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Foreword
Some of you may have already come across and read one or more of my breakdowns here on LO. This is actually the first time I am doing it for something outside of Codex: Space Marines.
A friend of mine who leads an army of the same xeno scum you all go to battle with has grown unsure of whether to use holo-fields on his skimmers or not. This issue has been discussed thoroughly on the forum and yet no final judgement has been consented to. Several different approaches to holo-fields are offered by different Eldar commanders and it is hard to decide which path to follow.
But never have I seen anyone dish out some numbers to enforce his statement and add some hard data to back up his point. This is what the Math Cavalry is there for, so here I am breaking down stuff I have no right whatsoever to get involved with: Eldar witchcraft (note that all technology we don't understand must be witchcraft, from a Mon-Keigh's point of view). Time to delight your pointy ears with some math-hammer...
Introduction
Holo-Fields, the Eldar tank's personal lifeguard. Buy it and your skimmer will be indestructible. Is that so?
Holo-fields are very expensive and do not help you avoid damage, though the damage you will suffer will most probably be by far less serious. Many Eldar players have difficulties to decide whether these upgrades are worth their points cost or not.
For this reason I shall provide tables with numbers that show what exactly holo-fields accomplish for your tanks, give my recommendations, explain my reasoning and leave you to judge whether this makes any sense. Enjoy, all feedback and comments welcome!
Math-Hammer
First let me list the probabilities for different damage results for glancing and penetrating hits each with weapons of different AP values, namely weapons without an AP value, AP1 weapons, or weapons of AP2 through AP6. These probabilities are given for vehicles both with or without the holo-field upgrade. Note that weapons shot by a unit with the tank hunters special rule will advance one level, from AP- to AP2-6, from AP2-6 to AP1. Above AP1 just assume that the holo-field accomplishes even less - you will understand what this means soon enough.
This detailed view gives us too little information on a more global scale which is necessary to judge the upgrades effectiveness. I have thus combined the probabilities of the individual damage results to -hopefully- reasonable families: the inability to move (as expressed by crew stunned, vehicle immobilized, and of course vehicle destroyed or explodes), the inability to shoot (as expressed by crew shaken, crew stunned, weapon destroyed, or of course vehicle destroyed or explodes), and permanent damage (as expressed by weapon destroyed, vehicle immobilized, and of course vehicle destroyed or explodes). For each of these damage families I have assessed the adjustments to the probability of them happening with holo-fields compared to without.
[I am aware that spirit stones would reduce the inability to move by the crew stunned result. This will be dealt with later, but for the purposes of the following calculations the spirit stone upgrade has not been included. I am also aware that a weapon destroyed result does not keep the entire vehicle from firing, but it does eliminate the primary weapon, so for the purposes of these calculations, the weapon destroyed result has been interpreted as part of the inability to shoot damage family.]
Interpretation
When we try to ascertain what these numbers mean we have to keep in mind that not all of these situations occur equally. By the logic of the rules and my gaming experience, penetrating hits tend to happen a lot more often than glances against your Falcons and Fire-Prisms (unless you are versing Necrons), and most of these are AP2-6, the second most probably being AP1, and only few being AP-.
What we can see then is that holo-fields do not help at all help prevent the inability to shoot. All they do is ensure that the skimmers remain mobile and do not suffer permanent damage. This means that the benefit of holo-fields is that of being able to keep moving and surviving. Your unit will not be able to deal more damage, but it will be more likely to continue posing a target for your opponent to consider shooting at to disable it again every single turn. They will draw far more enemy firepower than units without holo-fields, but if the enemy has dedicated anti-tank units that couldn't accomplish much else anyways, this doesn't help at all.
Conclusion
Three units have the option of holo-fields.: Vypers, Fire Prisms, and Falcons.
Vypers
The holo-field is almost as expensive as the base cost of the vyper. I need not say much more. The benefits are generally definitely not worth the trouble in this case.
Fire Prisms
The holo-fields increase the base cost of this unit by a good 30%. This is about equal to the benefits conveyed by the holo-fields. The question is whether this is worth the trouble, and this can be assessed most easily when considerung the fire prism's battlefield role.
