Personally SD/DO is my preferred playstyle.
Here's the thing; high level officers and pristine ships are the best way to extract the most amount of value per DP. And if by character level 15, you've got all the perks related to maxing the #, level, and elite skills of your officers, AND you've had the fortune of finding all 4 L7/E5 sleeper officers in your seed, AND you've spent all your story points building out your team with mentoring & elite skills for officers (which could require 30 or more points to adjust personality and/or elite skills selected to your needs), you could conceivably have a fleet of 4 L7/E5 officers and 6 L6/E3 officers. And in most normal engagements, you would have the better officers by a good margin, and thus be entitled to 60% of battle DP distribution.
The problem isn't the 95% of battles that fit this mold. The problem is the other 5%. The battles where you are facing off against 14 integrated alpha cores in a remnant fleet. The battles where 3 fleets of pirates attack you, and you learn the math that 30 * L5 officers gives a better value than your 10 * L7/6 officers. Where there was zero, ZERO possible way for you to win the DP distribution. And now you're facing a stacked deck; the enemy can field 50% more DP than you can, and you're obligated to go on the offensive to capture points just to get some of the DP and hopefully bring yourself to neutral. And that's not your only challenge. You've banked your money on 10 super ships winning the battle. And with SD you could have had all 30 of your ships basically acting as a L3/E0 officer.
You're asking "by the math". So let's do the math.
As a level 15 captain, you can pick up Derelict Operations, Crew Training, and Support Doctrine, plus one of either Best of the Best or Automated Ships. You can even get Officer Training and Officer Management along the way, allowing you to carry 10 max-level officers, park them in your atlases or prometheuses, and still benefit from them helping your DP distribution while not negatively impacting the DP savings DO/SD offers, if you REALLY feel you need that extra DP % allocation.
So let's take a hypothetical battle, 30 eradicators versus 30 eradicators. The enemy's commander dumped all their stats into combat skills, and is basically a L14/E5 officer. They also have 12 L6/E3 officers (they cheat), the other 17 ships are left without officers, and all their ships are pristine. Your dumped all your stats into leadership & industry, and are useless in combat. You have no officers, but SD makes it so all your combat ships basically have L3/E0 officers. You've got DO, and all your ships are 5 d-mods, 3 of which impact combat performance, 2 of which are logistical (50% more fuel, 50% more crew & supplies, 2x more crew, weaker burn drive, etc).
In the above example, the enemy has 1x L14/E5 officer, 13x L6/E3 officers, and 17x L0/E0 officers. That averages out to just below L3/E1.5 for each ship. And with 240 DP, they can field 10 eradicators. All your ships benefit from SD, basically having a L3/E0 officer. With 160 DP, and your ships only costing an effective 56% of base DP, you can field 12 eradicators.
Their 10 versus your 12. Let's dig deeper.
Officer skills basically add an extra 12 OP hullmod to the ship, twice that if the skill is elite. Eradicator has a base of 150 OP. I said the average mix for the enemy yields an average L3/E1.5 officer for their ships. So those skills add on average an extra 54 OP worth of value to the ship, so their eradicators are roughly 36% stronger than base. You, having SD, basically have a L3/E0 for every ship, which adds an extra 36 OP of value to each ship, so your eradicators are basically 24% more powerful than base.
The enemy ships are pristine, so get a 100% power multiplier (no minus). Your ships have 3 combat d-mods, each roughly detracting 10-20% from one specific area of a ship's combat capabilities (20% worse armor, 20% worse hull, 10% worse weapon range, etc.), out of an average of 12 possible combat d-mods. Let's say the worst possible, 20% malus each, times 3 out of 12 combat d-mod areas, so 20% x 25%, or a total of being a 5% weaker ship than pristine.
Enemy ships are 1 x 136% (officer power) x 100% (pristine) = 136% as powerful as base.
Your ships are 1 x 124% (officer power) x 95% (d-modded) = 118% as powerful as base
In sum; enemy fields 10 ships at 136% power, which feels like the power of 13.6 Eradicators. You field 12 ships at 118% power, which feels like 14.16 Eradicators. SD/DO wins versus the enemy's uber-combat fleet leader and cheaty large amount of officers.
I haven't even talked about how you can spend all your story points building s-mods into your ships instead of mentoring / changing officer personality / picking elite skills of officers. You could have added an extra 20 OP per s-mod to your cruisers ships by doing this, and now your 12 eradicators feel like 17.
I also haven't talked about Best of Best. Grab that skill, s-mod in your 3rd hullmod to your ships. Now you get 200 DP, which allows you to field 16 eradicators, each with 3 s-mods, a L3/E0 "officer", and 3 combat d-mods, in total having the effective power of nearly 25 base eradicators. Versus the enemy's effective power of 13.6. You're nearly twice as powerful, and you haven't even started capping objectives yet to be able to send in more ships.
The real beauty of all this is attrition. Focusing on super-elite officers, you're banking on 10 ships being A++ and the other 20 being as good as can be with nobody piloting them, which is "C+". So you deploy your 10 best ships at the start of the fight, but as you lose some or exhaust PPT and need to withdraw, what's left are ships without officers that are like 50%+ weaker than your best ships. This creates a snowball or cascading effect, where you lose some of your initial A++ ships and have to replace them with C+ ships, and it all starts to go downhill real quick. With SD/DO, all your ships are like A-, the first 10 ships you send in are just as powerful as your last 10. Not only does your opposition degrade while you stay just as powerful, but if you can cap some objectives you can become even more powerful and accelerate the enemy's rapid decline.
And have we talked about how you're saving $20-30k+ a month not paying the outrageous salaries of a roster of 10 max-level officers? You can drag along 2-3 paragons for that much money. No seriously, with the officer savings and the fuel & supply savings from the industry tree, you can run 30 cruisers for the same cost as you might otherwise have paid to run 30 destroyers.