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.