Bounceback Seasons

[danup edit: I'm out of town this morning and instead of the usual low-impact fanshot I thought I'd front-page this fanpost as the day's thread. Enjoy.]

There is a great deal of variability in an athlete’s hitting performance year to year.  There can be a number of reasons for this.  A players true skill level could change due to aging, injury, or poor coaching.  We have constantly improving batted ball data that give us some indication of when a drop in poor performance is related to bad luck.  A sharp change is likely usually related to a combination of multiple factors, to varying degrees.  This post is an attempt to look at the long term trends of hitters in the years following a season of poor performance.  For this exercise we are using OPS+ changes from year to year, since that metric is so widely available in B-Ref data pulls that were needed to compile this.  We will also be looking at the relationship that age of the hitter (at the time of OPS+ drop) has on future season’s performance.  Finally, we will be looking at the relationship between the OPS+ the season of the drop and the rate of improvement in future seasons.  In other words, does a person that dropped from 100 OPS+ to 75 have a better chance of improvement than one that dropped from 150 OPS+ to 125?

Before we get into the results of the study, I want to walk through the methodology used.  I have pulled data from 1986 - 2010 (25 seasons), filtering out all individual’s seasons that had more than 400 plate appearances.   I then looked for individuals that had both back to back seasons and had a OPS+ drop of 20 or more from one season to the next.  I then pulled these individuals stats from the following year, and the following 3 years and compared their OPS+ for both those time periods, and compared them to the season of the drop.  To look at the trends by age and by hitting level, I then created 5 subsets for each category, trying to keep the subsets at a similar sample size.   So now we’ll dig into the findings…

In the last 25 seasons, there have been 4,986 individual seasons with 400 PA’s or greater.  Clearly, in many of these cases the individual did not have 400 PA’s back to back.  This would reduce the size of the population from 4,986, but unfortunately I did not have the foresight to measure the exact number that had back to back seasons (and I am not going back to do it now!).   Regardless of that, we have 660 records of a hitter having back to back seasons of 400 PA’s accompanied with a drop in OPS+ of 20 or more, from 1986-2009 (drops in 2010 are excluded from the exercise since there is not yet a 2011 to compare it to).

I just want to make note of that number for a second, because the frequency of this was a little surprising to me.  If we assumed that all 4,986 seasons were by athletes that followed with another 400 PA season, that would mean that we can expect a sudden drop in performance over 13% of the time.  Of course we know that is not the case, so we know the frequency that this happens is even greater.  Possibly more like 20%, though I am certainly ball parking that.  In any case, it happens to about 25 hitters a season.


So what happens with those 660 records in the one year following?  

21 of the 660 did not play in the season following their drop
8 people had the exact same OPS+ in the year following
416 of the remaining 639 had an improved OPS+ in the year following
215 of the remaining 639 had a worse OPS+ in the year following
The median improvement in the following year is 8
The average improvement in the following year is 7.3
The standard deviation for an individual is 25.8
The standard error of the sample is 1.03 (I think I am applying this the correct way, but not 100% certain)


If we were to assume that hitters that drop 20 OPS+ or more in a season were as likely to get worse as better the following year, then we could do liken this to a series of 631 coin flips.  If you tried to flip a coin 631 times, up until the point you get 416 to come up either heads or tails, you’re likely to have your plans set for the rest of your life.   We can safely assume luck plays a factor in these drops, on the whole.  Certainly not the only factor present, but a very significant one nonetheless.  

Here’s the distribution of  the results, going from biggest gain to biggest drop…

47 people improved their OPS+ by 40 or more the following season
62 improved between 30-39
88 improved between 20-29
103 improved between 10-19
124 were between the same and an improvement of 9
77 dropped  between 1 and 9
65 dropped between 10-19
36 dropped between 20-29
16 dropped between 30-39
21 dropped 40 or more



Before we get into the 3 year result, I just want to mention what items I filtered out of this group.  People that had no stats were obviously removed again.  I’ve taken out those that only had stats the year following also.  There are a few instances where people did not play in the year following but did in years 2 and/or 3.  Those people are included even though it is not 3 full years of data.   People that played 2 years after and retire in the 3rd are counted as well.

