THE BOOK--Playing The Percentages In Baseball

Thursday, September 16, 2010

Wars of WARs

I’m going to link to Neyer’s piece mostly because I love his headline.  Rob also says:

But it’s probably not going to happen soon, and I guarantee none of those guys will listen to me. They’re subject to the same prejudices as the rest of us, prone to the same egos and interests. But they’re also more amenable to reason than most of us.

I just want to say that this has nothing, nothing at all, to do with ego.  But Rob is right that this is all about reason.

The WAR framework has developed over time.  It started at least as far back as Pete Palmer’s Hidden Game, where he started off with WAA (wins above average).  The basics were laid out: offense above average, defense above average, some sort of fielding position adjustment, some sort of relief adjustment.  After that came Bill James, who had offensive and defensive wins and losses, which he then compared against “chance that these number of W/L were put up by a .400 player”.  And then Bill James again in 1987 comparing Clemens/Mattingly and Rice/Guidry, where the first fresh talk of replacement level came in (specifically noting that the replacement level for pitcher, in that article, was one run above league average). After that, there was (I’ve been told) BBBA, and also Woolner’s VORP followed by Clay’s WARP, and Bill James with Win Shares.  Those guys brought it up a notch.

When I became involved was at the old Fanhome boards (RIP) where we had many many many discussions of replacement level.  Then, about three years ago, I had what I wanted: the positional adjustment and the relief adjustment.  The positional adjustment was, I think, the last big piece in order to stabilize the WAR framework.  It was one of those things that was bothering me for a long time, and with some help from the readers of this blog, I was able to crystallize that.  The relief adjustment was in due in large part to Guy’s contribution, though minor in the grand scheme of things, was major as it related to the very small subset of pitchers out there.

And that’s where we are: the WAR framework.  The WAR framework is about offense compared to average, fielding compared to positional average, a positional adjustment without relying on the offense for that position, a playing time value (replacement level); on the pitching side, different baselines for starters and relievers (a concept first introduced by Woolner); a league adjustment.  Fangraphs and Baseball-Reference agree on this.  And, I suspect that Baseball Prospectus is trending toward this framework.  If we don’t have consensus, we are going to get it.  I’ve been dealing with the WAR framework and chatting with the readers of this blog for so long that I think that any of the major issues have been hashed out.

So, what’s the issue then?  Well, now that we have a framework, everyone wants their own implementation of that framework.  Not all houses are built the same, are they?  But they all have the same foundation, the same basic structure.  There are two major differences in the implementation (the houses) built by Fangraphs and Baseball-Reference over the WAR framework (blueprint) that has been developed and championed by me and other readers of this blog:
1. UZR v Total Zone: the fielding systems are different; they are different because one guy has access to more data than the other. 
2. DIPS v Runs Allowed: one takes a belief system that they are only going to rely on non-BIP for pitching, while the other takes the belief system that all runs are attributed to the pitcher, regardless of sequencing of events, with some generic team-based fielding adjustment

There are other minor issues, like how park factors are used, what kind of relief adjustment is made, what kind of AL v NL adjustment is made, how low or high to set the replacement level, among a few others.

But, they’ve both agreed on the WAR blueprint.  Now, the discussions is on the peripherals, about whether to use a two by eight or a two by ten, about whether to use solar panels, about whether to hardwire the smoke detectors or use wireless.

In no way will further discussions lead to invalidating one implementation or the other.  In no way should anyone choose a position based on ego.  The implementation I favor is whichever one I can backup with evidence, one that I can verify and stand behind.  I stand on the side of truth, or at least one of reason.  I have no agenda other than to expose holes and make sure there are no cracks in the foundation.  (e.g., If someone is going to use Runs Created instead of BaseRuns or Linear Weights, that’s a crack, and I will expose it.)

Until then, presume that all sides have something to add, and just take the midpoint of them all. 

Tuesday, September 14, 2010

WAR as an example of critical thinking

My response, or addendum, to Colin:

I agree wholeheartedly with Colin.  When I was developing the framework for WAR, it was all about breaking it down by components, so that we can see how it works, and, if one so chooses, replace the calculations of one or more components with other sets of calculations.  WAR is a framework that is easy to follow and accept.

