Monday, February 16, 2009

The 1984 Cubs, Binomial Distributions, and Orlando Hudson.

“If I have ever seen a dead giveaway set-up for a miracle, this is it.”
– Bill James, in the Chicago Cubs essay, in the 1984 Baseball Abstract.

In the history of sabermetrics, there has probably never been a more gutsy, anti-conventional-wisdom, and bullseye-accurate prediction than that one. Or at least, there wasn’t until Nate Silver wrote this last spring. It’s appropriate that James and Silver, the man who literally coined the term “sabermetrics” and the man who applied the process to another field of study with equally seismic impact, also share a history of transmuting their analytical iron into prognosticative gold.

(My own best effort in this category came back in the 1997 Baseball Prospectus, when I wrote at the conclusion of my essay on the Marlins – for whom the consensus opinion was that they’d finish under .500 once again – “Last year in these pages, I wrote the Marlins ‘have everything in place to battle the Braves for dominance of the NL East for the rest of the decade.’ I believe that even more strongly this year. The Marlins went through growing pains last year, but they have too much talent to lie dormant any longer. This is the year the Marlins should reap the benefits of their patience, and prove that they had the right blueprint for success from the beginning”. The problem was that BP had not registered even a blip on the publishing radar at that point, which limited my ability to gloat. That, and the fact that Wayne Huizenga then turned the franchise from World Champions to a laughingstock in one off-season.)

But back to James’ original statement. In his essay, James went on to give a number of reasons why he felt like the Cubs had a much better chance to win the division than almost anyone realized. One of those reasons has a lot of relevance for the 2009 Royals.

“3) Miracles usually happen in compressed leagues, in leagues where the difference between the best teams and the worst teams is not too wide…there have been many moments in the history of baseball when there was no great team, no dominant team. It is in those times that miracle teams come forward. The National League in 1968, the year before the Miracle of Flushing Meadow, was only 25 games from top to bottom and had a standard deviation of 7.56 wins; the expansion spread that out artificially in 1969. The American League in 1966 was 26 ½ games top to bottom; the 1966 Red Sox finished ninth at 72-90, and the standard deviation was 8.96 wins…I certainly don’t see the Cubs as having the potential to be a great team, a dominant team over a period of time. But that’s not really germane; miracle teams are never great teams. They’re teams that have a moment, teams that slip through a window of dominance.”

I don’t think this revelation is going to astound anyone – compressed divisions, divisions which lack any obvious doormats but also lack any clearly dominant teams – are divisions that are open for anyone to win. And I don’t think anyone would argue with the notion that the AL Central is a compressed division. But what I think is being missed by the national media is that for the first time in a while, when we say “anyone in the AL Central”, we don’t mean “anyone but the Royals.” Tim Kurkjian didn’t get the memo. “Four teams, none of them great, have a legitimate chance to win the division in 2009. And a fifth team, the Royals, who didn't even finish fifth in 2008, “could have our best club since 1994 [their last season as a contender],” Kansas City general manager Dayton Moore said.” There is still this perception, and not an unfair one, that the Royals are still a cut below the other four teams in the division.

We can rebut this pretty easily by pointing out that last year it was the Tigers, not the Royals, who brought up the rear of the division. Better still, we can point to the (preliminary) PECOTA projections for 2009, which predict the Royals to finish with their exact same record, 75-87, and to once again finish in fourth place, two games out of the cellar – only this time, PECOTA projects the White Sox to finish last with 89 losses.

(It’s beyond the scope of this article to address the long-simmering feud between Kenny Williams and a computer algorithm. Even Silver will tell you not to hold too much water to the fact that PECOTA holds no love for the Pale Hose; while sometimes PECOTA is dead on about the Sox (see 2007), sometimes it’s dead wrong (2005, and to a lesser extent 2008). Williams is an unconventional GM, but I have a lot of respect for his fearlessness, and wouldn’t want to bet against him making a Commodore 64 out of PECOTA once again.)

