THE BOOK--Playing The Percentages In Baseball

Tuesday, May 15, 2012

Will Pujols end the season with at least 30 HR and .500 SLG?

Just fantastic work from Poz:

This is a very good example of how regression toward the mean works.  A better one would be to add pro-rate his current 2012 stats for one more week, and then repeat what Poz did starting May 22 to end of year for each season.

And the best way is to do the pro-rating for one week, then May 22 to end of month give him some random player’s stats for May 22-31 (any random player), and then take Pujols’ June 1-onward like Poz did.

As you can see, just going with the Poz approach gets you most of the way there.

Really, a very good way that Poz is doing it.

Wednesday, May 09, 2012

What does it mean when you age?  It means you can’t throw as hard

Good stuff from Jeff, whereby he controls for the lack of year-to-year change in fastball, and notices that there is no change year-to-year in FIP.

Tuesday, May 08, 2012

Pujols’ future

Matt tries to find comps for Pujols, comes up with a pretty small set, and see that those hitters continued to hit extremely well.

Monday, May 07, 2012

Ross Detwiler: Losing to the statistical gods

This was a mailbag question from nearly two years ago (Aug 26, 2010):

I noticed that Ross Detwiler has never had a HR/FB% over 6% in any of his stints in his professional career. In his last 6 stops, he has had a 4% HR/FB% or less in all of them. By my math, that is about 19 HR allowed in 552 estimated Flyballs which comes out to a 3.44 HR/FB%. Let’s say I was off a little and his HR/FB% is really 4%. Can we say that he has a skill for reducing his HR/FB% rate. Or is it a fluke based off his sample size (Around 500 professional innings)?

At the same time, Detwiler has allowed a BABIP over .323 in every stint in his career except for 1 4 Inning fall league appearance. He’s ranged from .323 to .378 in BABIP. By my math that might be slightly off, his BABIP in his career is about .345. It looks like his GB% is normal (Around 45-50%). Do you have any reason why his BABIP is so high consistently. In his short big league career he has a 24.8 LD% (89.2 IP). Assuming he is around that in the minors, does that even close to explain his abnormal BABIP. Does he have a skill for real high BABIP? And is there some kind of link between his real low HR/FB% and his real high BABIP?

Sure enough, in 2011, his BABIP was .272, and in this early 2012, he’s at .215.  So, the reader seems to think he sees a “pattern” of a high BABIP, but the sample size gods were not kind to the reader.  As for his ability to suppress HR, in 2011+2012, he’s given up 9 HR on 92 FB, which is right around league average.  Sample size gods are not nice.

I get these kinds of emails all the time, that someone thinks they found THE fluke guy.  But, it’s the same thing every time.  Seriously, if you really think you know more than the sample size gods, then pick out the twenty things you really believe more than everyone else, write it down, and then two years from now, tell me how you hit on 15 of 20.  (Of course, if enough people do this, SOMEONE is going to hit on 15 of 20 due to the binomial gods of random variation.)

My suggestion: stop looking at numbers looking for patterns and building narratives in your mind, and instead enjoy the numbers for the actual stories they tell.  Meaningless stories, stories that don’t carry over to the next day.

Saturday, May 05, 2012

Which team has been beating Vegas so far?

VegasWatch compiles this great data, and the winner is… Orioles!  Followed by Rays, Dodgers, and the Nats.

Now, let’s watch this unfold, and see if Vegas adjusts, or if they will consider this small-sample-sizitis.

Wednesday, April 25, 2012

What does a 12-game losing streak REALLY mean?

If you have (at least) a 12-game losing streak, can we predict what the rest-of-season record will be?  Let me show you a really easy way to do that.  First off, an (at least) 12-game losing streak means that in a 13-game period, you have one win and 12 losses.  The losing streak starts with your last win, and then is followed by (at least) 12 losses.  Everything after that 12th loss is undetermined.  To forceast the rest-of-season record, all you have to do is apply regression toward the mean, and that means adding 35 wins and 35 losses. 

So, our best guess for a team that is 1-12 is that they are a true 36-47 team.  A true 36-47 team will win 43.4% of the remaining games. If we figure a team will play about 161.7 games in a season, then of the remaining 148.7 games (161.7 minus 13), we’d expect them to win 64.5 games (148.7 times .434) and lose 84.2 games.

A 1-12 team is expected to play 64.5-84.2 in their other games.

Poz was nice enough to compile this list of teams that had (at least) as 12 game losing streak at some point in their season.  Their end-of-season record was 64.2 wins and 97.5 losses.  If we remove their 1 win and 12 losses in their streak, that leaves us with 63.2 wins and 85.5 losses.