As an example, look at the way Fangraphs lays it out for Ryan Zimmerman.

We see that he’s +31 runs above average in offense, +16 runs above position average in fielding, +19 runs for playing time, +2 runs for his position, for a total of +67 runs (rounding issues notwithstanding).  The conversion to wins makes it +6.9 wins above replacement according to Fangraphs’ implementation of the WAR framework (fWAR).

Now, suppose you don’t like the fact that fWAR uses UZR.  You are a Total Zone maven.  Well, guess what, you simply move one number in, and move one number out.  It doesn’t invalidate the rest of the metric.

Suppose you think replacement level is set too high, or too low.  Well, change that too.  Suppose you think Linear Weights makes no sense, and prefer BaseRuns.  Well, go ahead, knock yourself out.  Suppose you think that 3B is easier to play than 2B.  Change that too.

The important point is that you have a FRAMEWORK.  Create that, adopt that, follow it.  That’s WAR.  Now, once you have a framework, you need an implementation.  You can be lazy and let Fangraphs (fWAR) and Baseball Reference (rWAR) figure that out for you.  Or, gulp, you can do as Colin says here and think for yourself.

What you can’t do is just throw your arms up and say the solution is too difficult AND THEN proceed to give us your opinion as to who is the most outstanding player!  If it’s too hard to find the solution, then your opinion becomes irrelevant.  It’s a bullsh!t opinion, because it’s a summary opinion without evidence.

So, this is what sabermetrics is about, the journey, the thought process, the critical thinking.  Do it, because we can never have enough people doing this.

Monday, September 13, 2010

Poz’s ode to WAR

Perfect.

Saturday, September 11, 2010

Understanding Ryan Howard’s WAR

Crashburn Alley educates MSM.  Great job, and I agree with his thought processes as well.

Friday, September 10, 2010

Tango’s Lab: Game Score

Let me present you with 4 different versions of Game Score, where the starting point is not 50, but 40 (in honor of replacement level).  And, the Game Score should be akin to a win%.

Note that since a .400 win record is 40 Game Score points, that means that we have to multiply wins by 100 to get to Game Score points. So, .400 x 100 = 40.  Also remember that runs / 10 = wins.  So, runs x 10 = Game Score points.

Version 1
Let’s start off with the easy one, and look only at IP and runs allowed (and don’t you dare say ER… this thread has no place for you in that case… don’t even talk about it).  Each run allowed is 10 Game Score points.  The average pitcher will have 6 IP and 3 runs allowed (for an average of 50 Game Score points).  So, just solve:
50 = 6 * IPvalue - 3 * 10 + 40
Solve for IPvalue of 7.

That’s our equation:
GameScore = 7 * IP - 10 * R + 40

You’d have to tailor a specific equation for each season, but, this should suffice for illustrative purposes.

Version 2
Let’s look only at K and BB and IP.  We know that each K is worth as much as each BB, and each BB is about 0.3 runs, or 3 Game Score points.
50 = 6 * IPvalue + 3 * (SO-BB) + 40
Solve for IPvalue of 0.

That’s a nice one right?  If you have as many K as BB, your Game Score is 40 (replacement level).

Version 3
The FIP version.  We do the -13 * HR, -3 * BB, +2 * SO as our FIP part of Game Score.  The average pitcher will have a FIP portion of -13x1 -3x3 +2x6 = -10 in a 9 inning game, or about -6.7 in a 6 inning game.
50 = 6 * IPvalue - 6.7 + 40
Solve for IPvalue of 3.

Version 4
The LWTS version.  It’s -5 points for hit, -8 extra points for a HR, -3 points for a BB.  The average pitcher will have about -42 points in a 6 inning game.
50 = 6 * IPvalue - 42 + 40
Solve for IPvalue of 9.

Now, you just have to figure out which of the versions you like.  Let’s say you equally weight them at 25% each, you get this:

GameScore
= 40
+ 4.75 * IP
+ 1.25 * SO
- 1.25 * H
- 2.25 * BB
- 2.50 * R
- 5.25 * HR

You can try to get round numbers, and adjust the IP, and you get something like this:
GameScore
= 40
+ 4.5 * IP
+ 1 * SO
- 1 * H
- 2 * BB
- 2 * R
- 5 * HR

The question you have to ask yourself is: how much do I really want to weight each of the 4 versions?  Maybe to you, it’s all about runs (version 1).  Or it’s all about FIP, or all about Component runs.  Or some combination that you prefer.

