We've taken a look at hitter aging based on the top 25 and top 50 performances at each age in the 2000s. In both cases, we saw a pretty smooth curve with a peak near 27-29 years of age, which is in line with what most people think of as the "peak" years of a player's career. We can tease out a fairly predictable pattern of true talent progression for walks, strikeouts, home runs, etc based on rate stats generated from these aggregate numbers. Now what about the other side of the ball?

The setup

I took a look at all the pitchers from 2000-2010, and took the top 50 in batters faced at each age level from 22-40. I required a minimum cutoff of 100 batters faced, so this left me with just 35 pitchers in the age 40 bracket. This is convenient for me, since I am looking at everything in terms of rate stats per plate appearance, which is the same thing as batters faced. Also, since batters faced/innings pitched is a pretty good approximation of performance, I think I am getting a pretty even cross-section of starting pitchers at each age (this assumption starts to get a little dicey above age 33, because more and more pitchers are utilized in a relief role, which probably impacts the numbers a bit).

You can see the full player set and data summary here.

The results

So without further ado, here is what we see in terms of runs (in blue) and earned runs (in red) allowed per batter faced at each age level:

We see two more or less parallel arcs which peak around age 33-34, suggesting that those are the least effective pitchers. I would think it is no coincidence that it is around the same age that many starters are either out of baseball or converted to relievers.

How do we make sense of the downward curve at the higher age groups? Are these pitchers actually getting better? Are they using some veteran savvy they gained along the way? I think this is primarily due to attrition, from what we just said above. As you filter out the less effective starters, the ones who are left are just better as a group. So if you survive as a starter past age 34, your chances of continuing your success as a starter are decent.

We also see this trend where young pitchers actually allow fewer runs per batters faced. But we know that young pitchers are prone to walking lots of hitters and giving up a lot of baserunners in general, resulting in more batters faced. This explains why this number makes them look good relative to older pitchers, while in fact their ERAs are not as good as this would indicate.

Now let's take a look at hits allowed per batter faced as a function of age:

It seems that younger pitchers may walk more batters because they are reluctant to let big league hitters make contact with the ball. This high walk total makes them look rather unhittable, which is not the case. They pitch around hitters a lot, and hitters likely take a lot against a youngster until he proves he can throw quality strikes.

And now home runs:

Again, very similar trends. Young pitchers are actually very effective at preventing the gopher ball. But the tradeoff is they allow more baserunners in general.

Speaking of baserunners, what happens to walks (blue) and strikeouts (red) with aging?

Young pitchers have the best stuff, but they also walk the most hitters. Strikeouts decrease with age, as starters lose velocity and generally focus on lowering walks rather than blowing people away. The pitchers who last past age 35 have the best combination of strikeout stuff and control (guys like Curt Schilling come to mind).

And finally, is there a FIP trend in the data?

I'll be the first to admit this is not a very good fit at all. Maybe a flat line would be just as good a fit to this data. But if you believe this data, it appears that most pitchers do their best before age 30. But this you already knew, right?

What does it all mean?

I think there are some hints about an aging curve in here, but they are obscured by several flaws in the study:

I won't go so far as to say that youth beats all. If that were the case, no one would be paying $82.5M for John Lackey (sorry, Theo Epstein). I think it's pretty clear that pitchers who are good enough to break into the Majors at age 22 have some pretty electric stuff, so that selection bias is evident in this study.

The other selection bias we are seeing is the highly-effective old fogeys like Randy Johnson and Mike Mussina who made 39 and 40 year-olds look pretty darn good. Some of the 35 pitchers in the 40-year old bin only faced a couple of hundred batters, so the guys who faced 800 are counting eight times as much in our rate stats.

In some of these rate stats, it seems like it might be more appropriate to use at-bats as a counting stat in order to nullify high walk effects. I think it's clear that pitching metrics are harder to measure, because of various effects like starting vs. relieving.

I would like to improve this method. Do you have any ideas? Please comment below. Thanks!

Ever been frustrated by that MLB award going to that player because of reputation rather than performance? The 19th annual Internet Baseball Awards, hosted by Baseball Prospectus, are up for voting. You have until Friday, October 22 to cast your votes in the following categories:

• AL/NL MVP
• AL/NL Cy Young
• AL/NL Rookie of the Year
• AL/NL Manager of the Year

Make sure to cast your vote and let your voice be heard!

