Over the past four weeks, I’ve discussed a number of statistics that can help you win your fantasy baseball league. In each article, I’ve mentioned the influence that “luck” plays on the statistic. I realized, though, that I’ve never actually talked about what I mean by the word “luck.”

When we evaluate a player, there are several layers to look at. The most obvious of these layers is the results. This layer consists of stats like batting average, RBIs, ERA, and other categories that typical fantasy leagues use for scoring. Since they are used for scoring, lazy owners – or perhaps uninformed owners – focus solely on them. This, as I’m sure you’ve realized, isn’t especially sound. If we look at the relationship between a player’s batting average from year-to-year, we see that there is an unspectacular 0.37 correlation coefficient and a pretty poor 0.14 R2 (using 2004-2007 data for batters with at least 200 at-bats in both years). Other statistics, like ERA, perform even worse.

What we need to do instead is focus on a player’s skills and indicators. For a category like ERA, skills include the things we mentioned in our discussion on DIPS Theory, things like strikeouts, walks, and ground balls. When we talk about ERA indicators, we’re referring to stats like Left on Base Percentage, Batting Average on Balls in Play, and Home Run per Fly ball.

These indicators, though, tend to fluctuate a good deal, and this fluctuation is often referred to as “luck.” What I mean when I chalk some thing up to luck is, generally speaking, unexplained variation in a statistic. This does not, however, mean that “luck,” in the sense that I am using it, is completely random. It could just be that we don’t have the proper stats at the moment to filter out the noise.

For example, there is a great deal of fluctuation with hitter BABIP. Right now, we don’t really have a great method for predicting BABIP. I may refer to the fluctuation in BABIP as “luck,” but that doesn’t mean that skill isn’t involved in the parts of BABIP that we can’t currently predict. In fact, I have a feeling that within another couple of years we will have made significant strides in predicting BABIP. Greg Rybarczyk’s wonderful program, HitTracker, keeps track of how hard batters hit the ball (Speed Off Bat). Once Greg gets enough help to track all batted balls (not just homers, as HitTracker currently does), I think this Speed Off Bat data will be the key to a hitter’s BABIP. Greg actually penned an article for the 2008 Hardball Times Annual that briefly examines this idea, which definitely shows promise.

In other instances, we might have information but have no real way of quantifying it. While we try to objectify statistics as much as possible, we need to remember that we are studying human beings. And with human beings come unpredictability. Maybe a player’s father died or maybe the player has been diagnosed with a mental disorder, like depression. In July of this year, Matt Wise of the Milwaukee Brewers hit a player in the head with a pitch. He tanked the rest of the year, but how much of this was due to that stray pitch? These types of things can obviously affect a player’s performance, but they affect every player differently, and we therefore have no way of getting real feel for just how much of a player’s performance variation should be attributed to them.

Perhaps even more prevalent than being unable to quantify this information is the absence of the info in the first place. Again, we are dealing with human beings, and just because they are baseball players and are in the media spotlight does not mean that they are required to share every detail of their lives with us. Things may be happening behind the scenes that affect a player’s performance that we are oblivious to. We simply have no way of knowing, so we simply classify it as “luck,” which, as I mentioned, isn’t just random chance. It is unexplained variation in stats, which these personal issues fall squarely into.

Other times, this unexplained variation won’t be due to a lack of available stats or information at all. In some cases, it will be random chance that affects the numbers. In some cases, it will simply be pure, dumb luck. This is true when working with any set of statistics, and while it can’t be accounted for, it does need to be recognized. That is part of what we mean when we talk about a stat like HR/FB regressing to the mean. Stats, especially baseball stats, are subject to unexplained external noise that is not likely to be repeated. If it isn’t repeatable, than it isn’t really a skill, is it? And if it isn’t repeatable, than what possible forecasting value does it have? We need to focus on the stats that we have to work with now (while continuing to try and come up with new and improved ones), utilize the components that we can explain, and expect the pieces that we cannot explain to even themselves out, at least for the time being.

Moving away from my explanation of luck, I wanted to talk about how we should be expecting luck to affect future numbers. Say a pitcher posts a 2% HR/FB rate in the first half of a season. We know that pitchers tend to regress towards the league average of around 11%. Does this mean that the pitcher should post a HR/FB around 20% in the second half to even things out?

I’ve known many players to point to the “law of averages,” as they call it, to try to validate this hypothesis. They say that if a player was expected at the beginning of the year to post an 11% HR/FB rate and it is only 2% in the first-half (which is unsustainable), then there is a good chance he will post a HR/FB significantly higher than 11% in the second-half to make up for it.