Come up with your preferred weighting scheme, and tell me what you come in at.

Note: I didn’t double-check my math.  I just winged it, so don’t take anything here as official.

Tuesday, September 07, 2010

Reader mail of the day: Understanding wOBA

Someone asked me how do I figure out the formula without reaching base on error.  My answer below is why I love the logical underpinnings of wOBA:

You always start off at runs above out for each event that you have. And then, this is the important part, make sure that the weighted sum of your events equals the unweighted sum.

Suppose for example that all you have is BB+HR.  You have 60 BB and 20 HR, or 80 times on base. You also know that a walk is +.6 runs above out, and a HR is +1.7 runs above out. That means 0.6*60 + 1.7*20 = 70.

In order to align the two, you multiply by 80/70.

If all you had was say doubles and HR, you do the same thing. So, when it comes to ROE, or not, you do the same thing. 

Tom

Thursday, August 19, 2010

Run values by the 24 base-out states

I’ve posted this chart in the past.  Colin has done something along those lines.  What he did was focus only on contacted balls (not sure if home runs are included, I think they are; walks, strikeouts, hit batters are excluded), and then broke up the various outs (infield air, infield ground, outfield) into their own run values.

Here is what he shows:

I’m not sure what is going on with the out values.  It seems like he’s turned the relative run values into some sort of “total” run values by adding a fixed run value to each out.  That might be the reason you end up seeing a positive run value for 2 outs and bases empty.

Anyway, the interesting part is where the different kinds of ball in play outs differ at each base out state.  As you’d expect, the biggest ones are any of the states with runner on 3B and 1 out.  The difference between an outfield flyout and an infield groundout is around .30 runs, which is enormous.

The next set of big differences are states with runner on 3B and 0 outs.  In those cases, the gap is about .10 to .15 runs.

Among the non-3B states, it’s runner on 2B 0 outs, where the infield ground out is .08 runs more impactful than an outfield fly, hence the value to moving runners over.

Finally, the DP-killer is for runners on 1B 0 outs, and runners on 1B,2B 1 out, where the cost of the ground out is .05 runs more than the fly out.

In all other states, the difference between a ground out and a fly out is zero.  Which is a surprise.  I would have expected a difference also with runner on 1B 1 out, but apparently the cost of the ground out is less than that of a fly out.  That seems hard to explain.  Perhaps bunts are biasing the results?  I don’t know.  Colin also shows that the number of outs for each play at each state, and the ground out here gets 1.46 outs, and the fly out gets 1.02 outs.  So, I don’t see how this makes sense.  Unless he’s somehow showing the credit as -.13 runs per out, rather than -.13 runs for the groundball outs in total?

Anyway, good stuff overall.

***

Note to BPro webmaster: please remove P tags in the tables.  It makes it impossible to copy/paste.

The greatness, or not, of Josh Hamilton

Poz asks, and he’s a bit bothered with the fielding analysis part:

Fangraphs shows Hamilton as having (by a sizable amount) the highest WAR among position players in baseball at 6.7. ... However, Baseball Reference does not show Hamilton in the Top 5 at all....

So what gives? Tom Tango explains that the big difference is how the the competing WARS rate defense. Fangraphs’ WAR uses Ultimate Zone Rating to quantify defense. Baseball Reference’s WAR uses Total Zone to quantify defense. Tom thinks “UZR is better, but not markedly so.”

In Hamilton’s case, the competing systems judge him almost precisely the same on the offensive side. Fangraphs has him at +47 runs, Baseball Reference at +46 runs. The difference is defense. UZR has Hamilton as a very good defender — his UZR is +5.8.* Total Zone has Hamilton as a below average field, minus-7 runs.

Those 13 runs on defense make up the difference.
...
Tom Tango does not have a strong feeling about which WAR is more accurate (“Split the difference,” he suggests).