I think there are plenty of articles out there already stumping for particular players based on sabermetric data, but if there is a notable omission, we may write an article on the site. Happy voting!

For those of you not familiar with it, Tom Tango runs a fans' scouting report on MLB players and their fielding ability. You can vote on every player on every team on a 1-5 scale, and it turns out to be pretty darn accurate. The wisdom of crowds in action.

Go do your part now!

If you'll remember, a while back we took the top 25 hitters from 2000-2009 at every age level (from 22-38), and plotted their offensive production using Rally's batting runs above average (via B-R.com). We got a very nice curve showing a peak at around 29 years old. What if we look at the next 25 best players at each age?

Here we show elite (top 25 seasons at each age, blue curve) and second tier (2nd 25 seasons at each age, red curve). What we observe for the second tier players is a very similar graph, but shifted downward. The peak appears to be ever so slightly lower, perhaps at age 28 instead of 29. The trend is very similar both in shape and curvature, but it appears that the falloff is slightly slower for the second tier guys.

Who are these guys? The second tier consists of very good players still, ranging from Matt Holliday to Ichiro Suzuki among the 28-year olds. These are still All-Stars, though there are some "lucky" seasons mixed in there.

If we examine the same offensive rate trends from the first study, we see the following:

Again, the shape of the curves is unmistakably similar, but there is some translation. Walk rates are not nearly as high in the second-tier group as in the first, but they rise into the early thirties and then fall. Regrettably, I looked only at total walks, and did not compile the data for unintentional walks only. That would have been interesting to compare. Strikeouts fall continuously over time, and fit a linear regression better than an exponential one, just as in the "elite" group. XBHs peak earlier than HRs, and the change is remarkably similar between the two groups.

This seems like a potential aging curve method, and will be implemented in my projections for 2011.

Last time we looked at adjusting hitting lines using our team factors. This week, pitchers who changed teams:

Case Study 1: Dan Haren, ARI to LAA
ZiPS ROS: 3.78 ERA and 3.72 FIP in 60 IP with 13 BB and 57 K
TF Adjusted: 3.54 ERA and 3.71 FIP in 60 IP with 16 BB and 57 K

Just how good an acquisition was Dan Haren for the Angels? As it has been pointed out by many, his FIP is much better than his 4.47 ERA, and his contract extends beyond 2010, so even if the Angels don't make the post-season, he's still going to be around to help the Halos in 2011. Add to that the move from run-happy Chase Field, and even moving to the AL West shouldn't keep Haren from improving.

Case Study 2: Roy Oswalt, HOU to PHI
ZiPS ROS: 3.63 ERA, 3.46 FIP in 62 IP with 16 BB and 52 K
TF Adjusted: 3.75 ERA, 3.45 FIP in 62 IP with 16 BB and 50 K

Oswalt continues to have good success in a comeback season. Playing for Philadelphia might mean a few more runs cross the plate, but there shouldn't be much of a hit for Oswalt performance-wise (as long as he stays healthy).

Case Study 3: Matt Capps, WAS to MIN
ZiPS ROS: 4.29 ERA and 4.06 FIP in 21 IP with 5 BB and 17 K
TF Adjusted: 4.57 ERA and 4.55 FIP in 21 IP with 6 BB and 18 K

Uh oh. Hope the Twins took into account that the Washington Nationals play in a run-depressing stadium, division and league. Things could get ugly for the Twins' new closer at some point.

Contenders spent a lot of effort trying to improve their teams for the stretch run, and many spent rather freely in making moves. Perhaps one of the hardest questions facing a GM in making these deals is, how will the move to a new team, a new city, a new league affect this player? We can't address the human side of this so much here, but we can look at what statistics have to say about the numbers.

Using our newly-derived team factors, we will make rate adjustments to the ZiPS rest-of-season projections for players who switched teams, to see how the change in environments could impact player production.

Case Study 1: Lance Berkman, HOU to NYY

ZiPS ROS: .262/.385/.470 with 8 HR and 32 RBI in 201 PA
TF Adjusted: .259/.376/.475 with 9 HR and 32 RBI in 201 PA

As you can see, switching leagues and joining the toughest division in baseball should have a negative impact on Berkman's batting average and on-base percentage, but Yankee Stadium will likely boost his home run total by one or two dingers. Of course, this assumes that the Yankees will use Berkman in the same way the Astros did, which may not be the case at all. Given his splits and the other talent available on the team, New York may very well platoon him, limiting his PA and boosting his line.

