Archive for linear weights

In my last article, I explained how wOBA’s current implementation changes the value of walks, singles, home runs, etc., annually due to changing league characteristics.  Does this mean that the value of an event is the same for every team in the league each season?  Or in every park in the league?  No way.  If you’re talking about a weak offense in a high-offense era, then the overall constants for a weak offensive era are probably more applicable to that team.  However, it’s not really the point of standard wOBA to guess the run-producing contribution of a particular player to a particular team; I think it’s probably more accurate to say it’s about his probable productiveness in a typical team (although park effects aren’t taken into account, so not exactly… that would be more true of wRC+).

Anyway, Tom Tango realized this limitation, and produced a table that shows how the values change depending on a team’s runs scored.  He accomplished this system of “Custom Linear Weights” (“a necessary offshoot” of linear weights, he says) by making use of David Smyth’s BaseRuns formula, which is, in simplest terms, Runs Scored = base runners * (% of base runners that score) + home runs.  Home run hitters are not considered base runners, in this equation, by the way.  Makes perfect sense, right?

Tango realized that BaseRuns had a better handle on the team run-scoring process than his basic linear weights system (and all the other run estimators), so he translated the results of BaseRuns in various run environments into linear weights.  Specifically, the BaseRuns formula told him how many runs the team should score, and the linear weight value of each hit came from how many additional runs BaseRuns expected the team score if it had one more of that type of hit (the marginal value of each hit type).  Here are just the basics of his results, in graphical form:

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Well, it’s my first assignment as a real writer, having been promoted for my Community Research articles on pitcher BABIPs and ERA estimators, and I’ve been thrown into the deep end of the pool: linear weights.  It’s a tricky subject, but I’ll try to walk you through both the problems with linear weights and how they can be overcome.  This article series mainly draws from various works of Tom “Tango,” a.k.a. “tangotiger,” the creator of wOBA and FIP, as well as from David Smyth’s BaseRuns.  I’ll go deeper and deeper down the rabbit hole of stat geekishness as the series goes on, eventually emerging with a spreadsheet version of Tango’s Markov run modeler that I made for you all to play with.  Where the Markov mainly shines over wOBA is when it comes to extreme run environments, such as unusual offenses or extreme ball parks.

Who cares about extreme run environments?

Nerds like me, I guess?  Tom Tango cared enough to come up with ways to address the shortcomings his original wOBA formulation.  If you’ve ever wondered how valuable a certain player is to your favorite team, maybe you should care too; that low-OBP slugger might be more valuable than wOBA might suggest to your low-OBP team.  On the other end, a typical walk last year was worth considerably more to the high-OBP Cardinals than it was to the low-OBP Mariners (around 0.04-0.065 more runs each… which adds up over a season).

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Sometimes there seem to be two separate branches of saber-oriented blogging: one that uses sabermetric tools to analyze current events (player transactions, in-game strategic choices, etc.), and another which focuses on more theoretical issues (e.g., specific hitting and pitching metrics). Obviously, the latter is supposed to ground the former, but there still seems to be something of a disconnect between the two levels in popular perception. I say this because I was recently part of a discussion in which some were pointing out the superiority of linear weights run estimators for individual hitters to the approach of Bill James’ Runs Created. Someone then made a comment to the effect that this was simply a nit-picking preference for a “pet metric” that really did not make that much of a practical difference.

Sabermetrics is far from being a “complete” science in any area. Debates about how best to measure pitching and fielding are obvious examples of this. With respect to run estimators, there is a greater level of consensus. However, because of the progress (at least relative to pitching and hitting) that has been made with run estimators for offense, that also means there is less of a difference between the metrics. However, it does make a difference. Rather than arguing for one approach to run estimation over another, I want to simply look at a few different free agents from the current off-season to see what sort of difference using one simple run estimator rather than another would make on a practical level.

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With a classic World Series — the most exciting in a long time, if not the best-played or best-managed — now over, it is time to hand out individual awards for the 2011 regular season. Sure, some people are anticipating the Cy Young, MVP, and Rookie of the Year announcements, but I bet true baseball fans really pumped for stuff like today’s award, which attempts to measure how much a hitter has contributed to his team’s wins beyond what traditional linear weights indicates. Who is 2011’s King of Little Things?

