There are two basic types of scoring for most teachers when they use a rubric. Holistic rubrics look at the writing as a whole and evaluate, while analytic rubrics look at components and give weighted points to each section.
Now the problem with holistic rubrics is that they are usually just hidden analytic rubrics. What I mean by that statement is that they still ask graders to evaluate several pieces at once. If you are mentally evaluating several different pieces at once, you are analyzing! The only difference is that now you do not have a predesignated weight for each of your mental calculations and odds are you will decide in a biased fashion.
For example, if you believe organization and structure is the most important aspect of an essay you will essentially discount all other aspects of the essay. This is not grading the whole essay, it analyzing all the parts individually and deciding that what you find important is the most important. All you have done is looked at one aspect of the essay and then give a score based on that.
Another potential downside is the opposite effect. Instead of focusing on just what you believe is the most important aspect and discounting all the other aspects of the essay, you can find yourself reading an essay and believing it to be pretty good, but have one section like grammar be so awful that you fail the paper based on just one category. Again, this is not keeping the whole essay in mind when assigning the final grade. It is letting one category dictate your final score and this is bias at its worst because now you have failed a student.
Since people are going to mentally assign weights and points, consciously or unconsciously, it is better to just use a weighted analytic rubric that creates more reliability across each paper. This does not mean each category needs to be the same weight. If you have three categories, you can consciously decide to weight one as 50% and that is fine. This just means your mental and often unconscious decisions are on paper and hopefully less biased.
Finally, if you want to use a holistic rubric, there is a way to get around this mental bias. You basically need to turn your grading into a yes/no question. For example:
With this approach, you will actually have to decide about the grade using the whole essay with two simple questions. It does not reflect several different components that you can mentally weight and analyze in your brain. You are simply saying, "No, it doesn't answer the prompt. Yes, it answers the prompt, but I need to work to get answer, Or yes, it answers the prompt and I don't have to work to find it." Do not think about structure, grammar, or other component parts. Make it about the whole essay and it becomes safe to say it is holistic grading.
So there you go, traditional holistic rubrics really aren't holistic. They are just analytic rubrics in disguise. If that is the case, just be explicit about what you are doing and use an analytic rubric. If you do want to use a holistic rubric, make it a real holistic rubric. Decide what is important for a pass and ask yourself one or two very simple yes/no questions.