Case Study 2: Ryan Ludwick, STL to SD

ZiPS ROS: .303/.367/.552 with 9 HR and 36 RBI in 181 PA
TF Adjusted: .297/.362/.544 with 9 HR and 35 RBI in 181 PA

Ludwick is an interesting case of a player going from one contender to another. Interestingly enough, moving to PETCO isn't enough to kill his HR total or his overall power much, though he stands to lose about 2 doubles from the move. That's because the Cardinals don't play in a great hitter's park themselves. You can bet that stat-savvy Jed Hoyer did his homework on this one before pulling the trigger. Imagine what Albert Pujols would look like in Colorado. That's scary.

Pitchers coming up in a follow-up post later this week. Stay tuned!

Is 2010 the year of the pitcher? With Matt Garza's no-hitter this week, that makes five no-nos (six if you count Andres Galarraga) and three perfect games, and we're not even to August yet. There's no shortage of young talent on the scene, with pitchers like David Price, Jon Lester, Stephen Strasburg, Ubaldo Jimenez, Tommy Hanson and Brett Anderson. These youngsters feature just unprecedented stuff. Is it them? Is it just dumb luck?

The numbers

We will be looking at first-half statistics only, for a fairer comparison of previous seasons with 2010. Looking at the simplest measure of runs scored per game, it's true that scoring is trending down:

But run environments depend on more than just pitching, and there's that whole steroid crackdown to think about. Are sluggers just hitting fewer home runs?

Yes, that appears to be a trend, but the rate of home runs hasn't fallen off THAT much. A difference of about 0.3% here means that a full-time player with 650-700 PA will hit about 2 fewer home runs per season. So that's pretty significant. Fewer steroids, fewer dingers, fewer runs. But it still doesn't really explain the no-hitters.

Now here's another pair of related trends that does seem more significant:

Now we're getting somewhere! Strikeouts are on the rise in both leagues, and walk rates are slightly going up. It looks like batters are being more patient, working counts more as teams continue to embrace OBP and waiting for your pitch. That sounds plausible (maybe). Let's see... 3.82 pitches per PA in baseball this year, 3.83 in 2009, 3.81 in 2008, 3.77 in 2007, and 3.76 back in 2006. If that's true, then more batters striking out and walking, combined with good young pitching coming up, might give you a greater probability for no-hitters. Add in a little randomness, and you've got 2010.

Ok, so does this account for the lower run scoring around baseball? Subtract 0.3% HR and add 2% more Ks to a league average pitcher, and his FIP drops by about 0.04 runs per nine. So that's something, but runs per game have dropped a lot more than that.

What's missing?

Up to now we've totally forgotten to address defense! It appears that defense is also on the up and up. In 2010, we see 10 teams with a defensive efficiency rating of .700 or higher, including a lot of good ballclubs: Tampa (1st), Texas (2nd), the Yankees (4th) and Boston (8th). It has been reported that AL teams, especially, made a push to improve their defense this offseason, and it shows. The number of teams that cared that much for defense the previous four seasons? 5, 4, 6, and 6. Defense will also prevent runs, I'm told.

Put all of this together, and I think we have kind of a composite picture of what's going on with the run scoring around baseball. Batters are more patient, pitchers are throwing harder (19 qualified pitchers are averaging 93 mph or better with their fastball this season, while the previous four seasons saw only 11-12 meet that criteria each year), steroids are out of the sport, and defense is improving. That's your recipe for lower run scoring.

ISO, also known as Isolated Power, is commonly referred to as SLG minus AVG. While that is the easiest way to calculate it, it is also (TB-H)/AB, which actually tells us what ISO means. It is the number of extra bases per at-bat.

While it is called Isolated Power, I'm not sure that accurately describes it. My main problem with it is that it relies on batting average too much. Take these two imaginary hitters with small samples for example:

Player A: 10 AB, 2 2B, 8 outs

Player B: 10 AB, 4 2B, 6 outs

To me, these two players hit with the same amount of isolated power. However, Player A has an ISO of .200 while Player B has an ISO of .400. Now, this is obviously an extreme case, but it makes me wonder if ISO is, in fact, the best measure you can use to isolate power from batting average.

An alternative to ISO is POW(Power Percentage)(h/t Jack). POW is calculated by (TB-H)/(AB-SO). This just adds in the strikeout rate and is basically defined as extra bases per ball in play, instead of extra bases per at bat.