What really stands out about the PECOTA projections is that PECOTA has confirmed my two main suspicions about the division: 1) the Indians are the best team in the division on paper; and 2) that says less about the Indians than it does about the rest of the division. PECOTA has Cleveland at 83-79, and the other four teams with between 73 and 79 wins. From top to bottom, that’s a ten-game swing. Now a computer projection is, by its nature, going to regress teams towards .500 and possibly make a division look more compressed than it is. But still, no other division in baseball has a ten-game swing from first to worst. The AL West is 14 wins top to bottom (but there are only four teams in the division), while every other division has a spread of 19 wins or more.

So don’t look at this projection and say to yourself, “man, the Royals are projected for fourth place again?” or “75 wins again?” Look at the standings and say to yourself, “wow, the Royals are projected to finish just eight games out of first!” Eight games is nothing. Eight games is almost statistically insignificant.

If you flipped a perfectly fair coin 162 times, you’d expect to flip heads 81 times, obviously. But you won’t get exactly 81 heads each time – you might get 77, or 83, or occasionally even 69 or 92. If I remember my binomial theory correctly, the standard deviation on 162 coin flips is the square root of (162 * 50% * 50%) – about 6.36.

By definition, the odds that an outcome will fall within one standard deviation of its mean is 68%. So while a perfectly fair coin – or a .500 team – would be expected to win 81 games on average, the odds that such a team would win more than 87 games – one standard deviation above the mean – simply by chance is about 16%.

Using the binomial calculator I found here, we can say that if the Royals are truly a 75-win team, the chances that they’ll win 83 or more games is about 12%. The odds that they’ll win the division are less than that, because while PECOTA predicts that no team will more than 83 games, odds are that at least one of the five AL Central teams will outperform their projections by a significant margin. Once Clay Davenport has his Postseason Odds updated for 2009, we’ll have a more accurate answer to this question. But for now, let’s say that 87 wins takes the division.

If that’s what it takes, there’s about a 3.5% chance that a 75-win team will in fact win 87 games based purely on the way the coin – or ball – bounces. Those aren’t very good odds, but keep in mind, those are the odds that the Royals would win the division even though the team is fundamentally no better than last year. Those are the odds that a team that by all rights should be well under .500 – a team that is outscored by its opponents by 60 runs – still goes to the playoffs.

We saw this story play out with the 2003 Royals, who were outscored by 31 runs – and were lucky to have a run differential even that close – yet won 83 games. That year the Royals were in the hunt all season because they were lucky – but the underlying talent was poor enough that they needed to be really lucky to win the division.

But here’s the thing – what if the 2009 Royals aren’t really a 75 win team? What if Alex Gordon goes all .300/.400/.500 on the league? Or what if Billy Butler does the same? Or what if Zack Greinke is a Cy Young contender? By being just eight games out of first place on paper, the Royals are in a tipping point of sorts, where even a marginal improvement can lead to a dramatically higher probability of a playoff spot. If we knew for certain that Gordon was going to have a breakout season – and I still stubbornly believe he will – we could probably tack on two or three wins to the Royals’ projection.

The odds that a 75-win team will win 87 games or more is 3.5%. Add an additional three wins, and you’ve got a 78-win team – and the odds a 78-win team will actually win 87+ games is 9.1%. Three more wins on paper nearly triples the Royals’ odds of winning the division.

I’ve said all winter that the Royals need two of those three guys to have All-Star caliber seasons to have a realistic shot at a playoff spot. So let’s say we get two breakout seasons, each worth three wins, vaulting the Royals into a .500 team on paper. Now their odds of winning 87+ games is 19.4%. (This number is a little different from the number above because of fractional wins – the standard deviation is 6.36, but you can’t win 87.36 games.)

A 19.4% chance of winning the division basically means the Royals have the same shot as every other team in the division. That’s a crapshoot, and any Royals fan would be happy to have the season come down to a crapshoot.

So there’s reason for Royals fans to be, if not excited, at least guardedly optimistic about this season. It’s not likely that the Royals will win the division, but it’s a legitimate possibility – something that we could not have said about the team ever since the hangover that was the 2004 season.

This is what makes this off-season so frustrating. The Royals were not a good team last season, but they were approaching mediocrity – and playing in a division in which mediocrity is no impediment to being competitive. It would have only taken one significant addition to the roster to elevate the team to legitimate .500 status, just a breakout season away from true contender status in the division. Instead, Dayton Moore treaded water this winter, adding a whole lot of Kyle Farnsworths and Horacio Ramirezes but no Adam Dunns or Bobby Abreus.