For those interested, here was the full email response I had given Poz:

Read More

Tuesday, August 17, 2010

Twitter mail of the day

The question was raised on Twitter; given a 4th out each inning, would the M’s score enough runs to be league average? They’re in the neighborhood of 35% below average now. How would we go about determining the impact on run scoring of adding a 4th out to a team’s innings. Figured this was up your alley, and I would really appreciate your input.

This would be the same thing as randomly selecting an out and converting it into a Reached Base On Error (i.e., a 4-out inning).  Converting a sure out into a sure hit is worth about 0.75 or 0.80 runs.  Given that in a three out half-inning, you would score some 0.4 to 0.6 runs per inning, then getting a 4-out inning, every inning, means you will be the greatest offensive team ever.  It’s not even close.

Wednesday, August 11, 2010

Count-component Linear Weights

What Pat is suggesting is: if you get a triple in a hitter’s count, then you give the hitter +.10 runs for getting into a hitter’s count, and +1.0 runs for getting a triple.  If you get a triple in a pitcher’s count, you get -.10 runs for putting yourself in the hole, and +1.2 for getting out of it.

In either case, you get +1.1 runs for the triple.  It’s just a matter of how you split the value of that triple within a batter’s skillset.

Harry Pavlidis produced the LWTS chart by count for each component a year or so ago.

EqA (TAv) coalescing around Linear Weights

Looks like Colin is flexing his muscles at BPro:

From 1993 to 2009, you can figure TAv simply as:

0.260 + (RAA/PA)*.9

Now, we will be tuning those values slightly to match the batting average for that season, but other than that, that’s the formula for TAv we will be using once the new stat reports are rolled out.

This is exactly the framework wOBA uses.  wOBA uses runs above average per PA (RAA/PA), multiplies it by some constant (around 1.15 or 1.20, which is the 0.9 that Colin noted), and adds in the league OBP (around .335 or so, which is that .260 for batting average Colin is talking about).

On top of which, Colin is agreeing with my handling of the IBB.  And, it looks like he’s going to do the same thing I’m doing with the run value of each event:

There’s actually one great similarity between the weights at Fangraphs and the current formula for TAv—in both, the relative weight of the various events (walks, singles, home runs, etc.) are held constant over time.

Basically, there’s going to be a great deal of overlap between wOBA and TAv, with just the issue of parks and leagues to differentiate them.

In the end, it’s a question of whether you prefer your presentation along batting average lines, or on base percentage lines.

Friday, August 06, 2010

Margin of error on offense

Colin:

Now, for instance, we know that a bases-loaded home run scores a lot more runs than the average home run. Others would look at that and consider the hitter should get more credit for being “clutch.” To my way of thinking, the players who deserve credit are the players who got on base for the hitter, thus increasing the value of the home run. So I tend to look at batting events independently of what happened before and what will happen after, and simply consider what the player did, isolated from his teammates.

If I understand him correctly, he’s saying that he will not do a delta RE approach.  He doesn’t want to give +3.3 runs of credit for hitting a bases loaded HR with 2 outs.  And he doesn’t want to give +1.0 runs of credit for hitting a bases empty HR.  He just wants to give 1.4 runs of HR each time.

But then he gives us the margin of error on all the events, and for the HR he says 0.55 runs.  Presumably, what he did was take the difference of each of the 24 run values of the HR (one for each of the 24 base out states), subtracted it from 1.4, weighted it by how often each occurred, and came up with a standard error of 0.55 runs.  Here, let me try using the values I have in The Book (Table 5, page 23).... ok, I’m back… I get 0.53 runs.  So, yes, that’s what he did.

Here’s my problem: Colin is saying that he wants to treat each event as if it was base/out neutral, but then gives us a margin of error for treating each event as base/out neutral.  Therefore, why not simply use the run values by the 24 base/out states, and have ZERO margin of error?

That’s the part I don’t get.  It’s great to see what the margin of error is, if you treat things as base/out neutral.  So, I love it that he did that.  I just don’t see why it needs to be done for players in the Retrosheet era.

