Arguably the most politically charged issue for the average pubgoer is responsible drinking, as not to fuel MADD and other neo-prohibitionists, nor wind up in jail for having a few pints after work. The variability in alcohol in beer styles makes this an especially tricky subject. Compare the percent ABV (alcohol by volume: 1 ABV = 2 Proof = 1.25 alcohol by weight, I’ll use ABV in this column) of a Guinness Stout (4.2 percent) to an Eggenberger Samichlaus (14 percent), and you can see how the uninformed beer drinker can easily get too tipsy to do the math.

Unfortunately, those BAC (blood alcohol content) calculators they gave you in drivers’ education aren’t helpful for craft beer drinkers as they are based on a 12-ounce, four percent ABV beer, clearly skewing the “one-beer-per-hour” myth. Very few craft beer drinkers are consuming beers of either that low alcohol, or that low volume, as the pint and even Imperial pint are much more common than a 12-ounce glass. Considering this, I enlisted brewer/mathematician/computer whiz Bernard Hymmen to reformulate these charts, plotting 16-ounce drinks per hour against body weight for 3-10 percent ABV to maintain a legal-to-drive BAC of .08. This way, we can more accurately show how pints of your favorite beer affect your approximate BAC. Of course, the information is standardized; in the end, you have to know your own limits.

To utilize these charts, you must first know what ABV you are drinking. For years, the Bureau of Alcohol, Tobacco, and Firearms (BATF) didn’t even want you to have access to this information (?!). You can thank Coors for helping to make this information freely available (in certain states). Most beer packaging and labels contain ABV information, and if they don’t, they should. You can get a list of style guidelines and their percentages at www.beertown.org/education.

Most beer drinking nations address the BAC issue in a very sensible way: session or small beers (less than 4.5 percent). Though Americans love Really Big Beers (e.g. Sam Adam’s Utopias at 27 percent ABV), you don’t have to drink Lite beers to keep your BAC under the legal limit. Certainly it can be more difficult to make a flavorful light beer, but many countries have been doing it for centuries, and even in the U.S., in states like Utah which limit most beer to 4 percent ABV, there are lots of craft breweries.

The following information provides an alternate view of the data found in standard BAC charts. The ultimate goal is to display important BAC information in a way that’s relevant to people who enjoy a variety of beers.

(Note: We have no background whatsoever in physiology or law. So, if you are looking to us or this article for guidance in these areas you’re in big trouble.)

Ultimately, know you’re your own laws, know your own body, and know your own limits.

The standard BAC chart

Let’s begin by examining a standard BAC chart. The first, and most important, thing to note is that there does not appear to be a “standard” chart.

Interestingly, you can find charts that use the definition of a “drink” as either a 1, 1.25, or 1.5 ounce of 80 proof whiskey. For our purposes, we’ll use this chart which cites 1.25 ounces of 80 proof liquor as the basis for the standard drink.

These tables form the basis of everything else in this article so I encourage you to give them a good look. The chart shows the expected BAC level for a person of a given weight who has consumed a given number of drinks in one hour.

That looks like great information, and it is, but what is it really telling us? The gender and body weight stuff is pretty straightforward, but what about this business of a “drink?” What is a “drink” anyway? Well, you’ll notice the following note on the chart:

One drink is 1.25 ounces of 80 proof liquor, 12 ounces of regular beer, or 5 ounces of table wine.

This is helpful, it provides us with the information we need so we can figure out exactly what the BAC chart thinks a “regular” beer really is. Since 80 proof is 40 percent ABV it turns out (by doing a little math) that a “regular” beer is 4.2 percent ABV.

The standard BAC chart in the real world

So take a minute or two and think about the beers that you regularly drink. How many of them clock in at 4.2%? Here are a few resources to help you get a handle on that question:

You can look up most commercial beers on RateBeer.com

For homebrewed beers there’s the BJCP Style Guidelines

A 4.2% may be a tasty beer, but it’s definitely not a strong beer. In fact, you might actually have to do a little bit of work to find a beer that low in alcohol. Here’s a sample of ABV values from RateBeer.com

Deschutes Black Butte Porter: 5.0%

Red Hook ESB: 5.9%

Full Sail Amber: 6.0%

Rogue Brutal Bitter: 6.2%

Sierra Nevada Celebration Ale: 6.8%

The main point in all of this is that if you use “drinks” as the basis of measurement on a typical BAC chart, by the time you get into drinking Rogue Brutal Bitter, you’ll have an automatic error of 50% off before you even lift the glass off the coaster. That’s not good. And what if you’re lucky enough to be in a place that actually pours true 16 ounce pints, you’ll be taking in 33% more alcohol than the typical BAC chart thinks you are.

