Defining intoxication is somewhat akin to the definition of pornography, "I know it when I see it". Although, through an analysis of the blood alcohol concentration (BAC) one can obtain a reliable reading of the BAC of a selected individual, and from there induce their degree of intoxication, that number in and of itself is in most cases not proof-positive of actual intoxication. I am not here discussing arbitrary legal definitions of intoxication by percentage of BAC, which can change from year-to-year, state-to-state, and country-to-country, but actual intoxication.
We can say with a certainty that someone with a BAC of .00% is not intoxicated, that they are in fact, sober; whereas someone with a BAC of .40% is in real danger of actual death or could in fact, be dead. Somewhere between these two numbers, there lies an individual that is intoxicated. But even then, it's not that easy. For instance, two people of the same sex and of the same weight, drinking the same type of drinks and having the same percentage of BAC will not behave exactly the same way. Alcohol affects people in different ways, because people are different, process alcoholic drinks differently, their bodies are also different, and invariably therefore have different outcomes. That is not to say, that alcohol doesn't impair you, it can and it does, but that particular impairment will differ from individual to individual even with the same BAC, even, in fact, the same individual with the same BAC but on a different day.
Additionally, those that are alcoholic and that have been alcoholics for a long period of time have built up tolerance levels to the alcohol that they consume. Consequently, even with a BAC at .10%, a true alcoholic may not be impaired at all despite the so-called objective evidence that seems plain as day. This therefore points out an obvious fallacy in strictly relying on BAC levels to determine intoxication; they can and will be in error.
A meaningful definition of intoxication is "the person’s speech, balance, coordination or behavior is noticeably affected". This affection is because alcohol is ultimately a depressant and consequently alcohol slows down your central nervous system, decreases activity in your prefrontal cortex, which then impairs and impacts your coordination and your ability to make good judgments.
Another problem with alcohol and intoxication is the fact that alcohol is not immediately felt in your body and your brain. That is it to say, the recognition that you have drunk too much alcohol, far too quickly, may be something that you are not cognizant of, until significantly after the fact. In other words, that it's not just the quantity of drinks consumed, nor just the amount of time spent having those drinks, but critically, the amount of time spent and quantity consumed, when you first start drinking on a particular day that can intoxicate you. That is why binge drinking in all of its myriad forms, is the most dangerous type of drinking and the most toxic.
BAC levels that exceed the legal standard of alcohol intoxication are in most cases, a presumption of intoxication, but not proof-positive of intoxication. Real intoxication is far more nuanced than this, not nearly so cut and dry, except in those cases in which a person clearly cannot balance themselves or can't construct a coherent sentence.