Wednesday, July 28, 2010

SABR 101 / 111 - Bases and Outs

Just a placeholder for the four recent threads:

SABR 101 - Bases
SABR 111 - Base Values
SABR 101 - Outs
SABR 111 - Out value

SABR 111 - Out value

The good news is that we got the bases and outs to add up exactly to the number of runs scored.  The bad news is… it doesn’t work like that.

The base-value of the outs is simply to count the number of bases left on base.  Make the final out, stranding the runner on 3B?  That’s minus 3 bases.  Imagine therefore you have a high run environment where the average number of runners left on base is 1.6 runners (say a total of 3.0 bases).  Let’s call this a 10 runs per game environment.  Imagine a far higher runs per game environment, say 20 runs, where you leave 2.0 runners on base (say a total of 3.75 bases).  Imagine an even much much higher run environment, say 40 runs, where you leave 2.5 runners on base (say a total of 4.8 bases).  And imagine the biggest run environment, like ever, a gazillion runs, where you leave the bases loaded every time (for a total of just 6.0 bases).

So, making the third out removes 3 bases in one reasonably extreme situation, and it removes 6 bases in the other most extreme situation.  Hardly seems to make sense that an out’s impact can be capped like that.

Well, it doesn’t make sense.  The out serves two functions: one is to remove the base-value of the runners on base, which is what we’ve been discussing so far.  The other is to extend the inning.  By making an out, you are turning a 3-out inning, into a 2-out inning.  As you can imagine, an out in a run environment where 10 runs are scored is far more damaging than in an environment where 3 runs are scored.  You can afford to give up an out to get a base when you are facing Pedro.  You can’t afford to play small ball when runs are so easy to come by.

But, waitaminute, we already were able to exactly add up bases and out to runs.  If we have to apply an extra penalty to outs, then we’re going to get a number that is less than total runs scored.

Right, exactly.  Because it’s important to know the run environment you are in, the correct thing to match on is not total runs scored, but runs scored relative to average.  And so, bases and outs have to add up to zero. 

That’s why Linear Weights works.

SABR 101 - Outs

When you make an out, and no one is on base when you make an out, there’s no direct change in base advancement.  When you make the first or second out, the runners already on base, presuming they are not putout, also have no direct change in base advancement.

The direct change occurs on the third out, where all the runners on base are cleared off, and on putouts with less than two outs, like DP.

If you have a leadoff single (+1 base), the next two outs still leave that runner on base, but the third out removes it from the bases (-1 base), so that we are back to bases empty (and three outs).

In MLB, there are about 39 batters sent to bat each game, with 4.7 of those scoring a run, and 27 of them being putout, leaving 7.3 of them left on base (an average of 0.81 runners LOB per inning).

Where are these runners located?  I wish I would have thought to check myself last night, but, I didn’t.  I’ll take a guess that 0.35 were at 1B, 0.25 were at 2B and 0.21 were at 3B.  I just made these numbers up for illustration purposes.  So, the number of bases lost is 0.35 plus 2 x 0.25 plus 3 x 0.21 equals 1.48 bases.  Treating each base as 0.25 runs (i.e., 4 bases = 1 run), and we have 0.37 runs wiped from the bases each inning.  With 3 outs per inning, that’s -0.123 runs per out.

Basically, if you take the bases values for the events we’ve talked about:
5.40 HR
4.40 3B
3.22 2B
1.81 1B
1.42 BB
-1.48 innings

And apply that to how often each of those events occurred, and then divide by 4, you are going to get exactly, EXACTLY (*), the number of runs scored.

(*) Almost exactly.  In the bottom of the ninth of games won by home teams, you will have runners left on base that are in limbo: not cleared out by the outs, and not reaching home plate.  So, the “exactly” provision is true in 3-out innings.

I didn’t really test those numbers against any kind of real-life scenarios.  I could just make one up to see what kind of environment I’ve been using.  Say in a 9-inning game we have this:
1 HR
0 3B
2 2B
7 1B
3 BB
27 batting outs

We get 5.4 bases from the HR, 6.44 bases from the two doubles, 12.67 bases from the 7 singles, and 4.26 bases from the walks.  We remove the 13.32 bases from the 27 outs (9 innings).  Adding up all the bases is 15.45.  Divide by 4, and we get 3.86 runs scored per game.

