart formatted for four columns). The AP 0 and AP -1 column are unchanged from the previous chart. When Saviour Protocols is available the primary benefit of Nova Shield is against AP -2 or better weapons which can be applied to the 3+ invulnerable save and have an increased chance of mitigating damage.

So when should Saviour Protocols be activated?

1. As the Riptide is vastly more important than the Shield Drones, Saviour Protocols should be activated when the incoming attack has a chance of degrading the profile of the Riptide. The T’au player should also consider the guaranteed mortal wound from activating the Nova Reactor before choosing to activate it. Richard Siegler from the 40K Competitive Facebook group brought up a great point that the degradation can easily be mitigated using Stimulant Injector for 1 CP, so if you need to save a Shield Drone to capture an objective or something it’s viable to tank the wound on the Riptide.
2. Saviour Protocols should be used against all multi-damage attacks with an effective (including cover) AP modifier of -1 or more.
3. Taking the wound on the Riptide is mathematically more effective at reducing damage against attacks that deal or less damage with no armour penetration, and 1 damage attacks with an effective AP of 0, -1, or -2.
4. When Nova Shield is active the 3++ makes it mathematically more effective to take the wound on the Riptide against 1 damage attacks with an AP of -3 but otherwise does not change anything.

### When is Nova Shield appropriate?

In answering the previous question, we also gained some insight into Nova Shield. Under the protection of Saviour Protocols the 3++ gained from Nova Shield largely goes unused; there remains a 1/6 chance that a shot will pass through but as you can see in the chart below the effect is only significantly pronounced against high damage, high AP shots.

Whether or not the 19% to 27% reduction in total damage from something like a successful wound from a Heavy Laser Destroyer is worth the loss in firepower from not using Nova-charge is a question of risk management on the part of the T’au player. Where Nova Shield obviously shines is against those threats after the Shield Drones have been wiped out. Reducing the total wounds dealt has a cumulative effect as the opponent is forced to allocate additional attacks. Against threats which would otherwise provide no save going from a 5++ to a 3++ increases the number of effective wounds by 80%.

### Conclusions

Saviour Protocols is an incredibly powerful ability and a key part of competitive T’au play, especially when combined with the significant amount of firepower that can be produced by a Riptide (or three). We see from the analysis that, in general, it’s best to utilize Saviour Protocols unless the incoming attack deals a single damage and has a low AP. Saviour Protocols is so powerful that it almost renders Nova Shield superfluous; while the 3++ is extremely beneficial after the Shield Drones have been stripped away the opportunity cost of not using Nova-charge makes it seem less viable so long as a Drone can absorb the damage 83% of the time. The end result is a lot of toughness and flexibility that remains viable even with the prevalence of Space Marines.

If you have any comments, feel free to drop a note in the comments below or email us at contact@goonhammer.com. If you have any questions that you think would be a great topic for Hammer of Math we’d love to hear about them! We have a form set up that you can submit your questions here.