“Riddle me this,” wrote editor Dave Cameron to me some time ago, “what happens when an unstoppable force meets an immovable object?”  OK, that’s not exactly how it went down.  What he actually did was to present me with the challenge of research, with the goal being to develop a model that would forecast the expected odds of an outcome of each match-up between a specific batter and a specific pitcher. Rather than talking about how players have done in small samples, can we use our understanding of player skillsets to develop an expected outcome matrix for each at-bat?

For example, such a tool might tell you that Adam Dunn has a 40% chance of striking out against Stephen Strasburg, a 10% chance of drawing a walk, a 5% chance of hitting a ground ball, etc… Forget I said those particular numbers — I completely made them up in my head just now.  You may be thinking “well, why should I care about that?  Rather than just being inundated with match-up data that is little more than randomness, such a tool might give you some idea of how much of a gain in expected strikeout rate a team would get by switching relief pitchers with a man on third base and less than two out. Or what the probability of getting a ground ball is in a double play situation, which might influence the decision of whether or not to bunt. Knowing the odds of potential outcomes could be quite beneficial in understanding the risks and rewards of various in-game decisions.

This project has been — and will continue to be — a major undertaking, as you can imagine.  This isn’t the kind of thing that can just be thrown together, but I really think the results could be great. Today, I’ll be sharing with you the findings of my research into perhaps the most important aspect of these matchups — K%, or strikeouts per plate appearance.  This will introduce the sort of process that will be involved in figuring out all of the other elements of the matchup tool. Read the rest of this entry »

Last week, Mike Trout hit for the cycle. When asked for a comment, coach Mike Scioscia said, “If I’m a betting man, I’ve got to believe there’s another cycle in his career somewhere.” That got me wondering.

Whenever I was in a math class where probability was being discussed, the question often in the back of my mind was, “How can this be applied to baseball?” One of the things I love the most about baseball is how well it lends itself to situations of probability, compared to most sports. I’m not sure what that says about me. Anyway, I figured this would be the perfect opportunity to refresh my memory (and hopefully some of yours) on how to crunch the numbers on situations like this. Don’t worry — the principles work on useful things other than just calculating the odds of that gimmicky achievement we call the cycle. Read the rest of this entry »

“Stabilization” plate appearance levels of different statistics have been popular around these parts in recent years, thanks to the great work of “Pizza Cutter,” a.k.a. Russell Carleton.  Each stat is given a PA cutoff, each of which is supposed to be a guideline for the minimum number PAs a player needs before you can start to take their results in that stat seriously.  Today I’ll be looking at the issue of stabilization from a few different angles.  At the heart of the issue are mathy concepts like separating out a player’s “true skill level” from variation due to randomness.  I’ll do my best to keep the math as easily digestible as I can.

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I think we’re all aware that the lefty vs. righty matchup favors the batter.  But to what extent?  And what are the implications?  Prepare to be inundated with a bunch of charts and tables.

For the purposes of this article, I’ll be sticking to using wRC+, my favorite all-in-one, level-playing-field batting stat.  My sample consists of all batters from 2002-2012 who had at least 200 total PAs against lefties and at least 200 more against righties.

The charts in this article will break down the frequency distributions of wRC+ for left-, right-, and switch-hitting batters, grouped to the nearest multiple of 10.  For example, the chart below shows that 21.5% of right-handed batters (RHB) hit for over 85 but less than or equal to 95 wRC+ against right-handed pitchers (RHP).

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I’m always looking for new angles to unlock the mysteries of BABIP, so I was intrigued by Jeff Sullivan’s exploration of pull rates against pitchers.  So I grabbed the data from baseball-reference.com, and set to work subjecting it to my usual rigmarole of correlations and multiple regressions.  You know how they say if your only tool is a hammer, everything looks like a nail to you?  Well, plug your ears — there’s about to be a lot of wild, uncontrolled pounding going on in here…

I’ll cut right to the chase — did I find anything interesting relating to pitchers’ overall effectiveness when it comes to their Pull%, Middle%, and Opposite%, as I’m calling them?  Well, I found one decent connection that will seem obvious and stupid after you think about it, and a slight but kind of interesting connection.  I’ll provide you with some correlation tables that have left few stones unturned.  But, mainly, the research might help to set some things straight about how important this stuff actually is for pitchers.

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Some of you may recall that before being promoted from a FanGraphs Community Research writer to an actual FanGraphs writer, my primary focus was on the relationship between batted ball types (infield fly balls, in particular) and BABIP for pitchers.  At the time, I’d been leaving park factors out of the equation in a [vain] attempt to keep things simple, but now I want to give them a bit of attention.

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In my first article, I wrote about the limitations of the linear weights system that wOBA is based on when it comes to the context of unusual team offenses. In my second, I explained how Tom Tango, wOBA’s creator, also came up with a way of addressing some of these limitations by deriving a new set of linear weights for different run environments, thanks to BaseRuns. Today, I will tell you about the next step in the evolution of run estimators — the Markov model. Tom Tango created such a model that can be accessed through his website, and I’ve turned that model into a spreadsheet that I’ll share with you here.

I’ve told you that the problem with the standard run estimator formulas is that they make assumptions about what a hit is going to be worth, run-wise, based on what it was worth to an average team. That means it’s not going to apply very well to an unusual team. What’s so great about the Markov is that it makes no such assumptions — it figures all of that out itself, specific to each team. And when I say it figures it out, I mean it basically calculates out a typical game for that team, given the proportion of singles, walks, home runs, etc. the team gets in its plate appearances. It therefore estimates the run-scoring of typical teams better than just about anything, but it also theoretically should apply much, much better to very unusual or even made-up teams.
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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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