And this is what makes the recent flirtations with Orlando Hudson so intriguing. There are some real downsides to signing O-Dog – if I have time I hope to write a column about him in the next few days – but on the whole, Hudson would undoubtedly help the Royals. He’s just 31, he’s had an OPS+ of over 100 for three straight years, his defense may not be the Gold Glove caliber it used to be but is still good, and – this is key – he’s a switch-hitter who is much better against right-handed pitchers, which would make him a terrific addition to a lineup that was 36-24 when facing a lefty starter last year, but just 39-63 against right-handers. On a one or two-year deal for $5 million a year, Hudson would make a fine addition to the roster.

But the best case for Hudson is this: the Royals can not be considered realistic contenders at this point, because even if they do get a couple of unexpected breakout seasons, they’ll still need some luck to stay in contention. But they’re close enough to that gray zone of quasi-competitiveness that just one significant acquisition could change that calculus completely. Manny Ramirez aside, Hudson is probably the most significant acquisition out there just waiting for someone to acquire him.

I guess if Moore had used his pennies on Dunn or Abreu instead of The Professor, the Royals would have been taken more seriously by the Tim Kurkjians of the world as a possible contender, and we would have lost the element of surprise. But when they hand out postseason spots, they don’t factor in degree of difficulty. You don’t get to hang a postseason flag any higher on the pole because it was so unexpected. Any permutation of events that result in the 2009 Royals going to the playoffs is going to have the word “Miracle” attached it to somewhere. Adding Hudson would make those events a little less miraculous, but a lot more likely. That’s a tradeoff we’ll take any day.


Phil said...

Fun post, Rany. I was in Cleveland during the mid/late 90's, and while we don't have a young Manny, I can say for the first time since I've been back in KC that the season feels fun (like my time in Cle) for the right reasons; not just because it's spring and I want an excuse to drink beer in a parking lot.

Sure, I'll go to the weeknight games, have a beer, and chill in the outdoor air. But for once, all 51/54 outs will warrant my attention.

According to The Star (10:15 last night), Hudson is almost certainly not going to happen. Bummer.

Lastly, do you, or anyone else, have a grasp on how the Royals could cut payroll during Spring Training (other than a trade for cash)? I don't have the time or desire to understand MLB payroll structure.

Anonymous said...

Interesting post. Glad you know more about math than I do. Looks like there's an outside chance for a miracle, if you're correct.

Reasons for optimism: Crisp's an improvement over Gathright, Bloomquist´s an improvement over TPJ, Jacobs is going to be an improvement over Gload, Guillen isn't likely to play quite as horribly as he did last year, the starting rotation looks pretty decent, either Kila or Shealy is likely to turn out to be an OK player, Soria is an ace closer, nobody else in the bullpen is going to be God-awful, Gordon and Butler are likely to improve, and Hudson would be a very good signing.

Although the best-case scenario for Kyle Farnsworth is that he gets busted for contributing to the delinquency of a minor and we can exercise the moral turpitude clause to void his contract.

Anonymous said...

This sounds more like you're trying to convince yourself there's a reason to believe in the Royals this year, than an actual "wow they could sneak up on everyone" article.

I think the Tigers have a more realistic shot at the division than the Royals. Dayton Moore's holding this team back....and it looks like he's doing it on purpose, but that can't be as true as it looks.

Did Kurkjian skip from 2002 to 2004? How could he think '08 was the best Royals year since '94? I think '03 was far better than '08 even if KC collapsed in September.

Anonymous said...

I think best-case scenario for Farnsworth is mid-season trade back to a big market club, and (fingers crossed) an excellent final couple of months from Rosa, Pimentel, etc, in the bullpen. Also on the bright side, if we get Hochevar in the rotation and Bannister as the swing man in the bullpen, Banny may have enough spare time out in the pen to really advance sabermetrics and/or world peace.

Anonymous said...

