Post by svknoe on Jul 31, 2017 14:53:23 GMT
When playing a game of Warhammer 40k, there are many important factors contributing to your victory or defeat. This article is about only one of them, the mathematics of destroying your opponents units. Naturally mathematics will not lead to victory alone, but it can be very useful to keep in mind when building your lists or choosing which target to attack. This article is about some charts given below detailing the performance of many Tyranid units against various targets. They contain three types of information. In each case, green is good and red is bad. All of the tables can also be found here: imgur.com/a/VN5rY
[DMG] Expected number of wounds
The most basic piece of mathematics we can apply to a unit is to calculate the expected number of wounds it will cause to a target. Of course, Warhammer is a game of dice, so you can never be certain of the result. This chart only gives the average result that you can expect over time. Nevertheless this is very useful information. For example, if I want to get rid of a Rhino I would like to know whether I can expect my Exocrine to finish the job alone, or whether I should commit other anti-tank weapons to destroy it as well.
Here are two charts listing expected number of wounds caused. One is for shooting, and the other for melee. In both cases, the value given in the table is the average number of wounds caused by a single model on left hand side to a target on the top.
Shooting [DMG]: imgur.com/0T6rTHU
Melee [DMG]: imgur.com/6ym2VFs
[PPW] Points per expected wound caused
Let us go one step further and talk about efficiency. That a Tyrannofex with a Fleshborer Hive can expect to kill about 14 orks is all well and good, but how many points we have to spend on the Tyrannofex to do this is crucial. One measure of point efficiency is to calculate the number of points we have to spend on a Tyrannofex to be able to slay a single ork. If we are looking to slay orks, we want the unit that kills as many orks as possible for the price we pay for it. To arrive at this number, we simply divide the point cost of the unit by the expected number of wounds caused. Doing this, we see that we have to spend about 16 points on Tyrannofexes to be able to kill a single ork in a shooting phase. That’s not bad! This might seem a bit nonsensical because we can’t buy fractions of a Tyrannofex, but it is still a useful way to tell how much we get for our points.
Where [DMG] was most useful for informing our choices in battle, [PPW] is most useful in list building and planning. If I want to buy a shooting unit to kill orks, I can consult the ‘Ork’ column of the table to look for the units that kill orks most efficiently. I’d certainly like to avoid Hive Guard for this job, since they spend 43 points killing an ork, which is a lot more than 16. On the other hand, we might consider Termagants with Devourers. They can kill orks as cheaply as 11 points a wound! There are, of course, other concerns than this as well. The Hive Guard has longer range than the Tyrannofex, while the Tyrannofex might be tougher. Use the information in the chart as a part of your unit evaluation, not instead of it.
There are, again, two charts. One for shooting and one for melee. This time, the lower the value the better.
Shooting [PPW}: imgur.com/cPtwr5k
Melee [PPW]: imgur.com/xv5hIRK
[PPP] Points per point killed
We can take our analysis of point efficiency even further. We noted in [PPW] that we have to spend 43 points on Hive Guard to cause a wound to an ork. The table also shows that we have to spend 72 points on Hive Guard to cause a wound to a Land Raider. Since lower is better, does this mean that Hive Guards are better at killing orks than Land Raiders? This seems strange. Hive Guard is an anti-tank unit, not anti-infantry. And indeed, it is false. This is because a Land Raider wound is more valuable than an ork wound. To get a better measure of point efficiency we have to account for the point cost of the target as well.
To arrive at the [PPP] value, we multiply [PPW] with the targets point value and divide by its wounds. We now have a measure of how many points we have to spend on our unit to kill a single point of a target. Let’s revisit our Hive Guard example. In the table we see that we have to spend 7.2 points on HG to kill 1pt of orks, while we only have to spend 3.2 points on HG to kill 1pt of Land Raiders. Hive Guards are better at killing tanks after all!
An alternative interpretation of the [PPP] value that might be more intuitive is the number of turns required for a unit to kill its own point cost in enemies. Under this interpretation we see that Hive Guard spend about 3 turns killing their own point cost in Land Raiders. This is acceptable as the Land Raider is tough. But spending more than an entire game killing their own cost in orks is not. Some units, such as genestealers, are very efficient, often killing their own point cost in a single turn or less. Doing this should not be required of every worthwhile unit, but offensive units should be able to kill their own point cost of their preferred enemies within 2-3 turns.
The [PPP] charts are useful both in list building and in actual games. For list building, it lets us see whether a model will be able to do its job well enough. For instance, we see that the Haruspex is not particularly efficient at any job. In an actual game the table can be useful for directing your troops to do the job that they are best at. For instance, you would get better results sending your Termagants at ork boyz and your Hive Tyrant at bikes than the other way around. This is from a point efficient killing point of view; keep other elements of the game in mind also.
Low values are good in these two charts as well.
Shooting [PPP]: imgur.com/AsZC01D
Melee [PPP]: imgur.com/DWTUonA
Notes:
-The defensive capabilities of the targets that I have considered are Toughness, Armour Save, Invulnerable Save and FNP. If they have some other defensive ability, such as a -1 to hit aura, it is not included.
-I have checked some calculations, but enough abilities factor into the calculations that there is bound to be a few errors. I apologise for them.
-Other than what is listed in the entries, each unit has taken minimal gear. That means, for instance, that the single Deathspitter Hive Tyrant has taken MRC to preserve points.
-In the third chart, PPP, I have assumed basic wargear for the enemy units. This means that if they have special weapons or the like, the value given should be better than stated.
-The charts are calculated using Excel. I'll provide the Excel sheet upon request.
