# The Z Files: The Fallacy of Stabilization and an Early Look at Home Runs

One of the pitfalls of having more data to use is more people are misusing data. Something I have talked about previously is the notion of stability points and how they don't mean what many think they mean. Well, I'm back with my annual warning, but this time I've come with backup. In addition, I'll take a look at how the 2021 baseball is playing, which may not be as expected (or reported, at least very early).

## STABILIZATION POINTS

A stabilization point is loosely defined as when a particular metric becomes useful. I'll spare the next level algebra, but one way to look at it is the stabilization point is the sample size where half is a result of the player's skill and half is happenstance.

When I first read about the concept many years ago, it appeared incorporating stabilization points in rest-of-season projections could be cutting-edge analysis. For example, the stabilization point for strikeouts is around 60 plate appearances. Imagine being able to make salient adjustments to player expectations only two weeks into the season! Yeah, pretty cool.

As an example, if I projected a 30 percent strikeout rate for a batter and after 60 trips to the dish, he was fanning 20 percent of the time, I'd adjust my rest-of-season strikeout rate to 25 percent. The idea is there was a 50/50 chance the players new 20 percent mark was real, so I averaged it with my initial projection. I framed the analysis as a guide to identifying

One of the pitfalls of having more data to use is more people are misusing data. Something I have talked about previously is the notion of stability points and how they don't mean what many think they mean. Well, I'm back with my annual warning, but this time I've come with backup. In addition, I'll take a look at how the 2021 baseball is playing, which may not be as expected (or reported, at least very early).

## STABILIZATION POINTS

A stabilization point is loosely defined as when a particular metric becomes useful. I'll spare the next level algebra, but one way to look at it is the stabilization point is the sample size where half is a result of the player's skill and half is happenstance.

When I first read about the concept many years ago, it appeared incorporating stabilization points in rest-of-season projections could be cutting-edge analysis. For example, the stabilization point for strikeouts is around 60 plate appearances. Imagine being able to make salient adjustments to player expectations only two weeks into the season! Yeah, pretty cool.

As an example, if I projected a 30 percent strikeout rate for a batter and after 60 trips to the dish, he was fanning 20 percent of the time, I'd adjust my rest-of-season strikeout rate to 25 percent. The idea is there was a 50/50 chance the players new 20 percent mark was real, so I averaged it with my initial projection. I framed the analysis as a guide to identifying players likely to outproduce or fall short of their initial projection.

A couple years later, Russell Carleton, the developer of stabilization points, revealed we'd all been doing it wrong. In short, while the luck to skill ratio within the sample is evenly split, it isn't predictive of the next sample of the same size. Sticking with strikeout rate, the level of the first 60 plate appearances isn't indicative of the next 60, which is what I (and others) assumed. Oops.

Carleton did go on to say metrics with lower stabilization points should be reliable sooner than those with larger samples, so there is some utility. It's just not as fast-acting as suggested above.

I've explained this before and dropped the mic, so to speak. Not that everyone reads me or listens to me, but the preponderance of analysis akin to what I described illustrates many still have not received the memo. Stabilization points are by no means stable, nor are they predictive, reliable or even as useful as they are made out to be.

As such, I decided to look at the 2019 season and see what would have happened if I employed the 50 percent regression analysis. Every player with at least 240 plate appearances was included and broken into 60 plate appearance segments with the following calculated for each:

PROJ: Measures how far off I was projecting the K% for all the players within that pool compared to the final K%.

YTD: Assumes the newly projected K% is the mark at the end of the respective interval, then measures how far that is from the final K%.

50% Reg: Averages the K% at the end of each segment with the projected K% and compares to the final K%.

Weighted Average: Projects K% by using the K% at the end of each segment, then the projected K% for the rest of the season.

Admittedly, this is confusing, so here are some examples of each calculation.

PROJ: Player A has a projected 25% strikeout rate and finishes with a 30% clip. The math is (30-25)/30 = 16.7%, so I was 16.7% off. This is done for everyone within the sample. The absolute value is used to get the average "accuracy".

YTD: Player A has a 20% strikeout rate at the end of the interval. The math is (30-20)/30 = 33.3% and again done for everyone and averaged.

50% Reg: Using the data from YTD, newly projected K% is 22.5% (average of 20% and 25%). The math is now (30-22.5)/30 = 25%.

Weighted Average: Let's say I project Player A for 500 plate appearances and the 20% came at the end of the 60 PA interval. His new projected K% is ((60 x 20%) + (440 x 25%))/500 = 24.4%. The accuracy math is (30-24.4)/30 = 18.67%.

If you don't care about the math and are only interested in the results, the smaller the number, the better.

The first point of interest is the 50% regression does not improve upon the initially projected K%. The sample doesn't provide useful data as discussed above. In fact, not only that, but the original K% is also far more accurate than the 60 PA sample when compared to the final mark.

Here I could drop the mic as I've shown the 50% regression doesn't accomplish what I once thought, and others still desire. However, looking at the larger samples, the 50% Regression was best at 120 PA before the weighted average took over. At around 360 PA, the best predictor of final K% was in fact the year-to-date K%.

For those into this sort of thing, the results are a little different year-to-year, but the general trend is close. I gathered this data for several metrics and have refined the regressions to fuel my rest-of-season projection engine.

The following is presented for entertainment purposes only, please no wagering. It's the monthly data for everyone eligible for the study. It's interesting to see some of the individual player trends and how misleading it would have been to utilize the 60 PA data to make decisions shaping your team for the next 24 weeks.

## EARLY SEASON HOME RUNS

It's rather remarkable how early-season home run data portends end of season results. It takes around 450 games to be predictive, but the home run rate (HR/PA) at that time very closely projects the ensuing monthly totals. Here is the data, based on the HR% after around 450 games from 2017-2019:

It's not perfect, but the correlation between projected and actual is pretty strong. At minimum, it points us in the right direction. It should be noted weather/temperature is a factor as Opening Day was a few days earlier in 2019, and even though we're only dealing with three or four games per team, when the data is prorated based on just 15 games per team, that's 20-25% of the sample.

Through Friday's games, we're a little less than halfway to the 450 games target, as 212 games are in the book. If the typical pattern holds true, we're looking at a new MLB home run record. Even in April, as the weather warms in the Midwest and Northeast, power increases and so far, homers are ahead of the pace from 2017-2019. That is, the expectation is the already elevated mark will grow even more, to the points the home run rate after 450 games will eclipse the totals from the prior three years. Here is some of the relevant data, using a similar number of games from 2017-2019:

## Key

• Ave FB Dist: Average Fly Ball Distance
• AEV FB: Average Exit Velocity on Fly Balls
• HR%: HR/PA

At the same points of the season, at least in terms of games, 2021 is pacing ahead of 2019. So much for the softer, less bouncy baseball.

While it's too early to draw definitive conclusions, perhaps the fact the ball is 2.8 grams lighter counteracts the lower coefficient of restitution. A lighter object struck with the same force should incur a higher exit velocity.

There are other factors influencing the flight of the ball, notably air resistance. The narrative is fly balls aren't carrying, but the early data indicates otherwise.

I'll revisit this data in a couple weeks, when the sample is actionable.

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