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Luck and the Diamondbacks

"Nature creates ability; luck provides it with opportunity."
   -- François de la Rochefoucauld

Saying the 2009 Diamondbacks' season was "unlucky" seems like a cop-out. You might counter the quote above with one from Jefferson: "I'm a great believer in luck, and I find the harder I work, the more I have of it." But there does seem to be objective evidence which suggests that misfortune between the lines cost Arizona a significant number of wins last year. After the jump, we'll look at this, and the ways in which one can try to judge some of the impact of luck on a season overall, including the Diamondbacks' record in one-run games, clutch performance, and batting average on balls in play.

Pythagorean Winning Percentage
What is it? And why should we care? I'll start with the second, since if I began with the formula, I'd have to pepper the article with Megan Fox pictures to regain people's attention. To quote, "The rationale behind Pythagorean Winning Percentage is that, while winning as many games as possible is still the ultimate goal of a baseball team, a team's run differential (once a sufficient number of games have been played) provides a better idea of how well a team is actually playing... A team's actual W-L record will approach the Pythagorean Expected W-L record over time, not the other way around." Put another way, going forward from any given point, a Pythagorean WP is a better forecaster of future performance, barring personnel issues such as injuries or  trades, than their actual Win Percentage.

So, what is it? It's a formula that uses the runs scored and allowed (RS and RA) by team to work out their expected Winning Percentage. It's one of Bill James' greatest inventions - it's called 'Pythagorean', because in its most well-known form, it uses the square of RS and RA.


It works on other sports too, if you change the exponent - for basketballl's three-figure scoring, you have to use about the power of 15, not two. Also, the best fit is not exactly two; it depends on the era, and is about 1.85 now. However, you needn't worry about the specific math: this will not be on the end of year test, and it can be found on mainstream resources like ESPN's expanded standings. Below are tables for 2009 in each league which give a team's actual record, runs scored and allowed, their Pythagorean projected record based on those, the difference between the two ("Luck" - that's's term, not mine) - and also the team's record in one run games, which we'll talk about later.

Rk Tm W L R RA pythWL Luck 1Run
1 LAD 95 67 4.8 3.8 98-64 -3 28-22
2 PHI 93 69 5.1 4.4 92-70 0 24-21
3  COL 92 70 5.0 4.4 90-72 1 23-20
4 STL 91 71 4.5 4.0 90-72 0 24-21
5  SFG 88 74 4.1 3.8 87-75 0 21-22
6  FLA 87 75 4.8 4.7 83-79 3 30-20
7  ATL 86 76 4.5 4.0 90-72 -4 27-25
8  CHC 83 78 4.4 4.2 84-77 -1 16-22
9  MIL 80 82 4.8 5.0 78-84 1 20-23
10  CIN 78 84 4.2 4.5 76-86 1 19-20
11  SDP 75 87 3.9 4.7 67-95 7 23-18
12  HOU 74 88 4.0 4.8 68-94 5 24-23
13  NYM 70 92 4.1 4.7 71-91 -1 19-24
14  ARI 70 92 4.4 4.8 75-87 -5 20-27
15  PIT 62 99 4.0 4.8 67-94 -5 12-22
16  WSN 59 103 4.4 5.4 66-96 -7 22-24
Avg 80 81 4.4 4.5 80-82 22-22
Rk Tm W L R RA pythWL Luck 1Run
1 NYY 103 59 5.6 4.6 95-67 7 22-16
2 LAA 97 65 5.5 4.7 93-69 3 27-18
3  BOS 95 67 5.4 4.5 94-68 0 22-17
4  TEX 87 75 4.8 4.6 84-78 2 19-18
5 MIN 86 76 5.0 4.7 86-76 0 23-20
6 DET 86 76 4.6 4.6 81-81 4 28-21
7  SEA 85 77 4.0 4.3 76-86 8 35-20
8  TBR 84 78 5.0 4.7 86-76 -2 20-25
9  CHW 79 83 4.5 4.5 81-81 -2 19-27
10  OAK 75 87 4.7 4.7 81-81 -6 15-23
11  TOR 75 87 4.9 4.8 83-79 -8 21-28
12  CLE 65 97 4.8 5.3 74-88 -9 19-21
13  KCR 65 97 4.2 5.2 65-97 0 16-25
14  BAL 64 98 4.6 5.4 69-93 -5 17-22
Avg 81 80 4.8 4.8 82-80 21-21

