Evaluating the Republican Guard's effectiveness is far from a straightforward issue by virtue of the fact that the Republican Guard had an important political component to it. In addition to being an elite military force, formations like the Republic Guard are what some military specialists refer to as a parallel military. These formations are quite different than other military elite formations such as the SAS or Green Berets because the size of a parallel military is quite large and they have an explicitly political role within the state. These praetorian formations exist to protect the state, or more accurately, the leaders of the state, from revolts and coups. Saddam's Republican Guard, and even more so the Special Republican Guard, fulfilled this role and thus stood apart from from the standard military chain of command. Saddam sought to buy these formations' loyalty through special favors, expensive equipment, and personal connections to him. Thus when the Guard received T-72s ahead of the rest of the Iraqi Army, this equipment was simultaneously a political message as well as a military upgrade as it was a demonstration that this formation was an integral component of the regime's strength.

The performance of the Republican Guards in the Iran-Iraq War and the Gulf War demonstrate the strengths and weaknesses of a parallel military. Their military performance was seldom above average in both wars, which is typical of parallel militaries because frequently political loyalty is a higher priority for the regime than training or even competence. The Guard performed important counterattacks during the Second Battle of al-Basrah/Karbala V, but their formations were relatively inflexible and they suffered high casualties. The Republican Guard performed well during the invasion of Kuwait and reflected the larger reforms the Iraqi's instituted during the latter half of the Iran-Iraq War which emphasized the rote implementation of specific plans. The lack of initiative played a prominent role in the 1991 defeats, but the Republican Guard fought with much greater tenacity than other Iraqi units. In the Battle of 73 Easting, the Guard's Tawakalnah Division managed to damage or destroy more Bradleys and Abrams than other Iraqi units, but their tactical performance was significantly below par compared to the Coalition forces. When facing the choice between surrender or fighting in 1991, the Republican Guard units frequently chose to fight, and there their military deficiencies were apparent.

But it's important to realize that the subpar or average military performance is besides the point for a parallel military like the Republican Guard. In fighting, and in many cases, dying for the regime was a sign that the Guard was performing its main function as an institution loyal to Saddam. As such, evaluating the Republican Guard solely on its military efficacy obscures a vital component of its raison d'être. Comparing the Republican Guards ala Deadliest Warrior to other elite formations often produces faulty analogies because they sideline their political functions. In the preface of Iraq's Armed Forces, Ibrahim Al-Marashi expresses some regret to his participation as a cable news talking head where phrases like "elite Republican Guards," created a "terminological fog" that did not explain to the public how the Iraqi military actually functioned. While their military performance was less than stellar, they did perform their political duties quite well.

Edit: One more clarification, Saddam inherited the Republican Guard as an institution from al-Bakr, but he significantly expanded it. Saddam recruited from the Tikriti region to fill the ranks of the Guard and it became a prominent feature of Iraq's military. The prominence of this elite and its expensive weapons meant there was significant pressure during the initial reverses of the Iran-Iraq War to deploy this elite on the front. The Republican Guard started to induct draftees and there was an increase in its military training, but it was still an overwhelmingly Sunni force and its higher pay and status still bound it closely to the regime. But this political dilution of the Republican Guard and the destruction of many of its units in Kuwait led to the creation of the Special Republican Guard which was even more closely bound to Saddam and protect him from a possible coup led by the Republican Guard. The Special Republican Guard actually thwarted two abortive coups led by figures within the Republican Guard in 1992 and 1996.

Sources

Al-Marashi, Ibrahim, and Sammy Salama. Iraq's Armed Forces An Analytical History. London: Routledge, 2008.

Pollack, Kenneth M. Arabs at War: Military Effectiveness, 1948-1991. Lincoln, NE: University of Nebraska Press, 2002.

Sassoon, Joseph. Saddam Hussein's Ba'th Party: Inside an Authoritarian Regime. Cambridge: Cambridge University Press, 2011.

Can you be more specific as to what you mean by "effective"?