19 actual 1-12 teams ended up playing 63.2 - 85.5 in their other games.  Or, what happened in those 13 games was almost exactly predictable of their other 149 games.

Also note that three of those teams played at close to, or just above, .500 above in their other 149 games.  So, there’s a 16% chance that the Royals will play .500 ball in their other 149 games.

Wednesday, April 18, 2012

How much to value performance from 4 years ago?

Great work from Rob.  The 4th year should get about 15% of the weight. 

He notes that if you apply a 20% decay rate (100% weight for year t-1, 80% for t-2, 64% for t-3, 51% for t-4), then the weight of t-4 (51) divided by the weight of all 4 years (100+80+64+51) is 17%.  A 25% decay rate (i.e., weights of 100%, 75%, 49%, 34%) gives you 15%.

So, we know that year t-4 has to have SOME weight, and it’s going to be pretty low relative to year T, something on the order of about one-third.

If Rob is up for it, he can redo what he did, this time focusing on keeping fixed years t-4, t-2, t-1, and letting t-3 float. 

And so on, and so on, for the other two years (floating t-2, then floating t-1).  And then we’ll see wildly larger impact, the closer you are to year t.

Fantastic work!  This is the kind of work that more researchers should be doing, getting their hands dirty, and really getting into the data.

Tuesday, April 10, 2012

Do 2B age worse than the typical position?

Dave suggests that that’s possible.

...in the end, we were left with 23 second baseman who were well above average hitters. As a group, these 23 players hit .280/.361/.430 during their 27-29 years, good for a 118 wRC+, so Kinsler fits into the overall average pretty well. Looking at the same 23 players from ages 31-35, the drop-off is pretty severe – the median performance is just .266/.345/.402, or a 103 wRC+, and the corresponding drop in playing time is even more severe; they averaged 574 plate appearances per year from 27-29 but just 347 from 31-35.

There are some guys who beat the norm and continued to be productive into their mid-30s: Lou Whitaker, Bobby Grich, Roberto Alomar, Davey Lopes, Julio Franco, and Ryne Sandberg all posted at least +17.5 WAR during this five year stretch by maintaining their offensive value, and Placido Polanco also topped that mark through his elite glovework and durability. But, there are also a lot of somewhat inexplicable collapses from guys who were really good before they were 30 and pretty lousy afterwards.

Chuck Knoblauch was even better than Kinsler from 27-29 (125 wRC+, +17.8 WAR), but completely fell apart at age 31 and was a replacement level player until age 33, at which point he was out of baseball. Jose Vidro was a very similar hitter to Kinsler through age 29, but his power disappeared and he was also basically worthless after age 31. Jose Offerman went from posting a 110 wRC+ from 27-29 to an 85 wRC+ from 31-35. Dick McAuliffe went from 127 to 98. Jorge Orta went from 114 to 94. Denis Menke from 115 to 91 and didn’t even rack up 900 plate appearances after turning 31.

A 118 wRC+ in 574 PA (and presuming average fielding) is roughly 3.3 WAR for a 2B.  That’s from Dave’s list of his elite 2B from age 27-29 (which, we’ll presume they were 3.5 WAR at age 27, 3.3 at age 28 and 3.1 at age 29).

A 103 wRC+ in 347 PA (and let’s presume a 0.5 win per 162G drop in fielding) is 1.1 WAR for a 2B.  That’s for age 31-35, which we’ll presume is 2.1 at age 31, 1.6 at 32 1.1 at 33 0.6 at 34 and 0.1 at 35.

Dave doesn’t note what they were at age 30, but 2.6 is fine with me.

So, it seems to me that this what we’d actually expect for the typical player, to lose 0.5 wins a year once you hit age 30.

I think what Dave’s list does is really hit home what a loss of 0.5 WAR means each year.

(Now, if Dave’s original list is filled with really good glove men, such that we’re starting with 3.8 WAR 2B instead of 3.3 WAR, then we may be back to the original question.)

Basically, if Dave repeats his study for SS and for 3B, we should see the same kind of results.

Let’s just create a basic model of aging.  I have no idea if this is a good model, but it just provides a framework for discussion.  You have a hitter that is a 118 wRC+ hitter, and he loses 4 points per year (which is roughly 3 runs a year).  That’s for hitting.  And, let’s say he loses 1.5 runs a year (per 162G) on his glove.  So, if he’s an average fielder today, he’s -1.5 runs next year, and -3 runs the year after that.  And, let’s say that you lose 15 PA the next year, then 30 PA the year after that, and 45 the year after that, and so on.  We have this:

In the last 5 years, that’s an average of 102 wRC+, and an average of 410 PA.  So, I don’t know that it’s terribly surprising that Dave gets the results he gets.

