Batting 1000? How to “grade” batting averages

There is that moment in your professional career where something just makes sense – it clicks. For me the argument against the hundred point scale was one of those “aha” moments. It was in 2006 when I heard Debra Pickering discussing standards based grading when I was first confronted with the issue of the hundred point or percentage based scale. It was a multi-day presentation and I’m sure my mind was blown hundreds of times over that span. One thing that continues to speak to me is how the 100 point or percentage scale isn’t some magical best practice that’s been handed down over the years – it’s just a “made up” scale that isn’t any better than anything else!

The actual origin of the hundred point scale is probably no more mysterious than the simple fact that we can turn the points into a percentage easily. Additionally, the letter grades associated with those percentage based thresholds were probably just descriptions of general quality, and became the standard by which we base grades. A fundamental principle was probably that an F (failing grade) should be connected with getting half or less correct on an assignment or exam. Colleges probably did it first but in the industrial educational era the hundred point scale and letter grade equivalent stuck with us. But don’t be misled, the 100% scale is not research-based, or the best paradigm out there, or even a reflection of the “real world”. It just isn’t. We do it because that’s the way it has been done and that’s the way we expect it to be done, so do our parents, so do our kids, so does society.

I like to take the idea of the 100 point scale or the standard letter grades and try to apply them to the real world. This application of the scale and percentages to all kinds of different scales/systems is a great way to get a refreshing look at what standards-based grades could be. One great place to look at percentages is in baseball. The batting average is one of the most directly percentage-based statistic that you can find for any sports. Quite simply, a batting average is the percentage of the time that the hitter actually hits the ball. I don’t think this includes foul balls-and it doesn’t hold pop flies against the hitter (I do not pretend to be an expert on baseball statistics). For most of us, we know the batting average has a three digit number behind a decimal point. If you don’t know baseball, you might assume that the best hitters in major-league baseball connect more than half of the time. One might even assume that the greatest hitters have very high averages, perhaps close to 80 or 90%. The truth is that major-league baseball players almost never hit 50% with their batting average. Would someone think to give the greatest baseball players of all time an F for their batting average? It’s absurd, but it makes a great point that applying a 100 point scale or the standard letter grade equivalent to anything doesn’t always work out so well. Let me explain the process by which I looked at batting averages in comparison to the hundred point scale.

Here’s what I did. I got on Wikipedia and found an article about batting averages. In the article there was very specific numbers associated with the different levels of hitters in terms of their batting average. I was surprised at how specific the article could be in terms of giving numbers, ranges, naming the levels, and even giving historical data to help distinguish between the different performance levels and the quantified batting averages.

The article starts out by describing the greatest hitters and the ranges for their batting averages. Any major-league baseball player hitting over 300, or 30%, is considered to have a great batting average. There are several hitters that have even gotten over 400 at various short periods in their career, however they year-long batting average of 400 was unheard of. The article also described batting averages that would be unacceptable at the major-league level, anything under 200 or 20%. The mid level batting averages were broken up into other arrangements. 84 batting average was described as anything less than 260. Then the article described averages from all baseball players at the major-league level over the last few years. Based on that overall average, I set the next grading threshold at “C”. It’s common logic to set average”C”.

Here’s what I came up with:

20140605-155235.jpg

If you look at the top half of the graphic, you will see the five levels described in the Wikipedia article clearly attached to the five grade levels that schools typically use. Keep in mind there was some tweaking on my part to make the information in the article align with reasonable ranges in the B and C levels (described in the previous paragraph).

The very bottom part of the graphic distributes the actual percentage of the batting average across a 100% scale. It’s easy to see how ridiculous this direct percentage comparison is. I filled in the gap between 100% in 42% with a black bar, simply because that just doesn’t happen in baseball history across an entire season. I know some of you Gladwell fans are wondering why there isn’t an outlier. The reason there aren’t any random exceptions for ridiculously high batting averages is because the people in charge of baseball statistics believe that a large amount of evidence is required to get an accurate measurement of batting averages. So if a player only played one game and had a great batting average, does stats were disregarded because there wasn’t enough evidence to make an accurate measurement. My stats teacher would have said it is less reliable data because of such a low n.

The graphic in the center of the picture, right below the text is my attempt at stretching the range of 400 points across the standard hundred point scale. Even with that adjustment the 100 point scale still doesn’t adequately describe the different levels of performance like the first graphic does.

I hope this helps teachers parents and even students to realize that the 100 point scale and standard grade equivalents are not universal or even close to adequate to describe student performance. I’d love to see other examples that people can find where the old standby of hundred point scale and letter grades are mismatches – lots of examples waiting to be found.

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