What does it tell us about the '09 Diamondbacks? That they won fewer games than teams with their number of runs scored and allowed, normally do. The team was out-scored by 0.4 runs per game - the Padres, who went 75-87, were outscored by twice as much. On the highest level, it doesn't matter: winning is what matters, and you don't get any more credit in the standings for a blowout than a squeaker. However, let's look in a little more depth at why Arizona might have underperformed.

One-run Games
After 2007, and the sterling record of the Diamondbacks in one-run games, I tended to the belief that this was the result of Bob Melvin's managerial prowess rather than blind luck. Subsequent events showed the error of those ways, as the 12-game advantage we had in one-run games during our run to the NLCS evaporated entirely in 2008; the team went 22-23 and performed exactly at their Pythagorean expected record. The trend continued in 2009, with the D-backs a disappointing 20-27 in one-run games, and with a Pythagorean record five games better than actual, at 75-87.

Might this one-run record reflect Arizona's poor play? After all, their WP there (.426) was right in line with their overall number (.432). However, it seems that isn't so. According to Tom Ruane, "How a team does one year in close games is absolutely no use in predicting how it will do the next.  Things like that are usually called "the breaks of the game" or, more succinctly, luck." As virtual coin-flips, then are near-worthless as a measure of how "good" a team is. Two of the best in baseball history were the 1974 Padres and 1955 Kansas City A's, who went 31-16 and 30-15 in one-run games respectively. Their overall records? 60-102 and 63-91.

The top three teams in one-run baseball in 2008 - the Rays, Brewers and Angels - all won fewer games in 2009, in part because their one-run records all dropped (not by much in Anaheim's case, admittedly). Conversely, the worst three teams - Braves, Padres and Mariners - all won more games. Obviously, the more extreme the record, the greater the chance for regression to the mean. But even at Arizona's -7 record, history tells us odds are we'll pick up several games next year, simply by the law of averages. Looking at the chart above, I'd be taking the "under" for the 2010 Angels, Mariners and Marlins, while the Royals, Pirates and A's were the cruelest playthings of the baseball gods this time around.

Clutch hitting
This is one Mythbusters should probably cover. Certain players have a reputation of being 'clutch' - for coming through in high-pressure situations. However, study after study has shown that there is no such trait detectable in the numbers. This doesn't mean it doesn't exist - just that the random variation which is inevitable in baseball stats, is enough noise to drown out the evidence. Any player who appears clutch is basically the result of small sample size.  If one hundred .280 batters get 50 at-bats in a given situation, odds are fourteen of them will hit .360 or better (18-for-50); four of them will bat .400 (20-for-50). It doesn't make them 'clutch'; it's just blind chance.

So there is no real evidence that hitting with runners in scoring position is a significantly different skill from hitting generally. Numbers will vary in any situation, as noted above, but hitters will tend to regress towards their normal numbers: if they better than their normal numbers with RISP one year, they're not likely do so the next. Conversely, if they fail with RISP, relative to their usual stats, odds are they'll do better the following season. Which brings us to the 2009 Diamondbacks. Across the NL as a whole, OPS with RISP was 23 points higher than with no-one on base, mostly due to increased walk-rate; the Diamondbacks were 12 points lower, mostly because they hit less. They were even worse with RISP and two outs, batting a mere .220.

As with one-run games, this kind of thing is probably not likely to continue. It appears that the offense generated by the Diamondbacks 'should' have created more runs. There's a number called "second-order wins" - I defer to Wikipedia on explaining this one. "To further filter out the distortions of luck, sabermetricians can also calculate a team's expected runs scored and allowed... given their total singles, doubles, walks, etc. [This] helps to eliminate the luck factor of the order in which the team's hits and walks came within an inning." When those expected RS and RA are plugged into Pythagoras, the results are called second-order wins.