The fire prism is supposed to deal a hard-hitting alpha-strike. Thereafter it is often more or less disposable. Its range gives it the ability to stay out of range of most return fire anyhow. And its primary purpose will always be shooting, which it will most likely be unable to do anyways, so why bother. If its prism cannon is destroyed, the skimmer is virtually useless (barring some dirty tricks, some of which are explained in my landspeeder tactica), and if the crew becomes shaken or stunned the Fire Prism can't even combine shots with another Fire Prism. So unless you run a mechanized army with lots of skimmers to shoot at, the Prisms' higher chance of survival won't benefit you much. If you do, they may draw fire away from the rest of your units longer and the holo-field may be worth considering.
Falcon
Falcons are more a close-up type of tank, having lower-ranged guns than the Fire Prism, having more guns than the Fire Prism, and featuring transport capacity.
The Falcon thus actually benefits from still being able to move, it benefits more from remaining functional, and it isn't entirely robbed of its battlefield role when kept from firing, while also the weapon destroyed result will not make its entire shooting worthless.
For these reasons, holo-fields on Falcons make much more sense. Especially if they are used as transports and also outfitted with spirit stones that can further add to the ability to keep moving no matter the odds.
Summary
Sorry for being badly organized. I am very tired right now and shouldn't have begun writing this breakdown in the middle of the night. Nonetheless let me try to summarize what I think to be the essence of the truth about holo-fields...
Holo-fields convey very decent benefits, but these come at high cost.
They generally do not make sense on cheap vypers, because buying more vypers instead seems like a much more sensible option, increasing the chance of single vypers surviving while offering the enemy more targets and having more firepower to dish out.
Of the support skimmers, the holo-fields make the most sense on Falcons, especially if these are used to transport a hard-hitting unit to hotspots. In the latter case I recommend buying the holo-field, but generally I would suggest to invest the points elsewhere. The benefits are over-rated especially for fire support tanks, and unless you want to have your skimmers being harmless distractions for your enemy to disable anew every single turn but drawing fire away from the rest of your army, you will be much happier investing the points elsewhere. After all, vehicles -even with holo-fields- still are destroyed on a single lucky shot. The cheaper you keep them, the better for you. Redundancy is a better insurance than any upgrade can ever be...
Some of you may have already come across and read one or more of my breakdowns here on LO. This is actually the first time I am doing it for something outside of Codex: Space Marines.
A friend of mine who leads an army of the same xeno scum you all go to battle with has grown unsure of whether to use holo-fields on his skimmers or not. This issue has been discussed thoroughly on the forum and yet no final judgement has been consented to. Several different approaches to holo-fields are offered by different Eldar commanders and it is hard to decide which path to follow.
But never have I seen anyone dish out some numbers to enforce his statement and add some hard data to back up his point. This is what the Math Cavalry is there for, so here I am breaking down stuff I have no right whatsoever to get involved with: Eldar witchcraft (note that all technology we don't understand must be witchcraft, from a Mon-Keigh's point of view). Time to delight your pointy ears with some math-hammer...
Introduction
Holo-Fields, the Eldar tank's personal lifeguard. Buy it and your skimmer will be indestructible. Is that so?
Holo-fields are very expensive and do not help you avoid damage, though the damage you will suffer will most probably be by far less serious. Many Eldar players have difficulties to decide whether these upgrades are worth their points cost or not.
For this reason I shall provide tables with numbers that show what exactly holo-fields accomplish for your tanks, give my recommendations, explain my reasoning and leave you to judge whether this makes any sense. Enjoy, all feedback and comments welcome!
Math-Hammer
First let me list the probabilities for different damage results for glancing and penetrating hits each with weapons of different AP values, namely weapons without an AP value, AP1 weapons, or weapons of AP2 through AP6. These probabilities are given for vehicles both with or without the holo-field upgrade. Note that weapons shot by a unit with the tank hunters special rule will advance one level, from AP- to AP2-6, from AP2-6 to AP1. Above AP1 just assume that the holo-field accomplishes even less - you will understand what this means soon enough.

This detailed view gives us too little information on a more global scale which is necessary to judge the upgrades effectiveness. I have thus combined the probabilities of the individual damage results to -hopefully- reasonable families: the inability to move (as expressed by crew stunned, vehicle immobilized, and of course vehicle destroyed or explodes), the inability to shoot (as expressed by crew shaken, crew stunned, weapon destroyed, or of course vehicle destroyed or explodes), and permanent damage (as expressed by weapon destroyed, vehicle immobilized, and of course vehicle destroyed or explodes). For each of these damage families I have assessed the adjustments to the probability of them happening with holo-fields compared to without.
