Here's another summary* of results. This tally includes all of the data that acturater has up in the original post.
Per Orca_'s suggestion, I've included statistics dividing up data by time period. In keeping with Shampoohorn's analysis, I have also included average cost per ultra-rare. As wngmv has suggested that the data follows a binomial distribution rather than a Poisson distribution, I am using that assumption to generate error ranges for probability and average cost to the 95% confidence interval (CI).
TOTAL
Spectre Packs: 2734
Ultra-Rares: 155
Chance of Ultra-Rare per Pack: 5.6693% (+/-0.2106% to 95% CI)
Cost per Ultra-Rare: 1,058,322 Credits (+40,833/-37,908 Credits to 95% CI)
Premium Spectre Packs: 7258
Ultra-Rares: 966
Chance of Ultra-Rare per Pack: 13.3095% (+/-0.2909% to 95% CI)
Cost per Ultra-Rare: 743,832 Credits (+16,621/-15,910 Credits to 95% CI)
Resurgence Packs: 90
Ultra-Rares: 4
Chance of Ultra-Rare per Pack: 4.4444% (+/-0.9159% to 95% CI)
Cost per Ultra-Rare: 2,227,500 Credits (+578,199/-380,608 Credits to 95% CI)
PRE-REBELLION
Spectre Packs: 1682
Ultra-Rares: 79
Chance of Ultra-Rare per Pack: 4.6968% (+/-0.2236% to 95% CI)
Cost per Ultra-Rare: 1,277,468 Credits (+63,856/-58,052 Credits CI)
Premium Spectre Packs: 2592
Ultra-Rares: 256
Chance of Ultra-Rare per Pack: 9.8765% (+/-0.3683% to 95% CI)
Cost per Ultra-Rare: 1,002,375 Credits (+38,830/-36,037 Credits to 95% CI)
Resurgence Packs: 90
Ultra-Rares: 4
Chance of Ultra-Rare per Pack: 4.4444% (+/-0.9159% to 95% CI)
Cost per Ultra-Rare: 2,227,500 Credits (+578,199/-380,608 Credits to 95% CI)
PRE-REINFORCEMENT
Spectre Packs: 307
Ultra-Rares: 22
Chance of Ultra-Rare per Pack: 7.1661% (+/-0.7881% to 95% CI)
Cost per Ultra-Rare: 837,272 Credits (+103,462/-82,959 Credits to 95% CI)
Premium Spectre Packs: 1667
Ultra-Rares: 252
Chance of Ultra-Rare per Pack: 15.1170% (+/-0.6822% to 95% CI)
Cost per Ultra-Rare: 654,893 Credits (+30,953/-28,280 Credits to 95% CI)
POST-REINFORCEMENT (EARTH)
Spectre Packs: 745
Ultra-Rares: 54
Chance of Ultra-Rare per Pack: 7.2483% (+/-0.5115% to 95% CI)
Cost per Ultra-Rare: 827,778 Credits (+62,850/-54,564 Credits to 95% CI)
Premium Spectre Packs: 2999
Ultra-Rares: 458
Chance of Ultra-Rare per Pack: 15.2718% (+/-0.5134% to 95% CI)
Cost per Ultra-Rare: 648,255 Credits (+22,550/-21,083 Credits to 95% CI)
* I did not include the following data in these updated numbers, as they were described as estimates and I am uncertain as to how acturater was handling estimates as opposed to hard numbers. I also did not include data from Sacramentum's videos, because I do not currently have time to watch the entirety of those clips; if somebody could summarize them for me, it would be appreciated.
PRE-REBELLION
Bayushi Pochi: 7 URs/200-220 PSPs; 3 URs/400-450 SPs
Hunter of Deathclaws and Tanks: 3URs/~40 PSPs
Dark Absolution: 6 URs/~100 SPs; 0 URs/~50 PSPs and RPs
UKillMeLongTime: 2 URs/? PSPs
PRE-REINFORCEMENT
Dantexr3: 1 URs/? VPs
Sovereign24: 1 URs/?
RhythmlessNinja: 2 URs/?
a load of stanton: 2 URs/? PSPs
AldarionnEB: 7 URs/~30 PSPs
Sharteel: 15 URs/?
The Krauser: 7 URs/? SPs; 2 URs/? PSPs
POST-REINFORCEMENT (EARTH)
Sacramentum: video
Poulpor: 50 URs/600 SPs and PSPs
HNNNNNNG: 1 URs/5-7 PSPs
Havok1369: 4 URs/4 SPs and 4 PSPs (logged the other data provided)
SirFragsALot333: ~10%
ValorOfArms777: ~5%
Finnegone: 110 URs/~739 SPs and PSPs
iLaPis: 8-9 URs/71 PSPs