Hopefully this helps draw home the point that the standard BAC chart is based on weaker beers and the consequences of that can be significant. In fact, from a certain point of view it could be said that the standard BAC chart inadvertently promotes the over consumption of alcohol because the way the data is presented obscures the unrealistically mild nature of the beers it is based on. It would be nice if there were a more realistic, and therefore conservative, chart that gave you the latitude to gauge your consumption based on the strength of the beer you actually drink. In other words, we need a chart that we could take to Belgium.

To that end, consider the following chart.

Figure 1: A new presentation of the same BAC chart data

This chart is the same basic data found in the standard BAC chart but presented in a way that gives a better feel for real world consumption. The core feature of this presentation is the belief that the item of greatest interest in the standard BAC chart is a particular threshold BAC value (as generally determined by local drinking laws). The lines in the chart above represent a constant BAC value—specifically, 0.08% BAC--and only vary by the ABV value of the beer consumed. In other words, if you know your weight and if you know the ABV value of the beer you are drinking then chart shows the line that you cannot cross if you want to stay below 0.08% BAC. That’s the basic gist of it, but there’s a little bit more to it. Let’s take a look at what this chart really is, and just as importantly, isn’t saying.

The chart shows for various male body weights, the number of drinks required to reach a BAC level of 0.08% for beers at a series of ABV values. So, for instance, suppose that you’re a 180 pound guy and you are drinking Full Sail Amber (6% ABV). The chart shows that after two proper 16 ounce pints you are pretty much at 0.08% BAC. Had you been drinking Maredsous 10 (10% ABV) you would only be able to drink barely more than a pint before hitting 0.08%. Had you been drinking Coors Light (a “standard” 4.2% ABV beer) you would have been able to drink three full pints (in a superhuman feat of stoicism) before hitting 0.08%. These last two examples are instructive because they highlight some limitations of this chart’s presentation.

In the Maredsous example…first, vagaries of individual physiology aside, it’s not exactly clear when you would cross over 0.08% because the chart only shows data for the one BAC value. You can probably guess that it’s around one and a quarter drinks (so, 20 ounces) but that’s just a guess. Second, if you do consume two full pints of Maredsous, you are fortunate for having some great beer but the chart does not provide an indication whatsoever as to how far over 0.08% you are. Moreover, it also gives no indication of how quickly you reached 0.08% BAC or how quickly you would be pulling away from that BAC by having additional beers. Unlike the previous question of volume where you can eyeball a guess base on the grid line, for BAC you have but one single value and absolutely nowhere else to turn.

In the Coors Light example, if you go back to the standard BAC chart you will notice that for a 180 pound man, the BAC value of 0.08 corresponds to 4 drinks. The chart above, however, shows 3 drinks. Which one is right? The answer is both. The subtle detail behind this is the size of the drink. Whereas the standard chart is formulated around 12 ounce drinks, the one above is formulated around 16 ounce drinks. The 33% increase in drink size introduces 33% more alcohol per drink and accounts for the apparent discrepancy.

So in summary, to use this chart out in the field you must

•

Know your gender (always a good idea)

•

Know the ABV value of your beer

•

Know the volume of the beer you are drinking

•

Realize that the chart can never tell you how close you are to the threshold BAC value (0.08%).

The rest of this article is dedicated to describing both the theoretical and practical process of converting the standard BAC chart into the presentation shown above. There is also a link that you can use to download a copy of the spreadsheet used in the process.

A different view of the same data

The first thing to realize with the standard BAC chart is that the problem isn’t with the underlying data, it’s with the way that data is presented. In fact, all the data we need is already present in the standard chart. We just need to tease it out.

Each cell in the chart contains a BAC value that is correlated to gender, body weight, and some amount of alcohol represented as a drink. Though it obscures the precise measure of alcohol, the idiom of a “drink” is quite useful in practice because it’s easy to use when out on the town.

When you look at the standard BAC chart, what’s the first thing you look for? I’ll bet it’s the 0.08 BAC point for your body weight. What are the second and third points you look for? I’ll bet it’s the neighboring 0.08 BAC points, as in where is 0.08 BAC for the next heavier and lighter category (with obvious the subconscious question being “How far can I push things?”).

If you wanted to, you could draw a line from one 0.08 cell to the next and plot a 0.08 threshold line across the whole chart. In fact, you could so this with any BAC level you want to. Here’s the standard BAC chart overlayed with (approximate) lines of constant BAC values of 0.04, 0.08, 0.16:

Figure 2: The lines of constant BAC on the Standard BAC Chart

Because most people don’t happen to weigh an even multiple of 20 pounds, these overlays kind of give an indication of how the BAC chart is used in actual practice. For example, if you weigh 175 pounds you probably take a look at the chart and eyeball your 0.08 BAC value at just over…um…it’s actually kind of hard to tell, isn’t it? Let’s just say it’s on the high side of three and a half “regular” drinks.