I’d like to be surprised by seeing aging charts for SS and 3B that are noticeably better than those of 2B.

Wednesday, April 04, 2012

Lifetime Contracts for the best players in the league

I selected all nonpitcher born 1931-1971 who:
1. had at least 600 PA in his most recent season
2. had at least 1800 PA in his three most recent seasons
3. had at least 6 WAR in his most recent season
4. had at least 18 WAR in his three most recent seasons

There were 155 such player-seasons (meaning about 4 qualified per season).  Their average WAR was 8 in his most recent season and 23 in his last three seasons, with 660 PA in his most recent season, and 2000 PA in his three most recent seasons.  Basically, superstars.

I broke them up by age to see how many WAR they generated AFTER they did all that, to the end of their career.  That is, you want to give these players a lifetime contract, then how many wins do you expect from them?

I’ll give you a nice little shortcut: start at 100 lifetime wins remaining for superstar players at age 18, and subtract 5 WAR for every year older.  So, a player who is 28 years old will have 50 lifetime WAR remaining.

Again, this is only for the best players in the league, guys who got 23 WAR in their last 3 seasons. (UPDATED: see post #2 below for results of “standard superstars")

How about lifetime PAs remaining for these players?  I’ll give you another shortcut for that as well.  Start with 11,000 PA remaining at age 18, and remove 500 PA for every age after that.  So, a player at age 28 will have 6000 lifetime PA remaining.

This is only for nonpitchers.

Note that age is calculated as the just completed season minus his birth year.  So, a player born in 1983 would count as age 28 for these purposes.

***

What happens if you extend a superstar two years out?  Well, you’d have to remove the expected wins in his next two years.  I didn’t calculate it, but we can make a reasonable guess that they’ll get say 12 wins over the next two years.

Therefore, signing the best nonpitcher in the league who just completed his 2011 season at age 28, and extending him two years out should generate some 38 wins starting at age 31.

Tuesday, April 03, 2012

Fans like to bet the “over” when it comes to their team

No surprise, but we’ve got numbers. 

It reminds me when someone (Dave Allen?) looked at the Fan forecasts at Fangraphs, and concluded the average team was going to win 86 games. I also end up with biased results like that with the Fans Scouting Report (average must be 3.0, but I end up at 3.3), and I get similarly biased results when it comes to playing time.  Hence, adjustments always need to be applied when processing fan-data.

Saturday, March 31, 2012

If we can’t win over Allen Barra, who can we win over?

He said:

What would you consider an accurate prediction? Myself, I’d say you have to get it within 2-3 games to have a claim that you had it right. By that standard, the projection for 87 wins for the Braves last year and their actual total of 89 was spot-on. The projection that the Mets would win 80 when they actually finished with 77 also was pretty good.

Suppose that you knew from the outset that every team was a .500 team.  You are the perfect scouting god, and you know this.  Every team plays 162 games.  How many wins are you going to forecast?  Well, you MUST forecast 81 wins for each team.  But, how many will each of the 30 teams win?  Enter random variation around a true mean.  One standard deviation is .5*sqrt(162) = 6.4 wins.  This means that forecasting exactly 81 wins for each team means you will be right about two-thirds of the time within 6 or 7 wins.

Two or three wins as Berra posits?  That’s 0.4 standard deviations, or about 30% chance of being right… if you are perfect scouting god.

So, no, Berra’s “Myself, I’d say you have to get it” is simply an impossible standard.

If a forecaster wants to puff up his chest, he just has to beat Vegas.  That’s the standard, and preferably over a period of years.

Tuesday, March 27, 2012

Strikeouts and Walk spring numbers matter?

Mike shows that it does.

Given that the spring data has so many fewer innings than what Marcel has, that the weight of spring is 15 to 20% of the Marcel rate is fairly eye-popping.

Saturday, March 17, 2012

Introducing The Razors

I finally sat down last night and took the 2011 Community Playing Time Forecasts (of Games Played), and decided to convert those Game Played forecasts into Plate Appearances Percentiles (as Quartiles).  I spent a few hours on this last night and today, because this is the kind of stuff that is rather enjoyable for me to pass the time.  I know, I’m crazy.  But I’m quite lovable, so if you are going to be crazy, you may as well be the lovable kind.  I learned that from my dog.

