Is there an equation or system of some sort to determine if a card is worth its mana cost?
Almost all meta decks are based on value cards with the rest of the deck built around them.
Examples :
- Secret Paladin with Mysterious Challenger
- Midrange Hunter with Savannah Highmane, Ram Wrangler, Houndmaster, etc
- Control Warrior with Varian Wrynn, Thaurissan, etc
There is no equation for the base worth of a card based on its mana cost as of the moment. The only numerical and reliable mechanic of seeing a deck's strengths right now is the win rates, and you won't be able to see the specific card win rates, but the deck win rates.
However, there are a lot of card tier lists where people assign scores on specific cards. These aren't derived off of some formula, but it depends on the card stats, effects, the current meta, and how it synergizes with everything else.
Some card tier list examples :
ADWCTA
Trump
A simple test used to exist called the vanilla test to check if a minion's base statline (ignoring abilities as these obviously increase worth) was at an acceptable level. To see if a card beats the vanilla test simply see if the sum of the attack and defence values is greater than or equal to double the mana cost of the card. Back before Naxxrammas this test was hugely reliable and showcased the power of cards such as chillwind yeti (very popular at the time. Now, however, the advent of minions with special abilities and deathrattles more so than those which already existed has broken the vanilla test and it is largely no longer reliable. Saying this, minions which pass the vanilla test and also have an added ability are usually hugely powerful - examples being mysterious challenger, doctor boom, shielded minibot and knife juggler.
Usage of the term "vanilla test" can be seen in this battle.net post, under the Value heading.