A blue die has an average damage of .75

so you can say "on average" to spend a blue die to activate LS you will be sacrificing .75 average damage (effective damage is harder to calculate and can be situational, eg braces etc)

25% of the time you will be sacrificing an accuracy on a blue and 75% of the time you will be sacrificing a hit or crit

Both LS and OE are going to reroll whatever black dice you need to re-roll so thats a wash

LS will re-roll the OTHER blue die and the red dice as well (on average) so what what you are really looking at is -.75 damage (on average) to pay for an on-average increase of X. Since it is a selective re-roll it is much more powerful than a complete re-roll in that (for example) you can pick out your blanks and extra accuracies and now will increase your average damage potential for the total dice pool by X - .75

A blue die has an average damage of .75

so you can say "on average" to spend a blue die to activate LS you will be sacrificing .75 average damage (effective damage is harder to calculate and can be situational, eg braces etc)

You can't use averages in a calculation like this, you need to take a closer look at a distribution. What happens here is the following: for high X it is likely that all red/blue dices have at least one hit. In this case the only dices you can risk to reroll are black. And in the case of LS you need to get 1 more hit out of black reroll compared to OE and that drops the probability a lot (you need to get two doubles instead of one)

yeah but the problem with that thinking is that blacks already have a high chance of damage and you have a selective re-roll. In other words, you already have a statistically significant better chance of rolling well with the blacks so the chances you will actually use LS is when you will whiff on the red and blue dice, which is going to happen whether you have OE or not.

So yes, you can look at averages, because while you *might* need to re-roll your blacks, chances are (literally) you are much more likely to want to re-roll your lower percentage dice. In other words, we can take it for granted that you will get the SAME average damage increase for the blacks via both methods so the crux of the matter is if re-rolling the rest of the dice will overcome the .75 cost.

What you are arguing is that you will whiff the blacks (much less likely) and score on the red and blues (much less likely) in which RARE case, OE would be better mathematically

so then the question becomes (once mathier people than me work that out) what is accuracy fishing and medium range damage normalization worth to you over the nominal damage increase of 2 close range side-arc dice reroll

This is also why im considering having both upgrades. best of both worlds. You miss out on Intel officer but your final damage average damage out of all arcs is going to be maximized. I don't even want to start working that one out.

What you are arguing is that you will whiff the blacks (much less likely) and score on the red and blues (much less likely) in which RARE case, OE would be better mathematically

This is also why im considering having both upgrades. best of both worlds.

it could be overkill, yes. In fact it probably is. But in my experience once you are pretty good at deployment and pretty good at maneuvering, sometimes the difference in whether a game goes well or a game goes poorly ends up being edge-case rolling. That ONE extra damage that means the difference between a dead ship or not (With a reeikan list this can mean the difference between another guaranteed round or not for an asset). Sometimes they go your way, sometimes your opponent rolls a natural 8 damage on 4 blacks...when you add a lot of selective re-rolling you start eliminating cases where this happens.

When I watch truly good players play, they think in terms of what they need out of a damage pool before modifying dice, and that flexibility can be tremendous on a case by case basis.

For example, a case where you roll well with your blacks and just ONE accuracy will mean the difference between the target redirecting and living to jet away or dying.

I really want to see the math too, and im sure snipa will be on here soon with a full page breakdown.

I can help a bit.

Ordinance Experts is the easy part. Each black die has a natural value of 1.00 average damage. You're not going to reroll hit/crits because you could get a lot worse and cannot get better. Hits already represent 1.0 damage, and since a black die averages 1.0, the reroll does not improve its average capacity. That's more if you want to gamble on extra damage or if you're playing a build that depends upon black critical effects. So that leaves a 25% chance that you'll roll a blank or a .25 damage improvement. Your front arc improves by .75, and your side arc improves by .5. Those are pretty fixed numbers. Total improvement is: 1.25 average damage.

That takes us to Leading shots. You can potentially reroll anything, but you have to spend a die to do so. The first question is whether you care about accuracies. That's going to depend upon the situation in the game. If you've got an accuracy that you can spend, then you can get a real improvement on all of the dice that you reroll. The Intel officers make the accuracies look secondary, since if he braces this turn, he'll just not brace on the next shot or next turn.

