July 24, 2003
Lies, Damned Lies
Hitting the Wall
OK, so it might not have been the most controversial thing he's said this month--even our intrepid Derek Zumsteg didn't dare sweat out this Dusty Baker gem. But the Cubbie manager also made the claim that older players fare better in the second half. Here, in his own words:
"When I was with the Giants, we were a second-half team because we were a stronger team and in better shape the second half of the season than other teams. A lot of veteran teams tend to be like that. Young teams and players start well, where older players tend to find their swing and keep it together once they find it. [The Cubs are] a veteran team."Dusty's claim has at least some grounding in his own experience--under his management, the veteran-laden Giants were markedly better in the second half in both 2002 and 2000, and marginally better in 2001. (Over the course of his entire tenure, the record is far more ambiguous: in Dusty's 10 seasons at the helm, the Giants played .535 ball before the first of July, and .546 after it). While the Cubs' second half didn't get off to a great start with the injuries to Corey Patterson and Mark Prior, it'd sure be nice to see them still in the race come September. The acquisitions of Aramis Ramirez and Kenny Lofton have the Wrigley faithful in a frenzy; will Baker prove to be a sage or a charlatan?
Not to ruin the fun or anything, but this is a testable claim. By comparing the first and second half performances of players of various ages, we can see which ones really perform best down the stretch. A few simple rules:
So, for example, if Rafael Palmeiro hits .295 in 350 plate appearances before the break, and .275 in 300 plate appearances after it, we'll take the difference between the two figures (-.020) and weight it by 300, the lesser of the two PA numbers.
Here's how the figures work out by age group:
Improvement (Decline) After July 1 Age n BA OBP SLG OPS 21 15 +.018 +.021 +.030 +.051 22 41 -.002 +.004 -.008 -.004 23 98 +.007 +.001 +.015 +.016 24 141 -.005 -.009 -.015 -.024 25 167 -.003 +.000 -.011 -.011 26 168 -.003 -.005 -.003 -.008 27 180 +.001 +.001 -.007 -.006 28 181 -.012 -.009 -.018 -.027 29 166 -.006 -.003 -.022 -.025 30 143 -.009 -.010 -.025 -.035 31 141 -.013 -.012 -.030 -.042 32 117 +.001 -.002 -.013 -.015 33 95 -.003 +.001 -.009 -.008 34 94 -.009 -.008 -.022 -.030 35 73 -.001 +.002 -.021 -.019 36 53 +.001 -.002 +.001 -.001 37 29 -.022 -.025 -.050 -.075 38 14 +.001 -.009 -.013 -.022 Young'uns (21-24) +.001 -.002 -.002 -.004 Mid-Career (25-29) -.006 -.004 -.015 -.019 Veterans (30-33) -.007 -.007 -.021 -.027 Old'uns (34-38) -.006 -.006 -.020 -.026
One thing that jumps out immediately is that, at almost every age, the position players decline as a group in the second half. That doesn't necessarily imply that the second half is a panacea for pitchers--while September is a pitchers' month, the warm weather of July and August is favorable to offense. Instead, we're dealing with some selective sampling issues. To the extent that most managers fixate on the current season's stats when deciding who to place in their lineup, they'll be liable to continue playing a guy who outperformed his true level of performance in the first half well into the season--call it Tuffy Rhodes Syndrome (TRS). Conversely, a slow starter will get benched, even if he might not deserve to.
The age effects are what we're most interested in, though, and they provide a pretty clear refutation of Dusty's claim. Hitters between the ages of 21 and 24 exhibited almost no difference in their second half numbers, while mid-career (25-29) hitters lost about 20 points off their OPS, and veteran hitters (30-34) lost closer to 30. For all age groups, batting average and slugging average were relatively more affected than on base percentage, which suggests that those statistics are more susceptible to TRS.
We can take a more thorough look at this pattern by means of a regression analysis. We'll skip the details here--write me if you're interested--except to say that the regression was weighted such that the small sample sizes at each end of the age curve didn't have a disproportionate effect on the results, and that it produced the best fit line in the chart below:
Both age and age2 (age squared) were statistically significant predictors of change in OPS, which is why you get a curved line instead of a straight one. Dusty's claims notwithstanding, the downward trend observed on the left side of the graph shouldn't really be a surprise. All else equal, we expect a hitter to be better at age 24 than at age 23, and so we should also expect him to be better at, say, age 23 and 6 months than he is at 23 and 2 months. There's no reason that age-related improvement and decline need be limited to the off-season; to a lesser extent, it also occurs during the course of the season itself. The "rookie wall" phenomenon that's supposedly so prevalent in basketball--whether it's real or not is a question for John Hollinger--doesn't have any relevance in baseball. Young hitters fare relatively better as the season wears on.