[I am aware that spirit stones would reduce the inability to move by the crew stunned result. This will be dealt with later, but for the purposes of the following calculations the spirit stone upgrade has not been included. I am also aware that a weapon destroyed result does not keep the entire vehicle from firing, but it does eliminate the primary weapon, so for the purposes of these calculations, the weapon destroyed result has been interpreted as part of the inability to shoot damage family.]

Interpretation
When we try to ascertain what these numbers mean we have to keep in mind that not all of these situations occur equally. By the logic of the rules and my gaming experience, penetrating hits tend to happen a lot more often than glances against your Falcons and Fire-Prisms (unless you are versing Necrons), and most of these are AP2-6, the second most probably being AP1, and only few being AP-.
What we can see then is that holo-fields do not help at all help prevent the inability to shoot. All they do is ensure that the skimmers remain mobile and do not suffer permanent damage. This means that the benefit of holo-fields is that of being able to keep moving and surviving. Your unit will not be able to deal more damage, but it will be more likely to continue posing a target for your opponent to consider shooting at to disable it again every single turn. They will draw far more enemy firepower than units without holo-fields, but if the enemy has dedicated anti-tank units that couldn't accomplish much else anyways, this doesn't help at all.
Conclusion
Three units have the option of holo-fields.: Vypers, Fire Prisms, and Falcons.
Vypers
The holo-field is almost as expensive as the base cost of the vyper. I need not say much more. The benefits are generally definitely not worth the trouble in this case.
Fire Prisms
The holo-fields increase the base cost of this unit by a good 30%. This is about equal to the benefits conveyed by the holo-fields. The question is whether this is worth the trouble, and this can be assessed most easily when considerung the fire prism's battlefield role.
The fire prism is supposed to deal a hard-hitting alpha-strike. Thereafter it is often more or less disposable. Its range gives it the ability to stay out of range of most return fire anyhow. And its primary purpose will always be shooting, which it will most likely be unable to do anyways, so why bother. If its prism cannon is destroyed, the skimmer is virtually useless (barring some dirty tricks, some of which are explained in my landspeeder tactica), and if the crew becomes shaken or stunned the Fire Prism can't even combine shots with another Fire Prism. So unless you run a mechanized army with lots of skimmers to shoot at, the Prisms' higher chance of survival won't benefit you much. If you do, they may draw fire away from the rest of your units longer and the holo-field may be worth considering.
Falcon
Falcons are more a close-up type of tank, having lower-ranged guns than the Fire Prism, having more guns than the Fire Prism, and featuring transport capacity.
The Falcon thus actually benefits from still being able to move, it benefits more from remaining functional, and it isn't entirely robbed of its battlefield role when kept from firing, while also the weapon destroyed result will not make its entire shooting worthless.
For these reasons, holo-fields on Falcons make much more sense. Especially if they are used as transports and also outfitted with spirit stones that can further add to the ability to keep moving no matter the odds.
Summary
Sorry for being badly organized. I am very tired right now and shouldn't have begun writing this breakdown in the middle of the night. Nonetheless let me try to summarize what I think to be the essence of the truth about holo-fields...
Holo-fields convey very decent benefits, but these come at high cost.
They generally do not make sense on cheap vypers, because buying more vypers instead seems like a much more sensible option, increasing the chance of single vypers surviving while offering the enemy more targets and having more firepower to dish out.
Of the support skimmers, the holo-fields make the most sense on Falcons, especially if these are used to transport a hard-hitting unit to hotspots. In the latter case I recommend buying the holo-field, but generally I would suggest to invest the points elsewhere. The benefits are over-rated especially for fire support tanks, and unless you want to have your skimmers being harmless distractions for your enemy to disable anew every single turn but drawing fire away from the rest of your army, you will be much happier investing the points elsewhere. After all, vehicles -even with holo-fields- still are destroyed on a single lucky shot. The cheaper you keep them, the better for you. Redundancy is a better insurance than any upgrade can ever be...