Banner Years and Reverse Banner Years for a Player's BB rate (December 14, 2003)
MGL takes a look at Banner Years, with a focus on a player's BB rate...
I looked at all player since 1972 who had a sudden increase in their bb rate (bb per PA) - more than a 50% increase over their previous career average - with a min of 300 PA in each of the previous 2 years and the "banner" year. For example, player A might have 3 years of bb stats that look like this:
year 1: 500 PA 50 bb, bb rate (per 500 PA) =.50
year 2: 400 PA 40 bb, bb rate= 50
year 3: 450 PA 75 bb, bb rate= 85
How did they do (what was their bb rate) in the 4th year? Any guesses?
There were around 170 player years such that a player had a "banner year" for walks (bb rate more than 50% higher than his career rate), or 86,713 PA's. The same group had 86,878 PA's in the subsequent year (I only used players who HAD a subsequent year with the requisite 300 PA minimum), and 147,823 PA's in the 2 previous years (again, they had to have at least 2 prior years, before the banner year, with a min of 300 PA per year).
In the banner year, players averaged 48 bb per 500 PA. I guess that means that players who have banner years tend to be hackers (or young, or both) previously (low bb rates). In the 2 prior years, their bb rate was 29 in year-1 and 25 in year-2.
The 3 year unweighted average was 32 per 500. The next year, they had a bb rate of 38, somewhere between the 3-year average rate and the banner year rate - closer to the 3-year average rate.
If we weight the 3-year average, such that the baner year gets a "4" weight, year minus 1 gets a "2" weight, and year minus 2 gets a single weight (basically weighting each year twice that of the previous year), we get 37 for the 3-year weighted average, very close to the next year's average.
So it seems as if a banner year in bb rate is a combination of luck and an actual improvement in plate discipline. If it were shear luck, then the next year rate would be around the same as the 3-year simple or unweighted average, which it is not. If it were all "real" improvement, then the banner year rate would be very close to the next year's rate, which it is not.
What do you think would happen if we did the same test on players who have "reverse banner" years, such that their bb rates drop more than 50% from their career rates? Since you wouldn't expect a player's actual plate discipline to drop other than due to severe injury or very advanced age, we would expect to see a next year rate a lot closer to the 3-year unweighted average than the reverse banner year. Let's see.
First of all, we don't see many drops in bb rates of the same magnitude as the increases. I had to make the "rverse banner" year cutoff only 40% lower than their career rate, rather than "50% greater" in the banner year case, just to get less than half as many player years in the sample.
Anyway, this time we get a bb rate of 34 per 500 PA in year 1, 33 in year 2, only 18 in the reverse banner year, and 28 in the subsequent year. Even a 3-year unweighted average of 26 undershoots the next year. A weighted average, like above (4/2/1), is disastrous, as it "predicts" a subsequent year bb rate of 22!
As I suspected, a sudden drop in BB rate appears to be almost completely luck and is no indication of a change in a player's actual plate discipline. In fact, since even an unweighted 3-year average undershoots the subsequent year a little, a sudden drop (a reverse banner year), suggests that not only was the poor year a fluke, but it may have been due to injury such that the next year the player is more healthy, and returns somewhat to a pre-poor year rate.
Keep in mind that especially with the second study (the reverse banner year), there is some selective sampling going on. Remember I only looked at players who definitely had at least 300 PA's in a subsequent year after the severe drop-off. That means perhaps that there are some players who only played a little or not at all in the year after the drop-off that were NOT inlcuded in the study. These players may have experienced not only a sample drop-off in bb rate, but an actual decline in plate discipline as well (and either they or their manager recognized this, or the drop-off continued the next year before reaching 300 PA and they were released, retired, or sent to the minors). So be careful in concluding that a player who experiences a drop-off in any one year is expected to bounce back to around his 3-year average or even a little better.
The reverse banner year and banner year studies do tend to suggest that while both have a large luck or fluke component (you should use either a weighted or unweighted 3-year average rather than focusing almost entirely on that banner or reverse banner year), that a banner year has a large "improvement" component as well (use a weighted average for a projection), while a reverse banner year does NOT have much, if any, of a "true decline" in plate discipline component (use an unweighted 3-year average).
Finally, one of the problems with both studies is that we did not consider how age plays into all of this. Even though we find that a 3-year 4/2/1 weighted average works well for predicting a player's bb rate after a banner year, what if most of those players are young and we SHOULD expect a yearly increae in bb rate? In that case, our weighted average scheme may be a fiction. IOW, once we adjust each year for age, we may find that we don't want to use a weighted average at all or that we want to use a less agressive weighted average. Let's see.
I redid the banner year study, this time adjusting every player's bb rate in every year according to their age. I used a 2% increase in bb rate from one year to the next, up to age 37, and then a 2% decrease after that. Using Tango's aging charts, it appears as if bb rate increases at about that rate (it's not quite linear), and that it peaks at around age 37.
So what I will do is to simply adjust all bb rates to reflect age 37. If a player is 24 in year 1, I will take his bb rate and increase it by 13 (37-24) times 2%, or 26%. If a player is 38, I will decrease his bb rate by 2%. Etc. Basically I am redoing the above 2 studies (banner years and reverse banner years), this time controlling for age.