The wrinkle is that the trend appears to reverse itself, if only slightly, after a player passes the age of 32. The "average" 35-year-old suffers a second-half decline, but according to our model, it isn't any more profound than that of the "average" 28-year-old.
The trick is that average 35-year-old and the average 28-year-old aren't created equal. The 35-year-old has been selected out on the basis of his durability; most players need to have tremendous conditioning habits to stay in the league that long, and the same commitment to fitness may help those players to fight off wear-and-tear as the season rolls on. The 35-year-old is also more likely to be playing a less demanding defensive position, and to have received more rest days in the first part of the season, both of which can help to limit a second-half slump.
But what about the most demanding position of all--the guys on the mound? We can run the same analysis for pitchers, based on their opposition batting stats. For good measure, we'll also look at their strikeout rate (measured as K/BFP).
Improvement (Decline) after July 1 Age n BA OBP SLG OPS K Rate 21 11 +.005 +.035 -.024 +.011 -3.3% 22 36 +.019 +.014 +.036 +.050 -1.3% 23 69 +.004 +.002 +.004 +.006 +0.8% 24 100 +.003 -.002 -.008 -.010 +0.0% 25 101 +.007 +.003 +.011 +.014 -0.1% 26 114 -.001 -.003 -.018 -.021 +0.4% 27 113 +.000 -.006 -.011 -.017 +0.7% 28 111 +.011 +.007 +.017 +.024 -0.2% 29 96 +.001 -.007 +.002 -.005 -0.2% 30 97 -.008 -.009 -.006 -.015 +0.4% 31 88 -.002 -.007 -.007 -.014 +0.1% 32 83 +.007 +.009 +.009 +.018 -0.7% 33 69 -.007 -.007 -.023 -.030 -0.6% 34 50 +.003 +.001 -.001 +.000 +0.0% 35 33 +.002 -.004 -.009 -.013 -1.3% 36 26 +.016 +.019 +.015 +.034 -0.6% 37 23 -.006 -.006 -.022 -.028 -0.3% 38 19 -.009 -.009 -.040 -.049 +0.2% Young'uns (21-24) +.006 +.004 +.002 +.006 -0.1% Mid-Career (25-29) +.004 -.001 -.000 -.002 +0.2% Veterans (30-33) -.003 -.004 -.006 -.010 -0.1% Old'uns (34-38) +.002 +.001 -.008 -.007 -0.4%Pitchers don't exhibit the same clear aging patterns that hitters do, and so it shouldn't be surprising that their performance deltas in second half are also less dependent on age. Still, there's some weak evidence that older pitchers fare better as the season wears on. Pitchers between the ages of 30 and 33, for example, saw their opponents' OPS decline by 10 points in the second half, while pitchers between the ages of 21 and 24 saw it rise by 6 points.
The trend isn't statistically significant at any strict degree of confidence, but in the interest of equal time, we'll give the pitchers their graph:
Survivor effects play a role here, too--the pitchers who survive to a ripe old age have demonstrated the ability to withstand a heavy workload, while younger pitchers haven't. By implication, limiting a young pitcher's innings in the first half of the season may help to mitigate the extent of the decline, as well as the risk of injury in the future.
What's interesting is that the improvement that older pitchers experience in the later part of the season doesn't seem to bear any relationship to their strikeout rate--older pitchers are hit slightly less hard by their opponents in the second half, even as their K rate suffers a (modest) decline. Although the trend isn't as profound as I'm making it out to be, the first half of the year can be thought to be a power pitcher's part of the season, while finesse pitchers are at an advantage as the season wears on.
None of this is good news for the Cubs, a team led by veteran hitters and younger pitchers. On the other hand, a squad with the reverse arrangement, like the Twins, might seem to be at something of an advantage as the season draws to a close.
That said, it would be easy to make too much of this. Roughly speaking, a difference of 80 points of OPS is worth about one additional run per game. With 60 games left to play, our numbers imply that a team that consisted entirely of 34-year-old pitchers will improve by about six runs relative to a team that consisted entirely of 24-year-old pitchers. Conversely, a team that consisted entirely of 24-year-old hitters would improve by about 14 runs relative to a team that consisted entirely of 34-year-old hitters.
Real teams, of course, rarely display such extreme demographic patterns, and so the upshot of all of this probably amounts to a game or so at the most. Dusty Baker's suggestion that veteran players fare better in the second half is wrong, but in the grand scheme of things, it doesn't make a heck of a lot of difference either way. The quality of the players on the field--and the quality of the leadership coming from the dugout--are far more important determinants of success whatever the time of year.