I'm really, really hoping that at least one out of Davis, Hooch, and Banny has a good year as a SP, and that another one can be a good #4. That would give us a very good starting rotation

Anonymous said...

MLBTraderumors/Ken Rosenthal says Hudson "wants" to sign with Royals, but no room in budget... Trade Teahen! Trade Buck!! for PTBNLs, anything! I think this would slightly weaken the bench (but this is the AL afterall) and give us a decent shot at the division. Do it, Dayton/Mr. Glass!

Anonymous said...

It's easy to be hard on DM for the moves he made in November and December because of the way the FA market has shaken out.

I'm quite certain if he had known that Abreau could be had for $6 million he would have done that instead of Farnsworth. I can almost guarantee you if he knew Hudson was going to come so cheap he would have skipped Bloomquist.

But at the time he was trying to be aggressive and get the parts he thought the team needed. I'm not a fan of the Farnsworth signing but I understand it. He was getting out there early and trying to find good deals...when in reality the good deals would come later.

Anonymous said...

Baseball America Reports:

Lance Niekro, a former Giants first baseman, is trying to follow in the Niekro legacy with a comeback as a knuckleballer.

I know Rany will be following this... a submariner and a knuckleballer on the same staff, now THAT would be something!

Brett said...

Take out the parts about how the offseason moves were frustrating, and it sounds like Rany just wrote Poz's annual "the Royals could win the division" column.

I stopped at a gas station yesterday and while I was there, I bought a baseball season preview magazine that has the Royals finishing third. I don't remember right now which magazine it was, and I don't have it with me.

Devon, the quote about the Royals possibly having their best team since 2004 is from Moore. It doesn't refer to 2008 being a better season than 2003, it refers to the current roster (heading into Spring Training 2009) possibly having more talent than any Royals roster since the strike.

chrisc said...

I've got Spring Fever! I love it. Thanks for the encouraging article Rany. Even if your hypothetical season is full of if, buts, candies, and nuts...this is the time for believing.

Anonymous said...

You know, Rany, over at Royals Review (and Beyond the Box Score), we used a WAR spreadsheet and projections (mostly CHONE, PECOTA wasn't out at the time, although I'll probably incorporate it eventually when I get around to it -- stil probably has a small edge on CHONE overall, although CHONE and ZiPS are pretty close, as the "big shootout" shows.) Anyway, we used a wOBA (based on custom linear weights run estimator, so that's an advantage on the BP odds if they use VORP), and also have better defensive numbers -- that is, not FRAA. Now, a WAR-based projection has its problems, but in any case, I do think, from the looks of things, we have a more realistic playing time projection for bench guys than BP does (as one would expect, given that were a group of Royals fans). IN nay case, we have the Royals at around 78 wins.

Here's the link to that discussion thread:

The binomial distribution gives the Royals a 27% chance of going .500, and 85 chance of winning 86, and a 1% chance of winning 91.

(An earlier version I threw together myself contains a graph of various possibilites, although t hey are too optimistic).

In any case, you are dead on about the Royals potentially wasted opportunities this offseason. Jacobs' settlement somehow ended up being more than he would have deserved in arb (although he would have gotten more), since he's maybe a 1 WARplayer (if everything breaks right), or about $5M. In his first year of arb, that implies $2M. That wouldn't happen, but only highlights the... quality... of that trade.

We've been over this a million times, but as you said, if the Royals can't add Hudson (who would be a steal ats $5M/per, even in this market, and even though he's clearly on the decline -- a 2.5 WAR player at best), it stupid stuff like this we'll have to remember.

Anonymous said...

The Royals didn't win more games last year than in 2003, but I think it's a close call which was the better team, talent-wise. I don't know how it would shake out. I think it comes down to Beltran-Sweeney-Dye in the middle of the linup vs. Grienke-Meche-Soria anchoring the pitching staff. Wish we could mix and match to construct an actual good team!

I wonder if Glass would let go of the extra $10/2 for Hudson if somebody explained to him about standard deviations and tipping points.

Anonymous said...