Tldr: Green is good, red is bad. Charts: imgur.com/a/VN5rY
Edit 2: Fixed an error and added a note.
Edit 3: Added melee units, improved image quality, added a new chart, added prime buff and fixed an error.
Edit 4: Updated first post, fixed a couple of errors and improved the Excel sheet user friendliness.
[DMG] Expected number of wounds
The most basic piece of mathematics we can apply to a unit is to calculate the expected number of wounds it will cause to a target. Of course, Warhammer is a game of dice, so you can never be certain of the result. This chart only gives the average result that you can expect over time. Nevertheless this is very useful information. For example, if I want to get rid of a Rhino I would like to know whether I can expect my Exocrine to finish the job alone, or whether I should commit other anti-tank weapons to destroy it as well.
Here are two charts listing expected number of wounds caused. One is for shooting, and the other for melee. In both cases, the value given in the table is the average number of wounds caused by a single model on left hand side to a target on the top.
Shooting [DMG]: imgur.com/0T6rTHU
Melee [DMG]: imgur.com/6ym2VFs
[PPW] Points per expected wound caused
Let us go one step further and talk about efficiency. That a Tyrannofex with a Fleshborer Hive can expect to kill about 14 orks is all well and good, but how many points we have to spend on the Tyrannofex to do this is crucial. One measure of point efficiency is to calculate the number of points we have to spend on a Tyrannofex to be able to slay a single ork. If we are looking to slay orks, we want the unit that kills as many orks as possible for the price we pay for it. To arrive at this number, we simply divide the point cost of the unit by the expected number of wounds caused. Doing this, we see that we have to spend about 16 points on Tyrannofexes to be able to kill a single ork in a shooting phase. That’s not bad! This might seem a bit nonsensical because we can’t buy fractions of a Tyrannofex, but it is still a useful way to tell how much we get for our points.
Where [DMG] was most useful for informing our choices in battle, [PPW] is most useful in list building and planning. If I want to buy a shooting unit to kill orks, I can consult the ‘Ork’ column of the table to look for the units that kill orks most efficiently. I’d certainly like to avoid Hive Guard for this job, since they spend 43 points killing an ork, which is a lot more than 16. On the other hand, we might consider Termagants with Devourers. They can kill orks as cheaply as 11 points a wound! There are, of course, other concerns than this as well. The Hive Guard has longer range than the Tyrannofex, while the Tyrannofex might be tougher. Use the information in the chart as a part of your unit evaluation, not instead of it.
There are, again, two charts. One for shooting and one for melee. This time, the lower the value the better.
Shooting [PPW}: imgur.com/cPtwr5k
Melee [PPW]: imgur.com/xv5hIRK
[PPP] Points per point killed
We can take our analysis of point efficiency even further. We noted in [PPW] that we have to spend 43 points on Hive Guard to cause a wound to an ork. The table also shows that we have to spend 72 points on Hive Guard to cause a wound to a Land Raider. Since lower is better, does this mean that Hive Guards are better at killing orks than Land Raiders? This seems strange. Hive Guard is an anti-tank unit, not anti-infantry. And indeed, it is false. This is because a Land Raider wound is more valuable than an ork wound. To get a better measure of point efficiency we have to account for the point cost of the target as well.
To arrive at the [PPP] value, we multiply [PPW] with the targets point value and divide by its wounds. We now have a measure of how many points we have to spend on our unit to kill a single point of a target. Let’s revisit our Hive Guard example. In the table we see that we have to spend 7.2 points on HG to kill 1pt of orks, while we only have to spend 3.2 points on HG to kill 1pt of Land Raiders. Hive Guards are better at killing tanks after all!
An alternative interpretation of the [PPP] value that might be more intuitive is the number of turns required for a unit to kill its own point cost in enemies. Under this interpretation we see that Hive Guard spend about 3 turns killing their own point cost in Land Raiders. This is acceptable as the Land Raider is tough. But spending more than an entire game killing their own cost in orks is not. Some units, such as genestealers, are very efficient, often killing their own point cost in a single turn or less. Doing this should not be required of every worthwhile unit, but offensive units should be able to kill their own point cost of their preferred enemies within 2-3 turns.
The [PPP] charts are useful both in list building and in actual games. For list building, it lets us see whether a model will be able to do its job well enough. For instance, we see that the Haruspex is not particularly efficient at any job. In an actual game the table can be useful for directing your troops to do the job that they are best at. For instance, you would get better results sending your Termagants at ork boyz and your Hive Tyrant at bikes than the other way around. This is from a point efficient killing point of view; keep other elements of the game in mind also.
Low values are good in these two charts as well.
Shooting [PPP]: imgur.com/AsZC01D
Melee [PPP]: imgur.com/DWTUonA
Notes:
-The defensive capabilities of the targets that I have considered are Toughness, Armour Save, Invulnerable Save and FNP. If they have some other defensive ability, such as a -1 to hit aura, it is not included.
-I have checked some calculations, but enough abilities factor into the calculations that there is bound to be a few errors. I apologise for them.
-Other than what is listed in the entries, each unit has taken minimal gear. That means, for instance, that the single Deathspitter Hive Tyrant has taken MRC to preserve points.
-In the third chart, PPP, I have assumed basic wargear for the enemy units. This means that if they have special weapons or the like, the value given should be better than stated.
-The charts are calculated using Excel. I'll provide the Excel sheet upon request.
Tldr: Green is good, red is bad. Charts: imgur.com/a/VN5rY
Edit 2: Fixed an error and added a note.
Edit 3: Added melee units, improved image quality, added a new chart, added prime buff and fixed an error.
Edit 4: Updated first post, fixed a couple of errors and improved the Excel sheet user friendliness.