Again, don't worry about the specifics. Baseball Prospectus have done the legwork, creating adjusted standings. The second-order wins  are W2, and the difference to the 'actual' record is D2. For Arizona,  W2 is all the way up at 79.2, a gap surpassed in the majors only by Washington, mostly because of a sharp drop in the runs we allowed. Third-order wins (W3) also adjust for strength of schedule, and give Arizona 80 victories. Now, I'm sure the usual parties will continue to sneer at all evidence the 2009 D-backs didn't suck so much as they proclaim. But I'm not the one doing the math, or who wrote,: "Second- and third-order winning percentage has been shown to predict future actual team winning percentage better than both actual winning percentage and first-order winning percentage."

Batting Average on Balls in Play
The final element in the chain is Batting Average on Balls in Play. Purple Row had a really good piece on what this is, and why it matters, but in brief: three out of ten balls put in play i.e. not home-runs will become hits. This number is surprisingly close to constant, especially for pitchers: you can beat the odds in the short-term, but the longer you go on, the tougher it gets. Case in point: remember Dan Haren's brilliant first-half? His BABIP was .233 - basically, he was getting a large leg-up from random chance. His BABIP in the second-half regressed all the way back to .315, and we know how that ended.

On the pitching side, AZ hurlers saw a BABIP of .303 - that may seem only slightly worse than the league average of .298, but only one team (Houston at .317) were above .305. So it seems this was, to at least a small degree, another area where Lady Luck was not being ladylike to Arizona. As an aside, the Los Angeles pitching staff were easily the "luckiest", with a BABIP all the way down at .280. The Dodgers are not only going to have to replace Randy Wolf, they'll also have to cope with a likely regression of that BABIP number to more normal levels. The Giants were second, at .284, so their pitching staff may also have to work a bit harder in 2010.

The situation isn't quite the same for hitters, who do have a greater degree of control over what happens after they hit the ball [Ichiro has a career BABIP of .357, compared to MLB average last year of .300]. Line drives become hits at a much greater rate (BABIP of .718 for the 2009 NL) than fly-balls (.142) or ground-balls (.235). Hit lots of line-drives, and you'll have a good BABIP. That's why it's necessary to go further than "Arizona's overall hitting BABIP was exactly at the league average," since that doesn't tell the whole picture.

If you split our hits down into the same three categories, you'll find that - hallelujah! - the Diamondbacks finally got some luck going their way. Ground balls became hits at a .252 clip, seventeen points above average, while line-drives were eleven points higher, at .729. Only fly balls were lower than average, and only by one point at .141. So, given this, how did we end up being so close to the mean overall? One big reason, courtesy of Eric Byrnes and Chris Young in particular, is that we had a lot of pop-ups, which virtually never become hits. 14% of our fly-balls never got out of the infield. No team in the National League had a higher rate, and it knocked our BABIP down significantly.

Summary, and going forward into 2010
It would, obviously, be ridiculous to claim that bad luck is all that separated the Diamondbacks from challenging for a playoff spot last year - even the W3 number has us still sitting about ten games out in the wild-card race. But there is a credible case that, even with a myriad of problems, the 2009 Diamondbacks were significantly better than their final W-L record indicated. While BABIP doesn't seem to have been a major factor, the runs they scored  and allowed "should" have resulted in more wins, and their performance "should" have resulted in the opposition scoring almost forty fewer runs.

Now, you could argue that this doesn't matter: as my signature says, "Win or die", and last year, we did a good deal more of the latter than the former. However, if you accept the W3 numbers as the 'true' difference in talent between us and the wild-card Rockies, it was only  9.8 games, rather than the 22 games shown in the standings. This then suggests that closing the gap in 2010 is not such a monumental task as it first appears. Certainly, the current Vegas odds - 66/1 against the Diamondbacks winning the World Series - seem a lot better value for Arizona than those for Colorado (14/1) or San Francisco (16/1).

While still an "if", Brandon Webb returning to the average form he showed from 2006-08 (19-8, with a 3.13 ERA), would likely take care of the bulk of that gap, without taking into account any other changes or requiring further improvements. Should that happen, we may not need much good luck this season: a simple absence of bad luck could be all that's necessary for the Diamondbacks to be competitive.