Far from a complete analysis of the roster (I'll save that for if we DON'T sign Hudson)... here's a nugget from Dick Kaegel at the end of his Mike Jacobs wrap-up:

"Five others who were eligible for arbitration also signed one-year contracts: Catcher John Buck, $2.9 million; pitcher Jimmy Gobble, $1.35 million; pitcher Kyle Davies, $1.3 million; infielder Esteban German, $1.2 million, and pitcher Joel Peralta, $640,000."

It's my understanding these aren't guaranteed (regardless of whether you actually have an arb hearing, so we can release them and only pay 1/6 of the salary)... so, let's get cracking and find Orlando some money:

Peralta 640k
Buck 2.9m
Gobble 1.35m
German 1.2m
TOTAL 6.09m

5/6 of that is 5.075m, which should be plenty to sign Hudson for this year, or on average over 2 years. All of these are spare parts, with the exception of maybe Buck (injury to Pena or Olivo), so we'd probably need to spend 500-600k or so to stash an emergency catcher at Omaha...

+Tony Pena!?

Anonymous said...

On the brink of an economic collapse, one company is actually growing...Wal Mart. C'Mon Mr Glass, let's adjust the Royals budget in relation to your company's growth!

Anonymous said...

We need to get this done. Screw the budget, this player available at this price changes things. He will accept one year but I would prefer to strike while the iron is hot and sign him for 2. We could easily flip him at the trade deadline if the team bombs.

Anonymous said...

I can understand the Royals wanting to keep Teahen and his versatility. However, there are plenty of others already mentioned that they can drop to save cash. With O-Dog's asking price so low, what the hell are the Royals waiting for? Please, sign Orlando!

Anonymous said...

I agree, if the Royals can figure out a way to ink Hudson, I'll be as happy as Alec Baldwin playing Wii.

Anonymous said...

The biggest reason I am bullish on the Royals, despite the somewhat dipsomanaical signings pattern this offseason, is the fact that if they had gone .500 during their two horrendous losing streaks last season, they would have won the division. Having survived those horrors, and learned from them (along with learning from the positives, in particular the end of the season), I think the team will be much better equipped to handle a bit of adversity and keep it from snowballing into a serious losing streak.

Still, a series of tragic transporter accidents during spring training that result in Hudson signing wouldn't be a bad thing at all.

Ryan said...

The Royals need $5 million to sign Orlando Hudson. They can't afford it. If only they hadn't spent $4.25 millon Kyle Farnsworth.

Farnsworth cost them Hudson.

Anonymous said...

Well, I think we've shown they CAN afford it, but it SOUNDS like they are simply choosing not to... i.e. choosing to keep a whole lotta dead weight around so they feel safe. Reminds me of that George Carlin bit about baseball, and everyone wanting to go home and be safe.

Anonymous said...

Blue Crew just claimed Tug Hulett, (soon to be) 26 yr old LH hitting utility player from mariners and designated Neal Musser. Nothing quite like working on the bottom of the roster instead of the top to keep the fans breathless!

Jimmy Jack said...

Reading between the lines here a little (with a lot of speculation and blind hope), with the addition of Hulett, could this mean that we potentially picked up a replacement of Teahen to allow us to drop him freeing up money for Hudson??

Ryan said...

Our $36 million outfielder just removed an ingrown toenail by himself. I can't even afford (or get) health insurance, and Guillen is pulling out his mothereffing toenails.

Someone pay me $36 million. I'll show up out-of-shape to Surprise, Arizona right now and take out two of my toe nails.

Antonio. said...

"But at the time he was trying to be aggressive and get the parts he thought the team needed."

Royals fans: still ignoring that aggression is often a hindrance in baseball. Aggression for its own sake isn't good.

Clint said...

Would Hudson drastically change this infield and this lineup?

I'd like to think so.

Anonymous said...

Over the years, during the offeason, Glass has often promised higher team payrolls than actually occured. Now he has drawn a line in the sand on our total this year...that doesnt bold well with me, a season ticket holder. Its obvious to most everyone that Hudson would give this team a legit chance in an otherwise average division. Couple this with the $250mill the taxpayers just plowed into the K and the $30 mill Glass gets from revenue sharing and one must conclude that if we dont sign Orlando over $4mill, Glass is not the owner that will get this organization to the promise land.

Anonymous said...