Situation 1: You don't care about accuracies at all. You can reroll any red accuracies, an extra blue accuracy (if you get it), you can spend a blue accuracy if you have it, and you can roll all black blanks.

Dice possibilities:

Blue: Accuracy/Accuracy: 6.25%. No Accuracy at all: 56.25% Only one blue accuracy: 37.5%

Red: Average improvement per die: .28125

Black: Average improvement per die: .25

The red average improvement is higher because in this situation, you can and will reroll your accuracies. And yes, mathematically speaking, you can just take .25 and multiple it by 3 and take .28 and also multiple it by three. So the overall improvement is 1.59 in this situation, so now we're ready to reconcile this with the blue dice:

Accuracy/Accuracy: 2.34 (since you're also rerolling the other blue for an average damage of .75): Weighted damage improvement: .14625

No Accuracy at all: =1.59-1 (since you're spending damage): Weighted damage improvement: .3319

Only one blue accuracy: =1.59 x .375: Weighted damage improvement: .59625

Final Weight in this situation: 1.07 average damage improvement from Leading Shots

If you do care about the accuracies, then that changes things considerably. First, assuming you want to keep red accuracies so that you don't spend blue damage on a reroll, your reds only improve at .1875 per die. You might also not have a choice but to spend blue damage. But since the above situation is the best case damage scenario for Leading shots, its comparison bears noting:

On only the front arc shot, Leading Shots is slightly better, but Ordinance Experts surpasses it at range 1 when you add the side arc.

But since Leading shots can trigger at medium range, we should get the math there:

The blue dice possibilities remain the same as above.

The red dice also improve at an average rate of .28125 per red die, or .84375 overall. Since that number is under 1, that suggests we'll find plenty of situations in which we won't want to spend a blue die at all to reroll reds. What we're going to have is almost situation by situation basis: If you don't care about accuracies at all, then you're only dealing with the blue acc/acc reroll, which is very advantageous, but only occurs 6.25% of the time for 1.59375 or a weighted amount of .0996. You've got one blue accuracy you can spend 37.5% of the time for a weighted value of .316.

So to the conclusion:

Front arc: Leading shots is better, even at range-1.

Getting the side arc more than compensates for this, but we now have to think about the difference between how many medium and how many side arc shots will appear in a game. If you never take a medium range shot, then OE is clearly better. If you take one, then you still need at least two side arc shots to make OE better.

In the end, we're talking about very cheap upgrades whose overall value is somewhere just north of 1 point of average damage. The difference is going to be pretty marginal.

Someone mentioned the AS shots, but this is going to be marginal for both. 25% of the time, you can use the OE to reroll a blank black. 12.5% of the time, you can use LS to reroll a blank black. So OE is a little better.

One difficulty in putting both Leading Shots and Ordinance Experts is that they start overlapping and providing diminishing effects. For the second upgrade, your black die improvement is no longer .25 per die but .0625 per die. By the time you've rerolled it once, there just aren't high odds that you've got anything left to improve. You've still got a lot of improvement possible in the red dice. Basically, you should be able to get 2 points of damage improvement off of both upgrades, but you do start to lose some efficiency and may have better results with another upgrade.

Vergilius, this is pretty impressive analysis, but I'm afraid you're trying to answer a wrong question. It's not about average damage or accuracies, it's about maximizing a possibility of getting at least X damage (X depends on the opponent ship being attacked)

Vergilius, this is pretty impressive analysis, but I'm afraid you're trying to answer a wrong question. It's not about average damage or accuracies, it's about maximizing a possibility of getting at least X damage (X depends on the opponent ship being attacked)

I saw that earlier. I wrote what I did because your dialogue partner so far was curious about comparing the viability of the upgrades. That's partly going to be situational, since there are an array of offensive and defensive upgrades, a bevy of tokens, and the possibility that damage has occurred earlier in the round. I find that average damage is pretty meaningful since it gives an approximation of performance over time. There's also a concept called "regression to the mean." The idea there is that the more dice you add to the roll, the more the results tend to congregate around a particular spot. The more rolls you make per game, the more likely your overall results are going to be average. You're going to have some good rolls and bad ones, but overall, they'll be pretty close.

To go back to your earlier questions:

Probability of killing full health CR90 (with ram if nesessary) with front arc shot.

Probability of killing full health MC30 (with ram if nesessary) with front arc shot.