One thing I don't like right away about POW is that it seems to reward strikeouts. Example:

Player C: 10 AB, 2 K, 3 H, 3 2B, .375 POW

Player D: 10 AB, 0 K, 3 H, 3 2B, .300 POW

I'm not sure I agree with the idea that Player D is hitting for less power on balls in play than Player A. We don't know their exact batted ball profiles, but I have a hard time buying into a power formula that basically adds points for strikeouts. In the long run, it would probably even out but I'm still not sure I like POW.

My solution, and I'm sure it's been suggested before, is quite simple and has a very easy definition. I'd suggest just using total bases divided by hits(TB/H), which is just bases per hit. If a player has a TBH of 1.50, that just means they average 1.50 bases per hit. This doesn't factor at-bats, strikeouts, or anything else in it.

Of all these, it is the most simple, and I think it tells us the most about how much power a player hits for. Unlike the others(including SLG), this statistic has no reliance on batting average, which I think is a good thing if we're just trying to measure power.

Now, I think I'm going to go ahead and ruining this simple statistic by musing on a weighted version. One of the major problems with all of these stats is that they value a home run as four times the value of a single, and in a context-neutral situation, it is not worth that much.

My proposed wTBH would use Tango's linear weights and would look something like:

wTBH = [0.77(1B)+1.08(2B)+1.37(3B)+1.70(HR)]/H

I see two immediate problems with this formula. The first is that the scale would be totally different than the original. Ideally, I'd scale it so that they have the same average, but I am not trying to get into that right now(this is just a thought). The second is that it loses its simple and meaningful definition. Now, it's not just bases per hit; it doesn't have a true baseball definition.

However, if this were scaled correctly, I think it might be one of the best measures of pure power. For now though, I think I'll replace ISO with TB/H when I do my own evaluations.

I've written about my team factors before, but I decided to reformulate them and update them a bit, now that we're more than halfway through the 2010 season.

Methodology

The biggest contribution to these team factors is home park. But there are other effects, such as level of opposition which just can not be truly filtered out while maintaining any statistical relevance. These are intrinsically incorporated into the data, and actually allow us to neutralize the stats with the inclusion of these factors (I just can't quantitate the individual contributions for you).

For the past 2.5 seasons, I have taken rate stats for many primary baseball outcomes for each plate appearance (walks, strikeouts, hits, doubles, triple, homers, stolen bases) and compared home rates with away rates. I've made up a rate called stolen base attempt rate (SBAr), which is the number of total steal attempts divided by the number of times on first base (singles + walks + HBP). It's just meant to be an approximation.

How is this any different that traditional park factors? First, we use rate differentials, not ratios. To me, it makes more sense to look at how often a team hits home runs in each situation rather than using relative levels. Secondly, in order to minimize home field advantage (which is pretty significant for many teams), I average the differences in rates to determine the "team factor" for each of these rate stats.

The team factor is cut in half (since half the games are played on the road) and used to adjust recorded stats to a neutralized batting line. For pitchers, the factors remain the same on a total batters faced basis.

Results

Here are the calculated team factors since 2008, along with the adjusted team lines (second and third tabs) and player statistics through July 6 (fourth and fifth tabs). Please note that the Twins debuted Target Field this year, so their factors are based on only a half season's worth of data. Their factors are understandably not very reliable. Both NY teams opened new stadiums last year, so their factors are based only on a year and a half worth of data.

The stadium with the highest run environment is Chase Field, home of the Diamondbacks. With a very high rate of hits and doubles, you can see why. The second highest run environment is, not too surprisingly, Coors Field in Denver. The thin air lessens pitch break and correspondingly, strikeout rate is decreased. The rarefied air also helps balls carry, and the expansive outfield allows for a lot of hits to fall, though mostly for singles. On the opposite end we have PETCO Stadium in San Diego, which suppresses hits, and according to our factors is the hardest stadium in which to hit a home run. I respect you, Adrian Gonzalez. The most home run-happy parks are Chicago's US Cellular Field, followed closely by Great American Park in Cincinnati. The most double-friendly park? Fenway, with its Green Monster, increases the rate of doubles by almost 2% per PA.

We can talk a little bit about the newest stadiums. So far, it looks like Target Field strongly suppresses HR, yet the run environment is fairly neutral due to an increased number of doubles. The new Yankee Stadium increases your chance at hitting a HR by almost 1%, but it limits doubles relative to the league average. Citi Field appears to limit the number of base hits pretty severely, and dampens home runs quite a bit.