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With the increasing popularity of wOBA and other linear-weights-based offensive measures, OPS and its derivatives have become obsolete. That is as it should be. However, three “three slash” (AVG/OBP/SLG) still has its uses. While wOBA and its cousins are to be preferred as an evaluative measure of a player’s offense, the AVG/OBP/SLG combination still has a helpful descriptive role.

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I have done a number of posts since end of the 2010 season ranking players and plays based on stats not normally given prominence. But I haven’t yet done one of my “classics”: the season’s “King of Little Things.” As the name implies, it is an attempt to quantify a player’s contribution with regard to the game state beyond average run expectancy. Who were the best and worst in 2010?

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When the “rebuilding” San Diego Padres started 2010 well, most thought they wouldn’t stick. However, with with less than fifty games to go, the Padres are still in first place in the National League West. Predictably, various explanations have been given for this, and talk of how they are “staying within themselves” and being “consistent” is cropping up, as in this recent entry by Buster Olney (Insider) quoting a scout to the effect that the Padres don’t have a very good offense outside of Adrian Gonzalez, but are winning more due to their willingness to move guys over and play their “roles” in an intelligent way to maximize their plate appearances.

It is probably true that the Padres are outplaying their “true talent” to an extent, but teams and individuals overperform and underperform their true talent all the time. What is more interesting is the implication that the Padres are getting “more bang for their buck” offensively by doing the “little things” that just help a team win. My interest is not in taking Olney or the scout he quoted to task. Rather, I want to see if the numbers bear out the idea that the Padres are getting more wins out of their offense than they “should” because of their execution, because of the “little things.”

The “little things” are often brought up in reference to teams who outperform their run differential, e.g., some recent Angels teams. The first thing to note about the Padres, however, is that they are not outplaying their Pythagorean expectation: they are actually two wins under what their run differential suggests. So one could argue on that basis alone that the Padres are being “inefficent” in their wins.

But that does not specifically address whether their offense has generated more wins than they “should.” This implies that the Padres have a poor offense. At first glance, one would say “yes,” as the Padres’ team wOBA of .311 (43 linear weights runs [a.k.a. wRAA] below average) is the among the worst in baseball. However, that needs to be understood in context. The Padres have one of the most hitter-unfriendly home parks in the major leagues. In addition, runs above/below average is baselined against all of the MLB, and includes pitchers hitting. To get a better picture, let’s use the park-adjusted linear weights runs from the team value pages and compare to the rest of the NL. In this light, we see that the Padres’ offense is actually four runs above average, and the only team in the NL West above average. So the Padres’ offense has been one of the better in the NL, and the picture of a team miraculously scraping out runs with inferior hitters is already a bit distorting.

Still, even if the Padres offense has been good, is it doing things to deliver more wins than than traditional linear weights measures?

One way of trying to quantify this is to measure their traditional “context-free” linear weights (wRAA, Batting Runs, etc.) against the difference in run expectancy based on base-out state, as I discuss for individuals here. In short, we can subtract a team’s traditional linear weights (“Batting”) from their RE24 to see how much run value is added by hitting “to the context.” Doing this for the Padres (35.84 RE24 – 4.2 Batting) gives a “situational” added value of about 36 runs, which is obviously good.

However, if we’re going to emphasize “context” when discussing a situational hitting, shouldn’t we go all the way, and include not just base/out state, but inning and overall game situation? This is what WPA/LI does. For more detailed explanation of the following, click here, but a brief example can illuminate the difference. Take the following situation: tie game, bottom of the ninth inning, bases loaded, two outs. In this situation, wRAA and RE24 consider a walk and a home run to have very different linear weights values, whereas for WPA/LI it has the same, since it adjusts linear weights to game-state contexts. So if we subtract traditional linear weights (converted to a wins scale) from that, we see how many contextual wins they’ve added beyond the average value of events. And when we do this for the 2010 Padres, we get -0.79 wins. In other words, their offense has actually helped their team win fewer games than one would expect by just looking at the events out of context.

The 2010 Padres are a good team. Their pitching (particularly in relief) has been very good, although that praise should be tempered for the same reasons that we should realize that their offense has actually been better than one might think: the park. They also have been excellent in the field. Those are the reasons that should be given for their success this season. I don’t know whether or not the “little things” stat used above represents a repeatable skill, but whatever the case may be, it is not true that the Padres are getting more wins for less offense.