Average expected damage from the front arc: OE: 5x.75, 3 x 1.25 = 7.5.

Average expected damage from the side arc: OE: 4

Average expected damage from the front arc: LS: 7.84

Average expected damage from the side arc: LS: 3.5

The ships themselves are probably best run as Monte Carlo simulations. Maybe Snipafist can help out with that.

I can do a bit of logic and run a few calculations that will get me close. For example, you've got a 62% chance of at least one accuracy. In many of those situations, you need at least one accuracy to kill. You're going to be around 20% for at least two accuracies, and both the Gladiator and MC30 really want a couple of accuracies on the front arc shot if you're going to give yourself a serious chance to kill, though an exceptional roll will kill as well. I'd be surprised if a CR90 was less than a 90% kill chance. The Raider is harder because the brace likely takes 3 or 4 points off your front arc shot, but you'll pretty much always kill it if you have an accuracy (62% chance). Since many of these situations require accuracies, my sense is that OE is going to be far better than LS.

#SensorTeams

#SensorTeams

That's a good point. In most of the scenarios he highlighted above, the problem is not damage but getting accuracies. If you can get a second accuracy against a Gladiator or MC30, there's a good chance you can kill it all on the front arc shot.

#SensorTeams

That's a good point. In most of the scenarios he highlighted above, the problem is not damage but getting accuracies. If you can get a second accuracy against a Gladiator or MC30, there's a good chance you can kill it all on the front arc shot.

Not really. Any usefulness of sensor teams on ISD1 is trumped by H9.

Vergillious you say that since accuracies are neccessary for kills OE are better than LS

but only LS lets you go fishing for accuracies...so how is OE better? rerolling blacks has limited utility especially in the front arc as you accurately pointed out, but being able to reroll a blue and 3 reds looking for accuracies when banking on a decent damage pool from blacks can CERTAINLY be the difference of life and death for certain ships.

OE you can maximize the side arc by a piddly amount and maximize the front arc blacks by a slightly less piddly amount but if you roll no accuracies or a bunch of blanks LS gives you the biggest chance of boosting you EFFECTIVE damage which is what kills things, not raw damage.

At close range, you mostly need 2 accuracies to maximize effective damage and OE lets you pray you roll them while LS gives you 2 shots at it.

Sorry to come in so late to the party, the discussion got started when I was en route to Thursday Armada night and I only just caught up. At this point it's a rather confusing series of requests so I'm not even really sure where to start. In all honesty, I would prefer to focus on raw damage output averages because you get a series of decisions with Leading Shots that depend strongly on how the ISD is configured. If it's got an Intel Officer, it wants damage. If it doesn't you probably want 1 Accuracy for the Brace. These lead to very different decision making trees both on which blue die to give up as well as which dice are getting rerolled (say if you generated any red Accuracy results).

Once you start factoring in average odds of taking out specific ships it also depends on your original dice decisions (favoring this or that), whether you're double arcing, if those ships took any damage earlier and if so how much and the effect, and what defense tokens have been used or not and then further probabilities (damage generated/Accuracy results) that become very difficult to put together and effectively impossible for an amateur probability nut like me. You'd need an actuary for something like that.

Without even doing any math, my belief would be that the Ordnance Experts would be clearly superior at short range, particularly with a double arc where you get to reroll the black dice on the side arcs and Leading Shots does nothing. Ordnance Experts would be superior for flakking at close range as well where Leading Shots does nothing. You'd need at least two blank red dice (or Accuracies you don't care about) at medium range OR a blue Accuracy you weren't intending to use (for some reason) and 1+ blank (or unwanted Accuracy) red dice to make Leading Shots worth using at medium range. The thing that Leading Shots would excel at compared to Ordnance Experts would be if you're looking for a specific type of dice result from the red or blue dice (most specifically this would be when you're fishing for a certain number of Accuracy results, generally just going for only 1).

But once I'm given a specific desired outcome and configuration I can start to crunch numbers for average damage. You can feel free to apply that to various targets but I'd prefer to avoid the "odds of wiping out a CR90 in one shot" type math because it's dependent on so many variables that it's both painstaking to do and unlikely to represent actual scenarios on the table.

