If you haven’t read it, here’s the link.

For MY ball tests, the difference I found in COR was 2.6 standard deviations, as indicated in the article. The difference in seam height is around 1.5 SD. The difference in circumference is around 1.8 SD.

For those of you a little rusty on your statistics, the SD of the difference between two sample means is the square root of the sum of their respective variances.

The use of statistical significance is one of the most misunderstood and abused concepts in science. You can read about this on the internet if you want to know why. It has a bit to do with frequentist versus Bayesian statistics/inference.

For example, when you have a non-null hypothesis going into an experiment, such as, “The data suggest an altered baseball,” then ANY positive result supports that hypothesis and increases the probability of it being true, regardless of the “statistical significance of those results.”

Of course the more significant the result, the more we increase the prior probability. However, the classic case of using 2 or 2.5 SD to define “statistical significance” really only applies when you start out with the null hypothesis. In this case, for example, that would be if you had no reason to suspect a juiced ball, and you merely tested balls just to see if perhaps there were differences. In reality, you almost always have a prior P which is why the traditional concept of accepting or rejecting the null hypothesis based on the statistical significance of the results of your experiment is an obsolete concept.

In any case, from the results of MLB’s own tests, in which they tested something like 180 balls a year, the seam height reduction we found was something like 6 or 7 SD and the COR increase was something like 3 or 4 SD. We also can add to the mix, Ben’s original test whereby he found an increase in COR of .003 or around 60% of what I found.

So yes, the combined results of all three tests are almost unequivocal evidence that the ball was altered. There’s not much else you can do other than to test balls. Of course the ball testing would mean almost nothing if we didn’t have the batted ball data to back it up. We do.

I don’t think this “ball change” was intentional by MLB, although it could be.

In my extensive research for this project, I have uncovered two things:

One, there is quite a large actual year to year difference in the construction of the ball which can and does have a significant impact on HR and offensive rates in general. The concept of a “juiced” (or “de-juiced”) ball doesn’t really mean anything unless it is compared to some other ball – for example, in our case, 2014 to 2016/2017.

Two, we now know because of *Statcast* and lots of great work and insight by Alan Nathan and others, that very small changes in things like COR, seam height, and size can have a dramatic impact on offense. My (wild) guess is that we probably have something like a 2 or 3 feet (in batted ball distance for a typical HR trajectory) variation (one SD) from year to year based on the (random) fluctuating composition and construction of the ball. And from 2014 to 2106 (and so far this year), we just happened to have seen a 2 or 3 standard deviation variation.

We’ve seen it before, most notably in 1987, and we’ll probably see it again. I have also altered my thinking about the “steroid era.” Now that I know that balls can fluctuate from year to year, sometimes greatly, it is entirely possible that balls were constructed differently starting in 1993 or so – perhaps in combination with burgeoning and rampant PED use.

Finally, it is true that there are many things that can influence run scoring and HR rates, some more than others. Weather and parks are very minor. Even a big change in one park or two or a very hot or cold year will have very small effects overall. And of course we can easily test or account for these things.

Change in talent can surprisingly have a large effect on overall offense. For example, this year, the AL lost a lot of offensive talent which is one reason why the NL and the AL have almost equal scoring despite the AL having the DH.

The only other thing that can fairly drastically change offense is the strike zone. Obviously it depends on the magnitude of the change. In the pitch f/x era we can measure that, as Joe Roegele and others do every year. It has not changed much the last few years until this year. It is smaller now, which is causing an uptick in offense from last year. I also believe, as others have said, that the uptick since last year is due to batters realizing that they are playing with a livelier ball and thus are hitting more air balls. They may be hitting more air balls even without thinking that the ball is juiced -they may be just jumping on the “fly-ball bandwagon.” Either way, hitting more fly balls compounds the effect of a juiced ball because it is correct to hit more fly balls.

Then there is the bat, which I know nothing about. I have not heard anything about the bats being different or what you can do to a bat to increase or decrease offense, within allowable MLB limits.

Do I think that the “juiced ball” (in combination with players taking advantage of it) is the only reason for the HR/scoring surge? I think it’s the primary driver, by far.