In fact though, some singles and doubles lead to outs, we also have outs on steal attempts, etc.  It’s not as clean as all this.

But, that’s how bases and outs add up to total runs scored.

SABR 111 - Base values

Part 2.

Read More

Tuesday, July 27, 2010

SABR 101 - Bases

Triples and homeruns will advance all runners on base the maximum number of bases possible.  Runners on first base will advance three bases, runners on second base will advance two bases, and runners on third base will advance one base.

On average, there are 0.3 runners on 1B, 0.2 runners on 2B and 0.1 runners on 3B.  Therefore, the total number of bases advanced by the triples and homeruns is 0.3 times 3, plus 0.2 times 2, plus 0.1 times 1, or a total of 1.4 bases.  This is the base-advancement value of a triple and home run.

Doubles have the same base impact for runners on 3B and 2B.  For runners on 1B, 40% of the time, they will advance the runner three bases, and 60% of the time, it will be two bases, for an average of 2.4 bases.  Following the same calculation above, we have 0.3 times 2.4, plus 0.2 times 2, plus 0.1 times 1, or a total of 1.22 bases as the base-advancement value of a double.

For singles, they’ll advance the runner on 2B two bases 60% of the time and one base 40% of the time (average of 1.6 bases), and the runner on 1B will advance two bases 30% of the time and one base 70% of the time (average of 1.3 bases).  The calculation follows: 0.3 times 1.3, plus 0.2 times 1.6, plus 0.1 times 1.  That’s a base-advancement value of .81 bases for the single.

Walks advance all runners from first base one base.  The runner on 2B will advance only when there is also a runner on 1B (so the overall frequency is about .10).  And the runner on 3B will advance only when the bases are loaded (about 2% of the time).  So, we have: .3 x 1, plus .1 times 1, plus .02 times 1, equals .42 bases for the walk.

All these numbers are nicely rounded for ease of illustration.

Here’s the summary:
1.40 HR
1.40 3B
1.22 2B
0.81 1B
0.42 BB

This was based on having 0.60 runners on base per plate appearance.  If you have more runners, say 0.90, then all those numbers go up 50%.  If you have fewer runners, say 0.30, then all those numbers need to be cut down in 2.

Added to that is the number of bases the batter himself gets (4 for HR, 3 for 3B, 2 for 2B, 1 for 1B, BB).  Those numbers are independent to the run environment.  So, a HR gets 4 bases for the batter and 1.40 for the runners, or a total of 5.40 bases.  Here’s the summary of that:
5.40 HR
4.40 3B
3.22 2B
1.81 1B
1.42 BB

In this SABR 101 article (required reading) from Patriot, he shows some data I provided using actual data:
5.41 Home Run
4.46 Triple
3.23 Double
1.83 Single
1.39 Walk

You can see here how the theoretical pretty much matches the empirical.  This is how run scoring works in baseball. 

Given that there are 4 bases required to score a run, you can take the number of bases and divide by 4.  Taking the theoretical numbers, we have:

1.35 HR
1.10 3B
0.81 2B
0.45 1B
0.36 BB

That’s more or less the number of runs each event is worth.  All this is pretty standard for the regulars around here.  Hopefully, this brings all the new readers up to speed.

Monday, July 26, 2010

Blast from the past: The argument for subtracting HR in Runs Produced

I did this a few years ago, but seeing such strong comments at Primer makes me think there may be alot of people here who also may share their view.

http://www.tangotiger.net/runsproduced.html

Please read in entirety prior to commenting.

Wednesday, July 14, 2010

Elegant Simplicity of wOBA

Most of the credit in the linked article should go to The Hidden Game of Baseball, insofar as I’m concerned.  Anyway, yes, exactly:

This is a statistic that says, “Okay, so we know that singles are more valuable than walks, doubles are more valuable than singles, triples more valuable than doubles, and homeruns are more valuable than all of them. I’ll do all the work for you and show you how productive your player has been in one simple, easy-to-understand stat. Okie dokie?”

This is really why I love it, uinlike say OPS (a more cumbersome calculation as well as being less accurate).  OPS bothers me. 

wOBA for pitchers

I use wOBA for pitchers all the time.  I didn’t notice that Fangraphs did not have it.