My reason for presenting "odds of killing a ship" type scenarios is to show that average damage doesn't present the full picture. OE has higher standard deviation then LS and I believe that high standard deviation is good for ISD1. Also once the required number of hits to kill is set, the rerolling strategy changes once the initial roll is close to that number. I might do some computer simulation (or computer-assisted porbability calculation) to cover these scenarios and get probabilities for both LS and OE next week, as it seems to be an interesting exercise.

If you're looking to do sim, I have a pretty rough Python script that I tinker with from time to time that may be helpful.

https://github.com/sprintska/SWAM

It's a Monte Carlo sim with most of the optimal dice-modification logic implemented. LS won't fish for accs in it yet, and Sensor Teams isn't in there (because there were no ST apologists when last I messed with it), but it may give you at least a starting point.

It spits out average damage for the given scenario, but if you're familiar with Python you could pretty easily modify it to track probability to deal X damage.

If I'm not busy tonight I may do some more tinkering to try and get some answers for you guys.

Good post Snipafist. Yes, this thread is rolling with tons of discussion and posts.

One point that absolutely must be reiterated from Snip's post is that there are a lot of variables here. What tokens are available, what damage has already been dealt, what upgrades does an MC30 have?

Finally, all of these upgrades have a very key scenario in which they shine: bad rolls. If you roll three blank black dice, that's a significant improvement in damage. Leading shots will shine at this even more. Even Sensor teams opens the question of "What do I do about all those blanks?" by allowing you to spend a blank to change a red blank to an accuracy. The only place H9 will really be better on the ISD-1 is when you roll exceptionally well and absolutely must spend damage to trigger Sensor teams. But for pretty much all of your average and below average rolls, Sensor teams represents an improvement. Its just, that as Snipafist pointed out, Intel officers really suggest themselves to more damage.

I think part of the problem is that PT asked about killing small ships in one go (which is antithetical to the Intel Officers), and that's where the accuracies really started mattering. It looks to me like you want the accuracies against small ships and the Intel Officers against big ones. One curious question is whether you can come up with a way to use accuracies well against big ships.

That's an interesting thought.

The trouble with arguing for LS to fish for accuracies is that there are other upgrades that do accuracies significantly better. That's why Ginkapo said Sensor teams, and why PT109 suggested H9s. As soon as the conversation shifts to needing accuracies, there are just other better ways to get it, since if you think OE's damage benefit is piddly, then LS does roughly the same amount and is therefore also piddly, and it gets even worse if you elect not to spend accuracies or reroll accuracies. The above calculations were raw high damage totals.

But let's just look at how additional accuracies might affect the leading shots upgrade effect on various ships:

1. You still kill a Corvette almost regardless of upgrade

2. Raider: You have the damage against one, the only question is locking the brace. You do this 62% of the time naturally. Best case scenario, you've got enough damage showing and you can fish for accuracies, which raises your kill rate to around 81%, and probably more if we allow for ramming.

3. Gladiator/MC30: You get two accuracies around 20% of the time. With a ram, you can probably kill. You get at least one accuracy 62% of the time (62-20=42% of the time with the one accuracy). Here the problem is that spending damage is going to lower our chances of killing. Still, if you're only rerolling blanks, the overall boost is going to be around 5-10%, for about 25-30% total. This might be mitigated by the fact that PT109 is setting up side-arc shots as well, and that side arc in addition can help out the final damage total considerably, accuracy or not.

and Sensor Teams isn't in there (because there were no ST apologists when last I messed with it)

Ah but I WAS about, just didnt yet have a list that would give me a solid foundation for piping up in these discussions! Great work nonetheless.

PT - H9 vs Sensor teams

H9 - Remove 1 damage for an accuracy

Sensor teams - Remove on average, 1 or less damage for an accuracy.

H9 - 8points

Sensor Teams - 5points

Sensor teams really do get a bad name for unfair reasons. The only REAL argument against them is the slot in which they reside. And in a lot of cases that is the only argument which is needed.

and Sensor Teams isn't in there (because there were no ST apologists when last I messed with it)

Ah but I WAS about, just didnt yet have a list that would give me a solid foundation for piping up in these discussions! Great work nonetheless.

PT - H9 vs Sensor teams

H9 - Remove 1 damage for an accuracy

Sensor teams - Remove on average, 1 or less damage for an accuracy.

H9 - 8points

Sensor Teams - 5points

Sensor teams really do get a bad name for unfair reasons. The only REAL argument against them is the slot in which they reside. And in a lot of cases that is the only argument which is needed.