Overrated and Underrated by run environment

So now, the fun part. We can use these numbers in a lot of different ways. Now that we know some of the places where stat lines might be a bit inflated, let's see what the numbers "should" be like, given a neutral environment. For example, Kelly Johnson really impressed everyone with his fast start in Arizona, and his .268/.368/.495 line looks pretty good for a second baseman that nobody wanted. But as we mentioned above, that happens to be the best run environment in baseball. Would it change your mind at all if I told you his neutralized line is just .258/.360/.471? Still a good performance, but now some of that luster is coming off. The model says take away two doubles, a home run, and about 3 runs and 3 RBI.

Now how about the other direction? We've mentioned Adrian Gonzalez, who plays in PETCO, a bad hitter's stadium. His .293/.389/.517 line suddenly jumps to .305/.394/.543 outside of San Diego. Instead of 19 doubles and 16 HR, now he's got 21 and 17. Oh, and tack on 4 RBI for good measure. In fact, that whole San Diego team is not as terrible offensively as you might think; once you correct with these factors, they're actually middle of the pack in runs scored and only the 6th worst offense in baseball by OPS.

Now put Gonzalez in Arizona, and things REALLY start to look rosy for him. You get the idea. Now we can even "trade" players to a different team to see what we might expect from them. Awesome fun.

As for pitching, it's interesting to see that after correcting for team factor, San Francisco and St. Louis are right there with San Diego for best pitching staff. I might argue for the Cards' staff, looking at FIP. It's also interesting to see Texas as the second best ERA in the AL; their staff doesn't get enough credit because of - you guessed it - their run environment!

Jimenez or Johnson?

Now about the real baseball debates. One of the interesting things you can do with these factors is to put two players on a more equal footing. Ubaldo Jimenez captured everyone's attention with his amazing first half, but now Josh Johnson is mowing down hitters like there's no tomorrow. Johnson's got better numbers, but Rockies fans will point out that Jimenez has pitched home games at the second most run-producing park. With these factors, now you can figure some of the difference:

These numbers don't include Johnson's last start, sorry. But you can see that Johnson edges out Jimenez by a slim margin, thanks to his better control.

More to Come

I just noticed that B-R.com has now included L-R splits at each ballpark (yes!), so I want to recalculate these team factors on a righty/lefty basis, the way it really should be done. Thanks for reading, and I hope you've had as much fun as I have.

Well, it's officially halfway through the season, and it's time to take stock of the season so far. That means a lot of things to a lot of people. As someone who's always been interested in player projections, I'd like to see how those projection systems are faring, given the sudden decline of offense, especially in the AL.

Disclaimer: I know it's only halfway through, and a lot can change for many of these players. There's a lot of baseball left, so this is strictly just an entertaining exercise.

Without further ado, here are the 172 qualified hitters in 2010 (as of July 5) and their wOBA, compared with numbers predicted by various well-known projection systems (numbers pulled from FanGraphs):

Just as there was Raul Ibanez last year, there's Justin Morneau this year. I mean, we knew he was good, but THIS good? Likewise, Pedro Feliz is the worst regular to meet the qualification criteria. We all knew he would follow last year with a poor offensive year, but he's just been brutal. Due to the decreased run environment this year, we expect to see a greater number of players overestimated than are underestimated by the projections, and we found that 100 of these were projected too high, while the remaining 72 players were too low or right on.

The most difficult player to predict this year has been Gordon Beckham, whose youth, tools and early success gave no indication of such a poor first half to come. Then there's Adam Lind, who's collapsed offensively this year, and Carlos Lee. Notice a trend here? Todd Helton's low ISO and Morneau's breakout follow in this list.

The player everyone nailed on the head was Jonny Gomes, followed by Evan Longoria and Fred Lewis. You might say that these guys are having "average" years along their expected career numbers without too many statistical blips.

Now if we summarize these results, it might look something like this:

"Omissions" refers to the number of qualified players who had no projection in each system. Looking at the average of the absolute errors for these players, it looks like Marcel comes out on top, while the community Fan projections are every bit as good as the expert projections. Now, it should be noted that the 7 players NOT projected by the fans are rookies and other hard to project players, so had they submitted data for those, there's a good chance that that number goes up. But still, nice win for wisdom of the crowds (so far). And give the crown to the monkey, he's still tops.