New insight into fleet combat

I published yet another installment of my work on the math behind EVE: [Dynamics of Homogeneous Fleets in Combat].(https://eveismath.blogspot.com/2018/03/homogeneous-fleet-combat.html)

This time I focused on the dynamics of fleets in combat. Now, I know this work does not focus on the effects of logistics, but it still applies to a great many battles in EVE. I will post my additional logistics work in the near future. Take a look and let me know your thoughts.

I’ve included my summary notes below for the TL;DR crowd:

• The number of ships in the fleet has squared benefit over ship quality, i.e. DPS×HP product. This makes intuitive sense considering that bringing one more ship means you have also brought more EHP and more DPS, both. That is, for homogeneous fleets in combat, the rates of target destruction are determined by the ratio of each fleet’s figures of merit, or FOM: FOM=N×√(DPS×EHP). Some notes on the FOM concept:
• In EVE, as in life, time is the only thing you can’t go get more of. When fighting opponents in same-size or smaller-size targets, therefore, prelocking secondaries can have a dramatic effect on combat effectiveness. This can be counterproductive if hostile logistics are able to use pre-locks to send reps early, but logistics are outside the scope of this post.
• It is usually impractical to calculate a fleet figure of merit during combat. Instead, by comparing the fractional rate of loss for your own fleet and your opponent’s fleet for any time period, you are comparing the effective fleet figures of merit. Methods along these lines are already widely used.
• With a model for fleet advantage, it is possible to quantify the risk aversion of fleet commanders by comparing their fleet FOM against hostile fleets FOM where they choose whether or not to engage.

Enjoy,

S. Santorine

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Deep!

Even though it was alot of math mumbo jumbo, I got the idea. Well done!

Rove

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Rovain!

Thank you for your readership and your thoughts. I’m glad you found that it had some insight and was worth wading through the math. Was it Heaviside who said that “theory is the essence of facts.” I think that is true of this work, in that it tries to get at the underlying truth about homogeneous fleet engagements. Fortunately, EVE has many other things about PVP that make it unexpected and nuanced, so there is always more to think about.

Best,
S. Santorine

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This is also why ships with remote targeting dampers should carry both range and lock speed scripts. If you can hinder the speed at which logis can lock a target, you can skew this factor back into your favor.

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Thank you for this, I now have something to link to my corp mates whenever they tell me I am overthinking things. It’s also a fascinating read.

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Really like this actually super useful to see these numbers quantified like this.

Math is not my thing so I needed to take a minute to really make sense of all of this.

• DPS as a base number should probably be Applied DPS.

• HP is an extremely variable number based on different Hulls did you use anything to standardize this.

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Tristan,

Thank you for your readership. Did you mean ‘Applied DPS’ as distinct from the definition that I use in the text of ‘Effective DPS’?

Also, for homogeneous fleets, the ‘Effective HP’ for the same hulls will be quite similar, depending mostly on individual pilot’s skills.

Regards,
S. Santorine

Yes I believe I do mean both, but I was looking at it more from the side of how much damage can an enemy shrug, and less of a fixed number.

Definitely, sorry I should have mentioned that I was trying to take your thinking an apply it to small gangs against homogeneous fleets. With that in mind though I am seeing that ball park numbers are probably fine for this sort of thing.

I love the thinking,
Tristan Valentina

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Tristan,

I really wish I had time to get my next blog post done. It will definitely go into what fleets can ‘shrug’ off. Been busy lately though

I may also post a bit more data. Believe it or not, I actually modeled several different fleet fights before settling on the example. Other fights had more range dynamics to account for but in hindsight, I think they might have been even better.

Anyway, more to follow.

Sincerely,
S. Santorine, Ph.D.

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Maybe you can make an attempt to evaluate several possible figures of merit that might be considered in a fight where effectiveness in losses can be seen early on and maintained for several minutes.

Positioning, applicable range vs range control x mobility, FC presence, group cohesion and/or (or is it vs?) self reliant pilots playing independent roles. This is all I could think of myself.

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Oreb,

Thanks for the readership and comments! I certainly agree that it would be valuable to be able to make a FoM that accounts for many more degrees of freedom in combat situations. I want to do more of this, but it is actually quite challenging.

See, the temptation when writing such a number is to construct it by putting all the beneficial attributes into the numerator, and all the detrimental attributes into the denominator. So, we could imagine an individual ship FoM that tried to account for mobility, tank and damage, by writing the ratio:

`ShipFoM = MaxVelocity x DPS x EHP / AgilityTimeConstant`

Certainly this would rank ships along a plausible ordering. The issue is how do I know that I have weighted these correctly relative to one another? And how do I know that everything that is relevant is in there? How do I know I don’t need to add in, say, self-repair rate from tanking modules?

I could address this issue by building a model for how these factors affect the outcome of a conflict, and then look at the dynamics of conflict between the input parameters to extract a single expression that best predicts the outcome. As the number of degrees of freedom increases, this can become more and more difficult, even impossible. I want to add more degrees of freedom to my approach, but I’m not sure if I’ll have the time in the near future. If you have some thoughts on how some of the metrics you want to include can work in a model for fleet combat outcome, I’d be very interested in hearing about it and linking to work on this subject.

My next post is going to consider a couple basic topics in nonhomogeneous fleet interactions – things like what target order should we pick, or when should we target hostile logistics. After that, perhaps I’ll get time to return to the FoM effort. If you have some thoughts on these approaches, let me know.

Regards,

S. Santorine

As for the issue with self repair, it would simply rely on fitting programs to weigh in repair amount against capacitor range and have that be included in the EHP factor. When cap stable, perhaps the EHP metric might be adjusted to tankable dps, under a different respective formula.

The failure is in the fitting programs, I would say.

Also, optimal or range plays such a significant role, but I guess you can figure dps to zero if a ship cannot apply its dps.

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