In baseball – and anyone who has ever played poker seriously or has some knowledge of games theory knows this – it doesn’t matter how you arrive at a particular point. All that matters is that you are there and that you have a clean slate at every single new moment that arrives. By originally projecting an 11% HR/FB rate, we were expecting this pitcher to be unaffected by luck, or to be affected by neutral luck (however you look at it). Just because he catches a run of really good luck doesn’t mean we should change our opinion of him in this regard. We should still expect him to post luck-neutral stats.

Luck, when examining a large quantity of players over a long period of time, will tend to even itself out. But when you are looking at an individual player over a short period of time, luck should not be expected to correct itself so quickly. It just doesn’t work that way. You should always expect luck to be neutral moving forward, at all times, because as we said before, our definition of luck is “unexplained variation.” If it is unexplained, why would we try to predict it? It is a fool’s errand.

Over the past couple of weeks, we’ve been building a pretty good toolbox of stats... better yet, a utility belt of stats… like Batman uses… with which to evaluate pitchers. So far, we’ve discussed DIPS Theory, Batting Average on Balls in Play (BABIP), and Home Run per Fly ball rate (HR/FB). Today, we’re going to add another gadget to our utility belt by talking about Left On Base Percentage (LOB%).

Left On Base Percentage measures the portion of base runners that a pitcher (or subsequent relief pitchers who inherit runners, if the original pitcher leaves mid-inning) prevents from scoring. There are some slight variations to how it is calculated, but the formula that I use is as follows:


Left On Base Percentage is very important to a pitcher. It is really a measure of how many runs a pitcher allows given that there are runners on base. It is not surprising, then, that pitchers who allow a lot of base runners have worse LOB Percentages. Dave Studeman of Hardball Times put this concept quite succinctly:

The reason is simple: baserunners accumulate. If you allow only a couple of baserunners per game, chances are very good your LOB% will be 100%. However, as you allow more runners on base, chances are better that they will get on base in the same inning, making it more likely they will score. As you allow more runners on base, your LOB% will fall at an ever-faster rate. So good pitchers—who allow fewer baserunners—will have better LOB% rates.

We use Left On Base Percentage similarly to how we use BABIP and HR/FB. There is a considerable amount of luck involved, and we look for guys substantially above or below average to regress towards the mean. Like BABIP, there is also a significant amount of skill involved, as mentioned above.

Let’s run some tests to see exactly how much skill plays into LOB%. For this test, we’ll use Luck Independent ERA (LIPS ERA) as our independent variable. I know that I’ve mentioned it in passing, and I’ll be talking about it in more detail once we cover all of these other components, but for now just understand that LIPS ERA is a measure of a pitcher’s skill with neutral luck involved. Furthermore, we’ll use LOB% as our dependent variable.

Correlation Coefficient: -0.40
R2: 0.16
Adjusted R2: 0.16
P-value: 1.96E-22
Level of Significance: 1%

Essentially, what this all means is that as LIPS ERA decreases, LOB% increases. It also says that LIPS ERA can predict 16% of the movement of LOB% and that the tests are highly statistically significant.

16% might not seem like a lot, but it really is, and I’m not claiming that LOB% is entirely (or even mostly) skill driven anyway. It has a lot of luck involved, and that’s why we’re looking at it. In addition to luck, “clutch pitching,” if you will, can play a part in LOB%. If a pitcher tends to put up better (or worse) numbers when runners are on base, it will be reflected in this stat.

To further show just how important LOB% is, let’s run these same tests using LOB% as our independent variable and ERA as our dependent variable.

Correlation Coefficient: -0.76
R2: 0.56
Adjusted R2: 0.56
P-value: 1.3E-104
Level of Significance: 1%

Conclusion: As LOB% goes down, ERA goes up. 56% of ERA movement can be predicted by LOB%. It is extremely statistically significant. LOB% is very important.

So how do we use LOB% for fantasy purposes? Well, in general terms, the pitchers that are at the extremes of LOB% should be expected to regress. League average is generally around 71%, but here’s a table breaking it down by year in case you’re curious.


Check out how the 2006 LOB% leaders regressed in 2007:


As we saw last week with HR/FB rates, most guys tend to fall back into the typical, league average pattern. There are a few who did not, though. For most of them, the reason is because their skills support an above-average LOB%.

Roy Oswalt generally puts up good peripheral numbers and has had a LOB% below 76% just once in his career. Johan Santana hasn’t been below 76% since 2002 (which was also, not coincidentally, the last time his K/BB was below 3.00).