I get so amused at people complaining about payroll this off-season.. anyone care to do a percent-increased comparison? Pretty sure the Royals will be near the top. Yeah, he's drawn a line, but that line is so much farther out there I find it hard to musterany outrage. Plus, he's been quoted (I think I recall) as saying he's open to adding with a mid-season pickup if they're in the hunt.

Want to complain about who they're spending that Wal-Mart money on? Go ahead, that's what fans do.. but don't complain about the owner merely out of habit, because for once, he's doing his part.

Unknown said...

Amen, Tracy. Also, he was willing to stretch it. Keith Law of ESPN reports the Royals had a 4.6 million dollar base salary offer on the table for O-Dog. He took a lower guarantee with higher upside incentives with the Dodgers. David Glass is on board - get off him already. Tracy is right, look at the percent increase from last year. Go buy some tickets and quit yer....complaining - we're gonna compete.

Anonymous said...

Tracey, I guess you forget how cheap he has ran this franchise for years. Subtract the revenue sharing cash and our payroll is on the 40's. Do the same for a couple of seasons ago and our payroll was less than some years in the mid-90's when there was no revenue sharing. He has made promises in the past of payroll increases and in turm that year the payroll actually decreased. Or how about the drafts when he would only draft players willing to accept 1,000 bonuses. Or in 2003 when he promised to make big moves if in contenetion when in reality we got Rondell White and a couple of other cheap players. Sorry for not getting excitied about this season and a $74mill payroll ($30mill of which is paid for via revenue sharing)in a year after the taxpayers wrote a $250mill check. I think he owes us, taxpayers and season ticket holders a bit more.

Anonymous said...

As we all now know, Hudson signed with the Dodgers. A key thing to remember here is that if the Royals signed him, they would have to give up their #1 draft choice in 2009. We have the 11th pick. I don't think the Royals were willing to do that and I'm OK with that.

I think it is clear that the Royals are much improved from last year. We replace Pena/Grudzielanek with a full year of Aviles and some combination of Bloomquist/Teahen/Callaspo. We replace Gload with Jacobs. We replace Teahen with Crisp. In pitching, we aren't srting the year with Brett Tomko in the rotation. Our top 4 of Meche, Greinke, Davies, and Ramirez looks pretty good. If Bannister or Hochevar comes through, who knows? I like our team.

Anonymous said...

actually it would been our 2nd round pick.

Anonymous said...

now that orlando hudson is gone, i reiterate my sincere, though admittedly unlikely hope that dayton is saving the money for pedro.

Anonymous said...

Also, I believe we pick #12, because the Nationals failed to sign Aaron Crow... (they will pick #1 and #10 i think)... too bad this isn't our year at #1 so we could take Strasburg (oh wait, he went to college, so we would probably pass on him anyway) :o)

pjbronco said...

Two comments near the end of the first spring training game (if you can't be irrational after one game, when can you be irrational, right?): Sure glad we got Horacio Ramirez back. The season could have been disastrous without his steady arm. AND, who is JR House and what is he doing getting 1B at bats in game one? Where are Shealy and KK?

That is all for now.

Anonymous said...

So Cruz is now a Royal. We might give up our second-round pick, but we also DFA'd German. I like the overall net.

(Of course, if you ask Rotoworld, they argue that it's proof that there is no plan in KC. Big surprise.)

Anonymous said...

That guy that types those posts for Rotoworld is a Twins fan and he always sh*ts all over the Royals. It's pathetic how biased he is. I got so tired of reading one of his posts bagging on the Royals that one night I sent him an email ripping into him about it. It didn't help that I was drunk at the time. Go the Cruz signing and love it more that Twins fans are pissed they didn't get him. If Gordon or Butler or both can step up, if Jacobs can hit 25 bombs, and if Davies and Aviles can repeat, I think 2009 is going to be a great year. Now all we need is a new post from Rany. Isn't this the type of news to get you to stop popping zits and write about our Royals, Rany?

Anonymous said...

The bullpen, my biggest concern, just got waaay better. AL central title not exactly likely, but the dream just got a wee bit more realistic. We need a big year from The training staff to keep the arms healthy, and I like KC's chances to compete.