I love the readers who participate in my surveys because they do 99% of the work to my 1%, and their results are always top-notch… razor-sharp.  Hence, I’ll call what I’m about to do The Razors.

I’m going to try this for the 2010 and 2009 data eventually, and see if I get similar results.  (Maybe 2011 had anamolous injuries?) So, for now, consider this “Beta”.

This is what I came up with, that best fit the 2011 data.  You start with the estimate of how many games the fans think a player has.  Say that’s 150. 

We then figure what his 75th percentile number of PA per game is.  That formula is the following:
Games / 100 + 2.86

So, a player with 150 forecasted games is expected to have 4.36 PA/G as his 75th percentile.

Multiply the two numbers, 4.36 x 150, and 654 PA becomes his 75th percentile.

To calculate his 50th percentile (median), you take his 75th percentile, multiply by 92.5% and subtract 30.  In this case, that’s 654 x .925 - 30 = 575.  Therefore, someone forecasted with 150 games has a median PA of 575.

Finally, his 25th percentile is 75% of his median, minus 30.  So, we have 575 x .75 - 30 = 401 PA.

Therefore, we get this as his quartile thresholds:
150 G = 654, 575, 401

How do they end up working?  Well, I created a few classes of players.  I took the top 120 in forecasted games, then the next 120, and finally the final 512 players forecasted.

For the top 120 players, I had 32 players in the first quartile (that is, 32 players had more PA than their 75th percentile), 36 in the second quartile (number above the median, but below 75th percentile), 27 in the third quartile (between 25th and 50th percentile), and 25 in the last quartile (25 players had less PA than their 25th percentile level).

Here are those totals:

Not GREAT, but overall, pretty good, especially considering I tried to make the conversion equation as deathly simple as I could envision.

Anyway, so, there you have it, the Community Playing Time Forecasts from the Razor-Sharp readers… The Razors!

And that’s my challenge to all the playing time forecasters out there: the mean forecast only gets us so far.  The distributions are nothing close to normal.  There’s a heavy skew, so, let’s take the next step.  Do as I have here, and provide the range of forecasts for playing time.  Let’s see you do as well or better than the razor-sharp readers.

For those interesting in furthering this work, I can send you the file of forecasted games, and actual PA.  Maybe you can come up with something even better than I have, that gets those quartile results closer to reality.  Email me: tom~tangotiger~net .

UPDATE: see revised numbers in post 15

Friday, March 16, 2012

Tango’s Lab: Playing Time Percentiles (preliminary)

I’ll be creating playing time percentiles based on the Community Forecasts. I thought I’d share some preliminary results.  For those players that fans had forecasted for 148-155 games in 2011, this is how the quartiles broke out in terms of actual PA:
678 - 731 PA (average 702): 25%
644 - 675 PA (average 663): 25%
539 - 640 PA (average 592): 25%
149 - 525 PA (average 364): 25%

The median was 642 PA.  The average was 580 PA.

My current translation of Forecasted Games (which is what the fans give us) into PA is 607.  So, that estimate is above the mean, but below the median.

We see that there’s a 25% chance that an iron-man player will end up with 539 or less PA.

Therefore, I was thinking of presenting it in this fashion, in terms of quartiles (maybe quintiles, so that the median will be more obvious?  or is it enough to just do thirds, because otherwise, it’s just too much information?).

I’d like to hear from you guys as to how you’d like to see it presented.

Saturday, March 10, 2012

Why Pecota is not deadly accurate…

Keep in mind that I love BP and Pecota (and Oliver, Steamer, Zips, etc.) and this is not meant to disparage any of these forecasting systems or their associated web sites. I think they do a great job, considering, and put a lot (too much?) of honest, intelligent, and creative work into their forecasting methodologies.

That being said, a few things occurred to me while reading Colin’s article and the reader comments on the newest incarnation of Pecota:

http://www.baseballprospectus.com/article.php?articleid=16189

Given the incredible amount of nuance that goes into these projections, you would think that they would be deadly accurate. You really would. I mean just read that article. There has to be thousands of man hours that went into developing their methodologies. Yet, according to all the testing that’s been done on projections, the bottom line is that no sophisticated projection system is that much better than Marcel at probably 1% of the development time and 5% of the nuance, and even among all the forecasting systems, none of them seems to clearly rise to the top and I don’t think that Pecota is typically even near the top, however I could be wrong about that latter point - it all depends upon the nature of the test, the subset of players, etc.