Here are the 3 year results…

14 of the 660 are removed from the sample because they had no stats in the 3 years following. 80 people only had 1 year of performance and were removed as well.  29 of those are just because their drop occured in 2009.
 Leaves us with 566 records in the sample
12 had the same OPS+ result
363 had an improved OPS+ the following 3 years
191 had a worse OPS+ the following 3 years
Median improvement the following 3 years is 7
Average improvement is 7.6
Standard Deviation for an individual is 21.7
The standard error of the sample is .91


And the 3 year results categorized by margin of change, from greatest improvement to greatest drop….

32 improved by 40 or more
34 improved between 30-39
85 improved between 20-29
105 improved between 10-19
119 were between the same and an improvement of 9
108 dropped between 1-9
47 dropped between 10-19
19 dropped between 20-29
9 dropped between 30-39
8 dropped by 40 or more

We see that median and average stay roughly the same with the 3 year sample.  We also see that number of outliers on the edges reduce pretty dramatically by taking the longer view here.  Now part of that might be explained by the likelihood that anybody that is continuously playing at a lower level may not last more than 1 year after the drop and may only show on the 1 year sample.  The effect would be marginal though.  Of the 51 records that had data for 1 year only, 20 of them had an increased result in that one year.  There are enough Dwight Evans, Gary Sheffield, and Ray Durham’s in there to neutralize this effect somewhat, though it still does exist. 

Overall, there is a demonstrated bias towards improved performance in the season(s) following a dramatic drop.  Next, I am going to take a look to see how the data separates based on age of the hitter at the time of the drop as well as based on the OPS+ level at the time of drop.  I broke each of these categories into 5 subsets.  I tried to keep these fairly even in the number of entries in each subset.   It was easy to do based on OPS+.  Less so with age, due to the amount of clustering between the ages of 27-33.  As a result the age group of 33-43 will have more records in it than the others.  Other than that it is pretty balanced.


Just below are the tables of the results based on age.  The tables for the 1 year are at the top, and the 3 years following are below.   Each table shows the median result and the average for that group in the first couple columns.   The attrition column may need some explanation.  For the 1 year tables,  the column simply is counting the people that did not have data the following year.  For the 3 year sample, those that had nothing or only the following year of data are included - except the 2009 record.  The 2009 records are taken out of the table altogether, which explains why the number of records on the 3 year table are fewer than on the 1 year ones. 

The top table give the raw numbers in each category of OPS+ variance from the prior season.  The table below that just gives the percentage of the subset sample in each category.  The last line in each table is the overall average for the entire group, and gives a baseline to compare the subsets to.

As we can see, each subset shows an improvement following the drop for both the 1 and 3 years following, even the most senior athletes.  However, there is clear and significant difference in the margin of improvement from those 30 and under, and those older than 30.  Makes sense that the effects of aging would negate much of the bad luck factor that caused part or all of the drop.  It seems pretty clear that a GM that wants to take a chance on a bounce back candidate increases their odds of success significantly if they take their chance with a guy on the right side of 30.   The odds of a 33-43 year old athlete’s performance dropping or them being forced out the league are double of that of the group in the 20-26 subset.  That’s a significant difference, yet it is often the veteran types that give people a false illusion of security. 

The next set of tables is much like the last set, with the only difference that it is tracking results based off the hitters OPS+ the year of the drop.

We actually see a more pronounced disparity here than we did with age, which I have to admit surprises me.  All the one year results show improvement, but those with an OPS+ of 77 and below show an average improvement of 14.7,  compared to 1.9 for those whose had an OPS+ of 116 or higher the year of their drop.   That gap widens significantly in the 3 year sample.   Again, if we combine the percentage that attrition out of the league and those that have a decline in performance, over 3 years, we find that more than double in the highest bracket show a decline relative to those in the lowest.   That’s a significant difference, yet it is often the "proven" types that give people a false illusion of security.   Of course this does not suggest that, all things being equal, you should invest in poor hitter but rarely are all things equal.  If you want to take a low cost flier on a bounce back season, this might suggest you might get your best ROI by taking a chance on those that have fallen the farthest. 

It would appear that there is opportunity in investing in bounce back candidates.  An average improvement of over 7 points is significant.  There appears to be additional factors that can expand that edge a bit further.  Finally, there is ever-improving batted ball data that would allow anyone to look at the individual case before them, and make a reasonable projection as to whether the individual is more or less likely to exceed the average.