I apologize, my previous message was a bit confusing in terms of the explanation. Here is a simplified version of the maths. All of these scenarios are fighting
https://wiki.project1999.com/Oosa_Shadowthumper :
Solo Mage level 56:
1x cast of Vocarate Earth (Pet) = 320 Mana (including 1x Meditation tick loss)
1x cast of Burnout Pants = 60 Mana (including 3x Meditation tick loss)
1x cast of Cadeau of Flame = 175 Mana (including 1x Meditation tick loss)
1x cast of Scars of Sigil = 175 Mana (No Meditation tick loss due to cast speed)
Pet = 31 DPS
Damage Shield = 12 DPS
Scars of Sigil = 5 DPS
Totals: 730 Mana for 48 DPS and pet takes 3000 damage.
Mage/Shaman Duo, both level 56, Pet is Tanking:
1x cast of Togor's Insects = 175 Mana (This spell allows the pet to survive 3 encounters instead of 1)
0.33x cast of Vocarate Earth (Pet) = 107 Mana
0.33x cast of Burnout Pants = 20 Mana
0.33x cast of Cadeau of Flame = 58 Mana
1x cast of Scars of Sigil = 175 Mana (No Meditation tick loss due to cast speed)
Pet = 31 DPS
Damage Shield = 4 DPS (damage is lowered due to slow)
Scars of Sigil = 5 DPS
Totals: 535 Mana for 40 DPS and pet takes 1000 damage
Mage/Shaman Duo, both level 56, Shaman is Tanking:
1x cast of Togor's Insects = 175 Mana
2x cast of Chloroblast = 350 Mana
0x cast of Vocarate Water = 0 Mana
0.2x cast of Cadeau of Flame = 35 Mana (The Shaman has the DS, so you don't need to cast it as often)
1x cast of Scars of Sigil = 175 Mana (No Meditation tick loss due to cast speed)
Pet DPS = 47 (Water pet should do at least 16 more DPS than Earth pet)
Damage Shield = 4 DPS (damage is lowered due to slow)
Scars of Sigil = 5 DPS
Totals: 735 Mana for 56 DPS and shaman takes 0 damage (the increased DPS is reducing damage taken as well as the heals)
Ratio of DPS to Mana while Shaman is tanking: 13.125
Ratio of DPS to Mana while Pet is tanking: 13.375
Conclusion: The Tanking Shaman adds 16 DPS to the duo, while maintaining the same DPS to Mana ratio.
At the end of the day, the mana to DPS ratio between a Mage chain summoning and a Shaman face tanking is basically the same, but with the Shaman tanking you are killing mobs faster.
If the Shaman has Torpor and/or Fungi Staff + Fungi Tunic, having the Shaman Tank will surpass chain summoning pets in the DPS to Mana ratio.