Let’s Get Analytical

Of course if you enter the above table into a spreadsheet, you can start to interpolate the data (http://en.wikipedia.org/wiki/Interpolate) and come up with a more objective answer to the question of what all those intermediate BAC (or drink) values actually are. At this point, and from here on, it will be important to remember that precise calculations derived from imprecise data will necessarily be imprecise.

First, let’s take a more qualitative look at what’s going on in the chart shown above. Here’s a rotated view of the chart with all those distracting numbers stripped out. (Rotating the chart in this way makes it easier to correlate the picture with the spreadsheet calculations that we’ll eventually get to.)

Figure 3: A qualitative look at a BAC chart

The grey dots are the places where we can go to the standard BAC chart and read off a BAC value for a combination of drinks and body weight. Or, in other words, they represent the known data that we are starting with. Each of the red lines represents a constant BAC value, just as with the earlier view. Again, it’s not important to know what any of these values actually are. It is, however, important to note that sometimes a BAC line passes through a known point, but oftentimes it does not. The next step with be to estimate (a.k.a. interpolate) data values in these in-between regions.

But first, let’s take a look at those “drinks”. Technically, we could do everything that we are about to do in terms of “drinks” but as we’ve already seen, the “drink” is a slippery concept. It will be a lot easier to understand what’s going on if we start to think about this problem in terms of the amount (ounces) of alcohol consumed. The following table shows the number of ounces of alcohol in a 12 ounce beer at various ABV percentages. The values for the “standard drink” are shown in bold.

Ounces of Alcohol Number of Drinks
1 2 3 4 5 6 7 8 9 10
ABV
3% 0.36 0.72 1.08 1.44 1.8 2.16 2.52 2.88 3.24 3.6
4% 0.48 0.96 1.44 1.92 2.4 2.88 3.36 3.84 4.32 4.8
4.2% 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
5% 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6
6% 0.72 1.44 2.16 2.88 3.6 4.32 5.04 5.76 6.48 7.2
7% 0.84 1.68 2.52 3.36 4.2 5.04 5.88 6.72 7.56 8.4
8% 0.96 1.92 2.88 3.84 4.8 5.76 6.72 7.68 8.64 9.6
9% 1.08 2.16 3.24 4.32 5.4 6.48 7.56 8.64 9.72 10.8
10% 1.2 2.4 3.6 4.8 6 7.2 8.4 9.6 10.8 12

Table 1: Ounces of alcohol in a 12 ounce beer at various ABV values.

So what are the implications of this when reading the standard BAC chart? The following diagram illustrates how, as expected, an increase in the ABV per “drink” results in higher levels of alcohol intake.

Figure 4: Taking ABV values into account

Notice how the amounts of alcohol increase proportionally. That is, compared to a 4% beer, a 5% beer has 1.25 times the amount of alcohol in it and a 6% beer has 1.5 times the amount. As you can see, the cumulative effect can be quite significant.

The following diagram is a closer examination of just one of the higher ABV values. (Yes, the colors and positions just so happen to correspond to the 5% example of the previous diagram, but that’s really beside the point. The principles apply equally to any ABV level.)

Figure 5: Finding BAC values for a particular ABV and a constant body weight

The above diagram show that for a set of standard ounce values Oz1, Oz2, … Oz5 and some chosen body weight value, B, there is a set of known BAC values, BAC1, BAC2, … BAC5. This data can be read directly off the standard BAC chart once the standard drinks are converted to ounces of alcohol. Now, rather than look at a standard set of ounce values, let’s look at some other set of ounce values corresponding to a nonstandard ABV level. These ounce values are Oz12, Oz22, … Oz42 in the preceding diagram. It stands to reason that for the same body weight, B, there is some other set of BAC values that corresponds to the nonstandard ounce values. These are labeled BAC12, BAC 22, … BAC42.

Because the second set of ounce values fall between the ounce values from the standard BAC chart so too the second set of BAC values fall in between the standard BAC values. The following diagram shows a representation of this information in a way that allows us to figure out what the nonstandard BAC values are.

Figure 6: Approximating a BAC curve

Thanks to the standard BAC chart, we start off by knowing the BAC values that correspond to the standard ounce values. The thing that we don’t know is the mathematical relationship between the two. For all we know, the given BAC values could lie on some kind of a crazy curve, as suggested by the purple line in the above diagram. In reality, it turns out that the data is surprisingly linear (much more so than the exaggerated diagram above might lead you to believe). Having nearly linear data means that we can use a simple straight line to approximate the data and not be very far off. This is good news! It means that we can pretty easily get a formula for the straight line and then feed the nonstandard ounce values into that formula to get the second set of BAC values (BAC12, BAC 22, … BAC42).