Late to the party as usual, for the past few weeks I’ve become more and more interested in pitch-type linear weights for hitters.* In particular, I was curious as to what they might reveal about which hitters are particularly good at hitting particular kinds of pitches. For example, we sometimes call certain hitters “fastball hitters.” I’ve heard one of particular minor leaguer who shall remain nameless who hasn’t been called up because he allegedly has a “slider-speed bat” (given the dearth of other players in that particular organization that can hit the slider, you’d think that would be seen as a good thing…). And so on.

I thought that it would be interesting to look at differentials in linear weight values between pitches for different hitters. I found some interesting stuff, but I want to avoid the illusion than pretend that I’ve “discovered” anything at this point, so I’ll begin with a post (or two) about an individual . In the spirit of Dave C.’s earlier “questions” posts, this is the beginning of a conversation (and I hope to get more in-depth later) rather than the conclusion of a study. For today, I want to talk about Jimmy Rollins‘ recent problems against the fastball against the backdrop of his continued success against changeups.

* If you haven’t already read Dave Allen’s clear and excellent explanation of how pitch type linear weights work, I strongly recommend that you do so.

While Rollins is still a good player overall, there’s not denying that 2009 was a down year offensively, as he put up a mere .316 wOBA after a very good .357 in 2008 and an excellent .378 in his 2007 MVP campaign. This is well known. There could be different reasons for it (which may all have roots in age-based decline), for example, bad luck on balls in play. But what also stands out are his pitch-type linear weight values against fastballs and changeups.*

* Those of you who dutifully read Dave’s article already know that the linear weights are by count, there is the chance, of course, that recently Rollins is only falling behind on fastballs then crushing them later, but that seems pretty unlikely, and for simplicity we’ll be ignoring that possibility for now.

Over the last three seasons (2007-2009), Rollins has been +6.3 against fastballs, and +22.8 against changeups during the same period. As one might expect, during that time his best season against fastballs was 2007, when he was +10.7. He was even better in 2006, at +20.4. However, he’s been in (apparent) decline against fastballs since 2006 and 2007, sporting a -1.8 in 2008 and a -2.7 in 2009. His rates per 100 fastballs bear out the decline as well: from 0.58 in 2007 to -0.12 to -0.17.

In contrast, Rollins continues to be consistently good against change-ups. While prior to 2007, his numbers against changeups where generally unimpressive, in 2007 he smashed them for +13.3, and while he hasn’t been as good (against much of anything) since then, while he numbers against fastballs dropped off, in 2008 he was still +4.5 (+1.29/100) against changeups, and in 2009 +5.0 (+1.36/100). More interestingly, of the good hitters I looked at (bad hitters are terrible against most everything), Rollins had one of the biggest “gaps” in his numbers between fastballs and changeups. I’m curious as to what this means.

Obviously, players typically lose ability as they age, but I’m curious if the linear weights tell us something specific about how that works for hitters. I apologize for ending with questions, but that’s better than presumptuous answers. I want to know if readers a) have any insight (even educated guesses) into what’s going on with Rollins in particular and/or b) want to see more stuff on this. Is Rollins “sitting changeup” more often as he gets older? Maybe, I don’t know for sure from the data I have. It would be easy to say he’s doing this because he’s aware that he’s “lost bat speed,” but to me, that is also a leap — “bat speed” is a useful scouting term, but it is too quick to infer anything about that that from the data I’m looking at. Perhaps an aging study can be done down the road using this or other data. I don’t know what this means right now, but I’m interested to see if we can find out.

Frank Thomas, a.k.a. “The Big Hurt,” officially retired today. However his career ended, his up-and-down (but hardly bad) 2000s makes it hard to recall his utter dominance in 1990s. I’m not going to get into the Hall-of-Fame debate about Thomas or designated hitters. Yes, we have to adjust for his defensive “contribution,” but fortunately, Wins Above Replacement does just that. The “FanGraphs Era” currently only extends back to 2002, so for some historical WAR perspective, let’s compare some career WAR numbers from Sean “Rally” Smith’s historical WAR database.

Frank Thomas 75.9
Pete Rose 75.4
Johnny Bench 71.4
Brooks Robinson 69.2
Edgar Martinez 67.2
Duke Snider 67.2
Eddie Murray 66.7

To repeat: these numbers adjust for Thomas’s non-contributions on defense. If you think the players below him on that list are Hall-quality, then Thomas, who was “only” a monster hitter, should get in, too.