We get some interesting results when we (crudely) adjust for age. First of all, we get a smaller sample, as a banner year is harder to come by. The average year 1 bb rate is now 26, year 2 is 31, the banner year is 53, and the subsequent year is 42. One thing this tells us is that a large banner year tends to be preceeded by a small banner year, which most certainly suggests a real and continuing improvement in plate discipline. Remember that since we are age adjusting we should expect each year to have around the same bb rate for any large group of players.
Again, and of course, the subsequent year regresses somewhat to the 3-year simple (unweighted) average, but not nearly all the way once again. So the improvement plus luck is evident even after we adjust for age. IOW, the improvement is not just an artifact of age. Let's see what kind of weighting works best. As I said earlier I do not expect the weighting to be quite as agressive once we adjust for age.
I am wrong. Even with the age adjustment, a 4/2/1 weighting predicts a subsequent year bb rate of 41 when in fact it is 42. I guess my reasoning was completely backwards. After we adjust for age, we are probably left with more "legitimate" improvement in plate discipline, and not improvement due to age alone (and luck of course). In fact, a 5/2/1 weighting works better after doing the age adjustments.
Let's see what happens with the reverse banner year players after age adjusting their bb rates.
Using at least a 40% decrease in bb rate again as our reverse banner year criteria, we have 95 player years. The year 1 bb rate is 44, year 2 is 43, the reverse banner year is 25 and the subsequent year is 35. The 3-year unweighted average is also 35, so a revrese banner year appears to be a complete fluke or as a result of a temporary injury, after adjusting for age.
What about if we break the above players (those who had a revrese banner year) into two groups - under 30 and over 29, at the time of the drop-off?
Not surprisingly there are twice as many players in the older group, even after adjusting the bb rates for age, suggesting that an older player is more likely to have a severe drop-off in bb rate than a younger player, also suggesting that maybe a drop-off in bb rate is not necessarily always a fluke, at least for older players.
For the under 30 players, the unweighted 3-year average bb rate is 31, the reverse banner year rate is 21, and the next year is 33. This, like the first study (no age adjustments and only one group), suggests that for a younger player, a drop-off in bb rate suggests not only a fluke, but an injury (or some other problem that is corrected the next year) as well, and that you would expect the player to bounce back to a rate even higher than his 3-year simple average.
For the older players (30 and over), the 3-year simple average is 37, the reverse banner year rate is 27, and the next year, 36. This suggests that even with an age adjustment, a slight weighting might be in order in terms of predicting the year following the reverese banner year. In fact, a 6/5/4 weighting is right on the money.
(Keep in mind that these weightings are based on the average bb rates and are not best-fit coefficients of regression. Therefore while a particular weighting might work just fine on the average rates, it may not work well "across the board," like a best-fit equation from a regression analysis.)
Finally, what happens if we break the banner year players into two groups according to age?
For the under 30 group, they had a 3-year simple average bb rate of 33, a weighted (4/2/1) 3-year average of 40, and a next year rate of 44. So for the younger group, even a weighted average undershoots the next year. Either a much more aggressive weighting is needed or a weighting plus an upward adjustment. More detailed research is needed to determine which is more appropriate.
For the older players, above 29, the weighted average, not surprisingly, overshoots the next year rate. The simple 3-year average is 36, the weighted 3-year average is 42, the banner year is 55, and the next year is 39. For this group, a less agressive weighting is probably needed. In fact, a 4/3/2 weighting is right on the money. And of course, this suggests that for the older players, a banner year is more of a fluke than for the younger players, even after adjusting for age.
Again, be careful about the above conclusions after the age adjustments and after breaking each study into the two age groups, as the age adjustments are crude and linear for purposes of this study, whereas in "real life," a player's aging pattern with respect to his bb rate is probably not linear (it is probably greater at the earlier ages, and levels off as a player gets older).
To conclude, it appears as if a banner year in bb rate is fundamentally different from a reverse banner year, in terms of projecting the next year's bb rate. A banner year strongly suggests a signficant "true improvement in plate discipline" component, as well as the usual luck component. This is especially true for a younger player. The consequence of this is that we want to use an aggressive weighting system, like 4/2/1, when projecting a player's bb rate after a banner year. If we know a player's age, we probably want to use an even more aggressive weighting for a younger player, and a less agressive one (but a weighting nonetheless) for an older player.
For reverse banner years, it appears as if those drop-offs are mostly flukes, especially in younger players, such that for projection purposes, we want to use a simple 3-year average. For older players, not only do we not want to use a weighting system similar to that for the banner year group, but we may want to use a reverse weighting system (weight older years more heavily), to account for the suggestion that in older players, a severe drop-off in bb rate may be due to an injury or some other problem that improves or is rectified the next year.
I believe I have only scratched the surface in terms of refining our projection models such that we take into consideration the direction and magnitude of a change in one of a player's offensive components as well as his age at the time of the change. There is little doubt that other components have similar characteristics. It may be that Marcel the Monkey is soon to become a dinosaur.
--posted by TangoTiger at 08:33 AM EDT
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