Luckily I was able to call in some help from IcyMidnight. Hopefully the math I'm presenting here is correct, but please point out any errors in my calculations! So without further ado, let's talk about my proposed fix to combat battlecruisers!
It's a simple change, really, and it has a precedent in the form of deep space transports: an overheat bonus. We'll use a cut down version though:
+100% bonus to the benefits of overheating Afterburners and Resistance Modules
You'll notice I removed microwarpdrives and local rep from the original list. I like the idea of more classes using afterburners with a bonus, a 100% overheat bonus to microwarpdrives would be a little too powerful, and can you imagine a Myrmidon with 100% overheating bonus to its three armor repair modules? Crazy.
But why go this route? Well, it was mentioned in the original thread that spawned this series, and I like it, that's why! Plus it fits the role really well. Combat battlecruisers are meant to get in there and slog it out, withstanding a ton of punishment and giving back just as much pain. Currently they don't really have much of an advantage though, as we've spoken about before. They're out damaged and out tanked and out maneuvered by all the classes that you might consider their cousins. Giving combat battlecruisers a 100% bonus to certain modules when overheated gives them a nice niche: a short-term monster tanking ship.
So let's take a look at a bit of math that I promised. What kind of effect would this have in a practical sense? We'll take a Harbinger for example. Here's a sample fit that I threw together.
We'll focus on the EM resist since it's the highest. A Harbinger has a 50% base EM resist. Our EM Hardener gives us 55% more. We'll multiply that by 1.4 to get our 100% overheat bonus. Finally, our Damage Control gives us another 15%. We can use this formula to calculate our resists
1 - ((1 - 0.5) * (1 - (0.55)) * (1 - 0.15))
This gives us the same result as EFT: 80.9%. To calculate what it'd be like if we overheated we'd use this formula instead
1 - ((1 - 0.5) * (1 - (0.55 * 1.2)) * (1 - 0.15))
This would give us an EM resist of 85.555% (EFT shows an EM resist profile of 85.6%).
Now, to find what our resist would be like if we had a 100% overheat bonus we can use this formula
1 - ((1 - 0.5) * (1 - (0.55 * 1.4)) * (1 - 0.13))
This gives us an EM resist of 90.2%. We can simulate this in EFT by using a Red Giant Class 6 wormhole effect and overheating our module. It's good to have the math, because now we can also simulate these effects in a Red Giant Class 6 wormhole!
1 - ((1 - 0.5) * (1 - (0.55 * 1.8)) * (1 - 0.15))
This gives us an EM resist of 99.6%.
That definitely makes our Harbinger a pretty tough nut to crack. Our EHP goes from 72,000 to 122,000 but you'd burn out all of your hardeners in 60 seconds. I think that's a pretty fair trade.
Taking a quick peek at the effect on afterburners, we see an increase in speed from 486 m/s to 593 m/s. That's not a huge increase, but considering the fitting and signature benefits, it's still not a bad boost, certainly more than they're getting now. The afterburner lasts for about two minutes. These changes are definitely not going to make for prolonged fights of intense overheating.
Of course, the Harbinger isn't the toughest combat battlecruiser. The Prophecy, for instance, receives a 4% bonus to resist per level. What would it look like in this situation? Its base EM resist is 60%, so we can just plug that into our formula to see! We see a return of 92.2%.The Prophecy can easily reach 190,000 EHP, for about 60 seconds as well.
And yes, it's true that there are a few combat battlecruisers out there that see some use in some situations. There's the afforementioned triple rep Myrmidon or the bait tanked Prophecy. But overall, the class needs help. It needs a place in EVE, a niche that only it can fulfill. This idea really takes the combat battlecruiser into a new area, one where it can tank battleship-level damage, but only for very short times. I really like the idea; it's got some obvious advantages with some great disadvantages - our Harbinger goes from 122,000 EHP to 43,500 EHP once those resists burn out - which is a core tenant of EVE Online.
If this type of change came to pass, how would you use a combat battlecruiser?