This assumes no rerolls which doesn't sound reasonable on ISD.

And I'm only talking about ISD as I do believe that sensor teams may be a good upgrade for other ships.

Ok, I can see that.

But honestly at this point its starting to shake out as a matter of preference/play style due to the situational nature of the desired results

The list i'm now considering for tournament on saturday (to take rather than my "tried and true" list) now has 1 ISD with both upgrades and NO intel officer (this might be what you might call a small-ship killer as it will help side arc, help front arc and help fish for accuracies in that you can OE first so you can see if your front arc blacks can give you enough damage and then you know if/how many dice to LS re-roll). Might be a bit of "reroll overkill" but again, I so hate arc dodging fast ships when running an ISD1 and sometimes 1 shot is all you get.

The other ISD is OE and IO

the extra points are used to put Instigator on one of the raiders and the total is 399.

Edit: some might argue that Instigator is not worth it over other upgrades or even an ISD title, but ever since I managed to sit an instigator raider on the station engaging an entire squadron force while obstructed from their shots and sat him at speed zero for 2 rounds flaking and laughing like a mad man I have loved that title.

and Sensor Teams isn't in there (because there were no ST apologists when last I messed with it)

Ah but I WAS about, just didnt yet have a list that would give me a solid foundation for piping up in these discussions! Great work nonetheless.

PT - H9 vs Sensor teams

H9 - Remove 1 damage for an accuracy

Sensor teams - Remove on average, 1 or less damage for an accuracy.

H9 - 8points

Sensor Teams - 5points

Sensor teams really do get a bad name for unfair reasons. The only REAL argument against them is the slot in which they reside. And in a lot of cases that is the only argument which is needed.

This assumes no rerolls which doesn't sound reasonable on ISD.

And I'm only talking about ISD as I do believe that sensor teams may be a good upgrade for other ships.

If you're not rerolling, you're investing in ST to push through unreliable damage and there are better places to put those points..

If you're rerolling with Leading Shots, you're unlikely to have the two blank dice post-modification to efficiently sacrifice for ST.

If you're rerolling with Ordnance Experts, you don't have the slot for ST.

H9's and XI7's are both better in every case*, largely because of the slot they take. H9's because they're flexible and can hit whatever you need them to; XI7's because they reliably shwack redirects.

*referring to the ISD-I specifically

Did a little bit of tinkering this afternoon because I felt like exploding cyber-corvettes. Assumptions so far are that the target is not using evades (because they'll take some time to implement). I don't have ST or H9's implemented yet either. For standardization purposes, I'm assuming we're firing front arc to front arc.

Initial Monte Carlo results:

Naked ISD-I

Close

Average damage: 6.75

Likelihood of one accuracy: 62.44%

Likelihood to one-shot a CR90: 61.48%

Likelihood to one-shot a Raider: 43.37%

Medium

Average damage: 3.75

Likelihood of one accuracy: 62.32%

Likelihood to one-shot a CR90: 0%

Likelihood to one-shot a Raider: 0%

ISD-I + OE

Close

Average damage: 7.50

Likelihood of one accuracy: 62.45%

Likelihood to one-shot a CR90: 79.71%

Likelihood to one-shot a Raider: 55.39%

Medium

Average damage: 3.75

Likelihood of one accuracy: 62.32%

Likelihood to one-shot a CR90: 0%

Likelihood to one-shot a Raider: 0%

ISD-I + LS

Close

Average damage: 7.54

Likelihood of one accuracy: 62.21%

Likelihood to one-shot a CR90: 83.74%

Likelihood to one-shot a Raider: 60.33%

Medium

Average damage: 3.95

Likelihood of one accuracy: 62.35%

Likelihood to one-shot a CR90: 0%

Likelihood to one-shot a Raider: 0%


I'll flesh it out a bit more later if I get some time. If you see any glaring mistakes, please let me know.

Interesting. What strategy did you implement for dice rerolls?

Also i would assume that the likelyhood of one accuracy should be higher with LS.

I looked at the code and started to tinker with it but will need ro take avbreak until Monday.

ISD-I + Sensor Teams

Close

Average damage: 7.50

Likelihood of one accuracy: 100%

Likelihood to one-shot a CR90: 100%

Likelihood to one-shot a Raider: 100%