Once we have the formula for the line, we have a mathematical description of the relationship between ounces of alcohol consumed and BAC, for body weight B. This allows us to go back and forth between ounces and BAC. So, if we are curious about any old BAC value, say BACx, we can now use the line to find out the alcohol consumption in ounces that corresponds to that value, Ozx. This is shown in the following diagram.

Figure 7: Interpolating an arbitrary BAC value

This is the turning point, the “Eureka!” moment in the process. We’ve now shown that for any combination of ABV value and body weight, we can pick an arbitrary BAC value and determine the corresponding alcohol consumption. The only thing that’s left to do is to convert the alcohol consumption in ounces to the number of drinks for the given ABV of the beer.

The data in Table 1, already provides a table of alcohol levels that we can use to look up ABV values for various drink numbers. The tricky detail is that unless the value for Ozx just so happens to appear in that table, we’re going to have to do some more work. Luckily, the problem of using that table to find a random BAC value for a given ABV is, mathematically, completely equivalent to the interpolation that we’ve already seen in Figures 6 and 7. So, without any further charts or diagrams, let’s just agree that we can convert the value Ozx into a “drink” equivalent for a particular ABV through the process of interpolation.

Sicking Excel onto the problem

Let’s take a step back and examine exactly what all the analysis of the previous section produced. We picked a single ABV value (of many), a single body weight (of many), and a single target BAC value (of many) and then went on to find the “drink” equivalent for that combination of three parameters. So, in other words…

We calculated one data point.

To build a comprehensive chart that we can take with us from the corner pub, to Belgium, to our own beer fridges we’re going to have to do a lot more than calculate a single data point. We’re going to have to examine a range of ABV values and a range of body weights. Ideally, we’d look at a range of BAC values too, but that really starts to complicate how might ultimately present all this data. How? Well, basically it would require us to change from representing the data in a two-dimensional chart to a three-dimensional solid, and those are a lot harder to fold up and tuck in your wallet. So, we’ll just pick a single BAC value, hold it constant throughout our calculations, and make a chart out of that. I’m just going to pick the BAC value 0.08% and go on from there because it’s really the most relevant value in my neck of the woods.

The following screenshot shows the spreadsheet used to calculate the data for the new presentation of the standard BAC data. You can download a copy of the full spreadsheet for yourself from here].

Figure 8: The spreadsheet interpolates the BAC value

There are three sections in the above view of the spreadsheet. The first section, rows 11 to 15, sets out some general parameters used throughout the rest of the spreadsheet. The middle section, rows 19 to 30 with the grey background, show the exact data from the standard BAC chart. The lower section, rows 33 to 41, are where the fun starts. This block of data amounts to a BAC chart that has been adjusted for a given ABV value, in this case 3%.

The lowest row of data, row 41, shows the alcohol volumes in ounces associated with the drink numbers shown in row 29 for an ABV of 3%. This is a row from Table 1 because the beer volume set in cell F13 is 12 ounces, just like the standard chart. If the beer volume were greater, say 16 ounces, the alcohol volumes in row 41 would be larger, but the calculations to follow would still work just as well.

Cell H36 (chosen completely at random) is highlighted to show its underlying formula. It uses the standard Excel formula FORECAST to look up an arbitrary value for alcohol volume (cell H41) in a linear model of the standard BAC chart (rows 30 and 23) and a specific weight (180 pounds, cells D36 and D23). The FORECAST function is great for our purposes because it keeps us from having to implement our own least squares line fitting algorithm. The result if this formula is an interpolated BAC value for the alcohol volume and is a literal implementation of the concepts illustrated in Figure 5 and Figure 6.

The following screenshot shows the next step in the process.

Figure 9: The spreadsheet interpolates the number of drinks

Here we see the FORECAST function used again, this time to calculate drinks. The values in cells D33 to D40 show the number of drinks for various body weights to reach the BAC value in cell F12. The way this is calculated exploits some convenient aspects of the way the spreadsheet is physically laid out to accomplish, in one fell swoop, the calculation descried in Figure 7 as well as the conversion to “drinks”.

The spreadsheet contains a series of conceptually identical blocks of data lined up below row 43; one block for each ABV value. The data from column D in each ABV block is then aggregated into a single table that produces the following final chart.

Figure 10: The final revised view of the BAC chart for men

Figure 10: The final revised view of the BAC chart for women