Enough of that, let’s discuss Thomas’s greatness as a hitter. For this, I calculated linear weights using data from the Baseball Databank. I use the same basic version of custom linear weights/wOBA that FanGraphs does, but having it on my own database just allows me to manipulate the data for stuff like this.* The linear weights (aka “Batting Runs” or wRAA) are customized so that each event is weighted properly for each season. The runs above average are park-adjusted (thanks, terpsfan). I then convert them to wins, which further reflects the relative value of a run in that season.

* There are probably some slight differences due to discrepancies in source data, different park adjustments, etc. but it’s very close. The batting runs also differ from Rally’s, since his weights are adjusted to reconcile on the team- rather than league-level. Neither is “right” or “wrong,” they are simply two different perspectives.

The top six career leaders in Batting Wins Above Average since 1955 (the first season Baseball Databank records intentional walks):

1. Barry Bonds 126.3
2. Hank Aaron 108.5
3. Willie Mays 91.0
4. Frank Robinson 89.7
5. Mickey Mantle 83.0
6. Frank Thomas 71.5

Granted that good chunks of Mantle and Mays’ value came before 1955… that’s still impressive company. Among those with career numbers inferior Thomas are: Jeff Bagwell (64.0), Willie McCovey (62.8), Harmon Killebrew (60.0), Mark McGwire (56.9), Jim Thome (55.4), and Sammy Sosa (34.8).

Another way of judging impact is to compare overall career numbers with peak value in order to separate guys who just hung on. So let’s look at Thomas and two other great hitters of somewhat recent vintage and compare their career Batting Wins, their top three seasons, and the five-year continuous peaks:

Edgar Martinez
Career Batting Wins Above Average: 54.4
Career wRC+: 151
Top Three: 18.0 (6.8 in 1995, 5.6 in 1996, 5.5 in 1997)
Five-Year Peak: 27.5 from 1995-1999

Mark McGwire
Career Batting Wins Above Average: 56.9
Career wRC+: 161
Top Three: 22.1 (9.3 in 1998, 6.7 in 1996, 6.1 in 1999)
Five year Peak: 30.1 from 1995-1999

Frank Thomas
Career Batting Wins Above Average: 71.5
Career wRC+: 158
Top Three: 20.6 (7.1 in 1991, 6.8 in 1994 [!], 6.7 in 1992)
Five-Year Peak: 31.4 from 1992-1996 (includes 1994 strike)

I included Edgar because of the recent discussions about him, and also because, while he was obviously a great hitter, I wouldn’t have thought his numbers would stand up so well against say, McGwire’s. They aren’t quite as good, but they are in the same territory. McGwire was obviously great, but I think not only Thomas’s career numbers, but arguably his peak was better, too. His five-year peak is slightly better, and though his top three seasons (or best one) aren’t quite as good as McGwire’s, his second and third best seasons are better than McGwire’s.

Moreover, both Thomas’s top three and five-year peak both included the strike-shortened 1994 season. Regression to the mean tells us that Thomas likely wouldn’t have continued at that rate, but do you think he would have hit at a league-average rate or below the rest of the season? There are a lot of “what ifs” in baseball, of course, and in 1994 in particular, as Expos fans know. But 6.8 Batting Wins in 113 games is simply astounding. And keep in mind that the AL was the more difficult league starting in the 1990s.

I’m not sure what better compliment to end on other than to say that when all three were at the top of their game(s), Frank Thomas was a more dominant hitter than Mark McGwire and Edgar Martinez.

Most of us are still recovering from this week’s Big Awards Euphoria, especially from Monday’s announcement of the 2009 Carter-Batista Award winner (I recommend reading that post before this one), which found that Ryan Ludwick was the 2009 player whose RBI total most exaggerated his offensive contribution.

Personally, I feel that the RBI/wRC system is the best way for figuring out how much RBI totals reflect true offensive contribution. But I also understand that some prefer a more “contextual” approach. As I did at greater length in an earlier series, let’s revisit the same ground using one of FanGraphs’ more context-sensitive stats — RE24 (Cf. Part Two of my Driveline Series) — to discover an “Alternate Universe” winner.

