Witnesses generally lie in favor of the Agency for fear of retaliation.
Agency has all the resources at its disposal such as EEO counselor, EEO Directors, EEO investigators, managers, HR, and in-house attorneys. Despite their claims, EEO counselors, directors, and investigators are generally not "objective." They are on the Agency payroll and are encouraged by the Agency head to eliminate or sabotage EEO claims.
EEOC administrative judges (AJ's) are usually conservative and want to err on the side of the Agency. After all, Agency is innocent until proven guilty.
Agency can sit it out for a long time and has greater resources to do so than complainant.
Agency may produce misleading, if not altered, records in favor of their position.
Management would corroborate with each other and may even lie in order to protect each other.
The legal theories of discriminations are complex. You must first establish the prima facie case. And then establish the pretext in the decision makers' purported non- discriminatory/retaliatory reasons for acting the way they did which is at issue. In each theory of discrimination generally established by legal precedence, the prima facie case is different from the other theories; and how to prove pretext is also different from the others. See samples of AJ decisions for more on legal standards, prima facie cases, and pretext.
It is difficulty to establish favorable treatment of the "similarly situated individuals." Unless the case involves a direct evidence (where the decision maker states under declaration that he or she acted based on your race, age, sex, disability, national origin, prior EEO activity, etc.); complainant must establish favorable treatment of the other similar situated individuals by management who treated you unfavorably. Defining the "similarly situated" is always contentious; and establishing the favorable treatment of them under comparable circumstances involves large amount of data (on those individuals) which the complainant usually does not have, and which is difficulty to present due to large volume and difficulty in the comparative work that is necessary.
For the reasons stated above, it is better to enter into an amicable settlement agreement. More on settlement.