Chuck James, though, isn’t explained as easily. He has put up excellent LOB% despite LIPS ERAs of 4.72 and 4.55 in 2006 and 2007, respectively. These are the only two years we have of him, so we can’t call this a career trend as we did with Oswalt or Santana, and his peripheral numbers aren’t very good. He isn’t particularly better with runners on base either. In 2006 there was relatively no difference between his overall peripherals and those with runners on, and in 2007 he was only marginally better. I’m calling for some serious regression next year.

Curious who else you should be looking out for next year? Here are the best and worst rates of 2007:


That concludes Stat Head for this week. You guys now have some great ways of evaluating pitchers, and I’ll be explaining how to put a lot of this stuff together within the next couple of weeks. After that we’ll move onto hitters for a while.

Last week, I talked about DIPS Theory, its relevance to pitchers, and the fantasy implications that can give you an edge over your competition. If you recall, I digressed a couple of times to say that home runs are not completely within a pitcher’s control. I’d like to talk a little more about this today.

To measure a pitcher’s home run prevention, there are a couple of statistics we can use. The first is the method we use to typically measure strikeouts and walks, which is per nine innings, calculated as follows:


The second stat we can use is the Home Run per Flyball statistic. It is a simple ratio that is calculated as follows:


If we test the year-to-year trends of the two (using 2004-2007 data), we see that HR/9 has a correlation coefficient of 0.33 and an r2 of 0.11. For HR/FB, the correlation coefficient is 0.18 and the r2 is 0.03. These tests are statistically significant and show that pitchers have a little control over their home run rates, but that control is not great. Much of it is unexplained.

To help explain it, and to forecast future performance in this area, we turn to the HR/FB stat. Tests show that pitchers tend to regress to the mean, which is typically around 11-12%.

Pitchers have a little bit of control over their HR/FB rates, and home ballparks can explain a small portion of deviation, but pitchers who are significantly above or below this mark should be expected to regress.

As a quick example, let’s check out the pitchers in 2004 that had the lowest HR/FB rates and their corresponding HR/FB rates in 2005. To qualify, a pitcher needed at least 12 starts in both years.


As you see, they all got higher, and most of them put up HR/FB rates near 11% in 2005. Of course, just because a pitcher was heavily affected by luck in 2004 doesn’t mean that he can’t be heavily affected by luck in 2005. Hudson’s luck actually went the other way. But that’s why they call it luck. It happens, it is unpredictable, and the best we can do is assume that it will be neutral.

Here’s another thing to keep in mind when using HR/FB to make your own assessments. It is not uncommon for pitchers with extreme ground ball rates to have slightly higher HR/FB rates. Below is a breakdown of the league average HR/FB and the average among pitchers with at least 50 innings pitched and at least a 50% and 53% expected ground ball rate. The differences aren’t enormous, but you should be a little more lenient with these guys.


So which players’ ERAs figure to significantly change when their HR/FB rates regress? In the following tables, I’ll also include the pitcher’s ERA and xFIP to highlight the affect that these rates can have on an ERA.

I talked a little about xFIP last week; it measures a pitcher’s ERA using his peripheral stats while normalizing his home run rate. There is a stat that I like better than xFIP – LIPS ERA – which I’ll talk about at some point in the future (in three weeks, probably), but for now xFIP does the trick. First, let’s check out the HR/FB losers.


Some people will look at Chris Young’s HR/FB rate and quickly write it off as a function of Petco Park. There is no possible way, however, that a ballpark caused his HR/FB rate to be 7% lower than league average. It’s just not possible. There were other factors at play, and we shouldn’t expect him to put up anything lower than a 9% mark in 2008. Here are the winners.

Like I said last week with BABIP, don’t take these numbers at face value. Make sure that they are supported by solid skills. Felix Hernandez has excellent skills, and the HR/FB rate in 2007 serves to suppress his value going into 2008. He is a guy who should probably be targeted. Dontrelle Willis, on the other, has declining skills, and it is now being said he’ll be moving to the more hitter-friendly American League. Despite his higher-than-normal HR/FB, he figures to go higher in fantasy drafts than he deserves to.

Also, HR/FB is not the only luck component of ERA, so the affect of it won’t always be as apparent as it is in most of the cases above. In some cases, a pitcher’s xFIP and/or LIPS ERA will be higher than his actual ERA, even with an unlucky HR/FB rate. In these cases, there are likely other indicators (like BABIP, for example) that are acting even more powerfully. HR/FB does have a significant affect, though, and should be considered by all fantasy owners who take winning seriously.


That wraps up Stat Head for this week. If you have any questions about HR/FB or anything else in this vein, feel free to send me an e-mail. Next week I’ll probably talk about Left on Base Percentage (also known as Strand Rate), which is another critical indicator for pitcher ERAs.