RE24 might appeal to those who believe situational hitting is a repeatable skill (I’m currently agnostic on this). The basic difference between RE24 and traditional linear weights (e.g. wRAA) is that it takes base/out state into account. For traditional linear weights, a double with two men on and two outs “counts” the same as a double with none on and no outs. RE24 recognizes that in those situations, the run expectancy both before and after the plate appearance are different. To quote myself:

There are 24 base-out states (hence the “24” in “RE24”): eight different combinations of baserunners (e.g., runner on first, bases empty, runners on second and third, etc.) multiplied by the three out states in which hitter might have that situation (no outs, 1 out, 2 outs). RE24 measure the difference in Run Expectancy from the beginning of the play until the next play.

For our purposes, the application is obvious — RE24 might identify players who were particularly good in situations with high run expectancy, and thus “earned” their RBI more than wRAA lets on.

To convert RE24 to an “absolute” measure like wRC, subtract the wRAA from wRC and add RE24. I call this “24RC“. Divide RBI by 24RC to get the comparison of real (situational) production to RBI. [Note that it’s not quite apples-to-apples, RE24 is park-adjusted, and the RBI are not, although it’s not a big problem.] The players are ranked by RBI/24RC. I’ve also included a number that sort of isolates situational contribution by subtracting wRAA from RE24. I dubbed it “Sitch.” Clever, huh?

Here are the 2009 Alternate Universe Carter-Batista Award leaders (among qualified hitters with at least 90 RBI).

5. David Ortiz, 1.134 RBI/24RC. .340 wOBA, 99 RBI, 6.40 Sitch
4. Alex Rodriguez, 1.138 RBI/24RC. .405 wOBA, 100 RBI, -10.03 Sitch
3. Michael Cuddyer, 1.141 RBI/24RC. .370 wOBA, 94 RBI, -17.48 Sitch
2. Cody Ross, 1.188 RBI/24RC. .342 wOBA, 90 RBI, -3.02 Sitch
1. Jose Lopez, 1.202 RBI/24RC. .325 wOBA, 96 RBI, 3.72 Sitch

Congratulations, Mr. Jose Lopez! You may have been just outdone by Mr. Ludwick on Monday, but here in the alternate universe, You’re the Man. Maybe in that alternate universe you’re on Shaq Vs., too. Kate Hudson works wonders, I wonder what B-list actress Big Papi is dating? Michael Cuddyer is showing that it’s not his Sitch (or defense) that got him resigned, but those awesome RBI. And what can I say about Cody Ross? Seriously, what can I say?

2009 “Trailers”

47. Adrian Gonzalez, .772 RBI/24RC. .402 wOBA, 5.29 Sitch
48. Joe Mauer, .751 RBI/24RC. .438 wOBA, 0.32 Sitch
49. Chase Utley, .727 RBI/24RC. .402 wOBA, 4.14 Sitch

Someone recently asked me what it would take for Chase Utley to win the NL MVP. I said to wait a couple years for Pujols to reach free agency and come home to Kansas City. I guess I didn’t realize how terrible Chase is at maximizing his RBI opportunities.

2007-2009 Leaders and Trailers (qualifed, 250 RBI minimum):

1. Jeff Francoeur, 1.30 RBI/24RC. .313 wOBA, 252 RBI, -17.62 Sitch
2. Bengie Molina, 1.28 RBI/24RC. .317 wOBA, 256 RBI, 23.29 Sitch
3. Robinson Cano, 1.28 RBI/24RC. .346 wOBA, 254 RBI, -53.47 Sitch
4. Garrett Atkins, 1.19 RBI/24RC. .339 wOBA, 258 RBI, -6.31 Sitch
5. Mike Lowell, 1.18 RBI/24RC. .359 wOBA, 268 RBI, -4.79 Sitch
6. Ryan Howard, 1.16 RBI/24RC. .385 wOBA, 423 RBI, 22.80 Sitch
…
43. Lance Berkman, 0.80 RBI/24RC. .397 wOBA, 288 RBI, 25.32 Sitch
44. Albert Pujols, 0.80 RBI/24RC. .440 wOBA, 354 RBI, 15.22 Sitch
45. Hanley Ramirez, 0.72 RBI/24RC. .409 wOBA, 254 RBI, -27.34 Sitch

Note how much the Sitch scores fluctuate on both ends of the rankings and draw your own conclusions. Any list with Frenchy and Bengie on one end and Pujols and Han-Ram on the other speaks for itself. Other than noting Cano’s Sitch issues (!), I’ll leave it to you all to fill in the blanks. Perhaps this spreadsheet with complete rankings will help.