While reading the comments, I was struck by how many bugs there were in the outputs.  The ones that are noticed will be fixed, but my experience in programming is that the more complex the code - and arguably the code for Pecota is quite complex - the many more bugs it contains, and of course the ones that are not noticed will not be fixed. In other words, there are likely still plenty of bugs in the code which leads to subtle but nonetheless incorrect (from the stand point of what they intended to do), or at the very least, noisy, outputs. There is not a year that goes by that I don’t find a few bugs in most of my old programs. It often makes me wonder whether any complex code which is supposed to yield a small gain in the accuracy of the outputs is ever worth it. It may be a toss-up at best.

The second thing (that makes Pecota not so deadly accurate, I think) is that there is a lot of speculation and assumption that goes into some of the sophisticated nuances of their methodology. For example, to what extent do the “comparables” actually help the projections rather than introduce noise and bias?  They say that they take the actual average aging curve of a player’s comps and regress that toward a more generic aging curve. Is that even correct? I have no idea. I really don’t, and I’m not sure that they do either. They also make great use of minor league stats, as do most sophisticated systems.  We know that minor league stats are inherently problematic - selective sampling in establishing the MLE’s, difficulty with park factors, how much to weight them as compared to MLB stats etc. Then there is the issue of how many historical years to use and how to weight them. I think the jury is still out on what is correct on that front.

Finally, as Tango always says, even if all if your sophistication is reasonably “correct,” how much do you really add to a Marcel-like system? Another 1%? 2%?

Basically, I think - and this is just speculation - that between the inevitable programming bugs that go with the territory when constructing a complex and nuanced forecasting system like Pecota, the fact that you may be making a lot of assumptions and inferences that are not necessary true, and the more complex your system, the more the noise you introduce, I wonder whether any of these systems is any better than if the person or person spent 10% of the time and effort they did on developing it and if they left out most of the nuance and complexity.

Friday, March 09, 2012

Forecast differences: hitters

Comparing ZiPS, Steamer, and Marcel.

When r is around .9, there’s not going to be much to talk about.

Thursday, March 08, 2012

How many years out can you possibly make a forecast?

Colin re-introduced the 10-yr forecasts, and he shows some fascinating data:

That’s for True Average, which is a wOBA-like metric set to batting average.

The true talent spread in wOBA is around 1 SD = .035, which in TAv speak is 1 SD = .027 or so.  Random variation is a bit more complicated to figure, but it’s around 1 SD = .025 in wOBA and 1 SD = .020 in TAv.

So, our OBSERVED spread in wOBA and TAv would be roughly 1 SD = .043 wOBA and .034 TAv.  (Someone can show the actual observed wOBA and TAv over the past few years if they can.  I’m sure it’ll be close to these figures.)

Looking at Colin’s data, and it would imply that if he simply forecasted league average for every single player starting 4 years out, then he’d end up with better results.

Presuming all my numbers are right above (which, being 7:52 AM, and I just woke up a few minutes ago they may not), then why should we go more than 3 years out in individual forecasts?

Wednesday, March 07, 2012

Pitch speed, injury, aging, and changing roles…

I’ve been doing some interesting research on all of the above - actually how they relate. The data I am using is this:

Average seasonal fastball pitch speeds from FG, which uses BIS data, not pitch f/x, I think. DL data, which for this research, was just number of days spend on the DL in a season. For most of this research, I only noted “on DL” or “not on DL” for a particular season. Finally, I used my own NERC (normalized component ERA) data which are ERA looking numbers produced from a BaseRuns formula on the underlying components, including WP I think. They are all adjusted for context - defense (as best as I can, using UZR data), park, opponents, and league. 4.00 is defined as a league average pitcher in both AL and NL and a 4.00 in the NL is equivalent to a 4.00 in the AL since I do league adjustments. Anyway, those details are not that important.

Here is some really interesting data and discussion:

Read More

Forecasting Playing Time - mini-challenge

I asked the Fangraphs readers, one of who did the work, this:

Do me a favor. Take the top 20 in PA in 2008-2010, and tell me two things:

1. what was their average PA per season in 2008-2010
2. how many PA did they have in 2011 on average

One responded with:

The average is 680 for 2008-10, and the actual for 2011 is 612.  Marcel forecasted 605.

Can those with access to Oliver, ZiPS, PECOTA, Bill James, etc, tell me what their forecasts were?  And heck, let’s throw in the Community forecasts as well (both mine, and those at Fangraphs).

Forecasting Mailbag

I made a ton of replies at this Fangraphs thread.  Nothing new for the regulars, but, it might be a good read for those who had forecasting questions:

http://www.fangraphs.com/blogs/index.php/forecasting-mailbag