When making evaluations on player ability in terms of their quantifiable actions, there comes a point when you have to take into consideration sample size to determine the validity of the numbers you’re seeing.

Take a batter who comes up 100 times and gets 27 hits. That’s a .270 batting average. Not bad. Another batter comes up 1000 times and gets 270 hits for the same .270 average. So, are both hitters the same? On the surface, yes. However, can you expect the hitter who came up 100 times to continue to hit .270? Is that a reliable amount of at-bats to make an inference? Can we assume the batter with 1000 at-bats is more likely to continue to hit around .270 going forward? I believe we’d all agree, since this is pretty basic-level statistics, that the higher at-bats, the more reliable the batting average.

Statcast has a new-ish measurement of balls hit on the barrel of the bat, or ‘barrels’. This is useful because now we can see how well batters are squaring up on pitches.

Let’s say you have two different batters. One that bloops singles off end of the bat or sneaks grounders past the infield may have a similar batting average as a guy who regularly rips hits into the outfield. So how would you judge the better hitter? They both (with exceptions) produce the same result. Would you go with the guy who regularly squares up on pitches; a hitter that is likely to produce more ‘effective’ hits? Or a batter who tends to hit the ball off the end of the bat, in on the hands, etc. who tends to produce weak contact that could result in groundouts, pop-ups, etc?

If you have to pick one to pinch hit, who would you rather have walking to the plate?

Before I roll up my sleeves, glance below at the type of contact MLB hitters have been producing on average the past three years.

What I’m going to do is determine if three years of data is enough to make an inference on what we can reasonably expect an average hitter to produce in terms of barrels per contact; have we reached a point where the three-year sample size is reliable to make inferences going forward?

First, I looked at the collection of batted ball events since 2015. Each year had roughly 900 hitters with at least one batted ball event. All together it accumulated a total ‘population’ of about 2700 hitters. I decided it would be easier and more educative to try and break it down year by year.

Using the 900-something batters per year, I wanted to develop a sample size from that group with a confidence interval no higher than five. Using the entire three-year ‘population’ of hitters would show results all over the board; the data became very volatile as the batted ball events decreased.

By taking no less than 100 occurrences of contact, it’s more reasonable to scale. The average batted ball event (BBE) per qualified hitter (with at least one event) is roughly 40% of the overall average of 253 events per hitter. This is closer to the overall ratio of hitters that had several dozen BBEs instead of batters with a few events, which produced large fluctuations.

You could ask “*Why didn’t you take ALL the data and average it out?*” Well, I could have. The problem I had was the variation is incredibly high; too many of the 2700+ had a very small amount of events (and barrel rate) which cannot lend itself to fidelity. On a scatter plot, it tells us almost nothing.

Instead, I cut the ‘population’ down and required at least 100 BBEs. That gave me a total of 1170 players, or a little more than half of the entire 2015-2017 hotter population.

This is the scatter plot, based upon BBEs (Y-axis, horizontal) and total barreled hits (X-axis, vertical) that was produced using that criteria.

In the above chart, the coefficient of determination (or, r2) equaled 0.161; not a great, but certainly not menial, expectation of correlation between BBE and total barrels.

In layman’s terms, the more events you produce, the higher the expectation of having more barrels becomes. You could have made that inference without the chart, however, I was curious to see if the increase was as sharp as I expected it to be (it wasn’t).

So I wanted a more reliable correlation, as it is logical to assume that the more you do something, the higher the amount of times you achieve your goal.

I took all of those BBEs and compared them to the percentage of barrels (X-axis) to BBEs (Y-axis). I feel that ratio produces a much more accurate relationship.

This time, the r2 equaled a much more stable 0.006 with several outliers present. The further you look down from those outliers, the more concentrated the chart. For the most part, roughly 80% of the plot points are 10% or below. The amount of hitters above that 10% mark would be baseball’s elite power hitters.

It appears we may have concrete proof of normalization.

So, for now, we can assume that your average batter can expect to have maybe 5%-7% barrels per contact; slightly more as your contact events increase.

But, let’s break it down a bit so we can say with certainty that this ratio is dependable for hitters going forward. I wanted to keep the sample size the same throughout the three years of collected Statcast data; 66%, or 395 batters.

We’ll start with 2015.

Below I took the total population of 915 batters in 2015 and used a confidence interval of 4.89 to get the sample size of 395. And, as with all subsequent charts, I worked with a 99% confidence level.

*-With all remaining charts, the X-axis is the percent of BBEs to barrels and the Y-axis is the BBEs.*

For 2015, the coefficient of determination is 0.032 with maybe nine outliers. There is a minor amount of regression but mostly a stable trend line. And, we see the line staying within a 7%-9% ratio of barrels to BBEs.

Here is 2016’s data; a population of 909 hitters with a 5.00 confidence interval.

Now, even with a similar r2 as 2015 (0.039) we are starting to get larger variation and a few more outliers. Yet the trend line again regresses, this time at a slightly sharper scale.

For 2017, 905 total hitters and a confidence interval of 4.88.

2017 comes across as a mess of variation with dozens of outliers. The trend line produced an r2 of 0.007. And, in contrast to the previous years, there wasn’t a regressive trend as BBEs became more frequent; it actually shows a slight increase.

What does that mean? No idea. Could it be, now we have this information available, that hitting coaches are working with batters to improve their contact? Shot in the dark but I can’t come up with a better inference.

Now, lets use each year sample size combined (1175), use a confidence interval of 4.9 (average CI of the three years of study) to come up with a sample size of 66%, or 552 batters.

Now we have a very stable (with a negligible increase) trend, 0.003 coefficient of determination, with some variation and exceptions at a rate of 10%.

Most of those outliers from the graphs are represented in the following chart. And, of those aberrations, several appear in all three groups.

So, the question is whether or not the available Statcast data on barrels is considered stabilized after three years; can we reliably scale a batter’s barrel rate? Do we have a reliable sample size for hitters?

It looks as though we do.

After three years, the overall trend line(s) appear to be somewhat stable in the 5-8% window for an average batter; we can expect most hitters to be at or below 10% barrels per batted ball event.