The second part of a look back at 2005 for the top two teams in the AL West. Part one was published here yesterday

In the end, the difference between the Angels and the A's 2005 was that the Angels had a more optimal distribution of runs scored and runs allowed than the A's did. The peculiar run distributions of the Anaheim run prevention unit and Oakland's run producing unit are the culprits here, and given the similarities in their aggregate runs scored and runs allowed, the run distribution almost wholly accounts for the gap in the final standings. I don't think I can put it any more plainly than that.

Remember, if a team is most likely to meet its Pythagorean projection if its run distributions match up exactly with the Weibull, since the former is derived from the latter. In advanced metrics, this manifests itself as over- or underperformance, and what is often pushed aside as "luck" at sabermetric cocktail parties (okay, chat rooms) is really an effect of run distribution.

The obvious question is: are run distributions a product of luck? Can a team not control its distribution of runs scored or is there is an inherent bias in the roster construction that makes a team more prone to being shut out other than its overall offensive prowess? This is an important issue, one on which I have not yet formed a complete opinion.

On the one hand, it seems that the Angels, who had plenty of baserunning ability and an excellent bullpen (3.52 ERA), were in a position to win close games when the utility of a single run was extremely high. They also had Vlad Guerrero in the middle of the lineup, who could change a close game in a hurry. On the other hand, the Angels had OBP issues outside of Guerrero, and a bunch of hackers is no way to start a rally when you need baserunners. Oakland had a reasonable OBP through most of their lineup spots, but no big power threat who could turn around a game. Then again, the A's had a similar team ISO (145) to the Angels (139), and an even more effective bullpen (3.39 ERA).

Did the A's simply tee off on bad pitchers and did the Angels take advantage of weak-hitting teams? Not as far as I can tell. The Angels hit better against the worst pitching in the league than the A's did. The A's posted a 106 mOPS+ and 5.14 runs per game against the three worst pitching teams in the league (Texas, Tampa Bay, and Kansas City); the Angels had a 108 mOPS+ and 5.54 runs. Conversely, Oakland pitched better against the three worst hitting teams (Minnesota, Kansas City, and Seattle) than the Angels did: 6.9 K/9, 2.68 ERA for the A's and 6.5 K/9, 3.96 ERA for the Angels. So it was not simply that Oakland hitters could hit only the worst pitchers or that Angel pitching was tough against only the terrible hitters.

Because run distribution is a product of discrete events - individual games - it is tempting to think that bullpen management and in-game strategy might play an effect. Judging by SBNation team websites, A's fans were burning Macha in verbal effigy even as he kept the team together after a rough start (17-32), while Angel fans were canonizing Mike Scioscia despite his bizarre obsession with the five-man infield. We don't have access to the data managers use to make decisions - day-to-day player health, a glitch in a starter's delivery or pickoff move, the blood-alcohol level of his LOOGY - and so I am loathe to judge managers by anomalies in the run distribution. But I'll make an attempt anyway.

Anaheim's peculiar runs allowed distribution suggests that Scioscia had optimal bullpen usage. According to Baseball Prospectus' Adjusted Runs Prevented statistic for relievers, the best pitchers in the Angel `pen were Shields (20.9 ARP), Rodriguez (14.5), and Brendan Donnelly (10.8). Escobar had a fantastic 8.4 ARP in only 19.0 IP relief innings. According to Baseball Prospectus' Leverage statistic, which measures the importance of the game situation when a reliever pitches a la WinExp, Scioscia used Rodriguez (2.21 LEV), Shields (2.03), Escobar (1.76) and Donnelly (1.38) in the most important situations. These are extremely high LEV numbers, reflecting the number of close contests for the Angels, and Scioscia used his bullpen marvelously. This could account for the anomaly in the runs-allowed distribution. It's a myth that a good bullpen will help a team outperform its Pythagorean projection. A good bullpen will reduce the overall number of runs allowed; it is good bullpen usage that helps a team outperform its Pythagorean projection, and the 2005 Angels were an object lesson in optimal bullpen usage.

(Macha, on the other hand, had the incredible relief trio of Street (35.0 ARP), Kiko Calero (16.4), Justin Duchscherer (14.7). Duchscherer's 1.28 LEV led the team if you don't count Dotel's abbreviated season, and Street was not far behind (1.19). Calero, however, was wasted on neutral situations (1.00). Still, Macha did a decent job, considering he wasn't presented with very many high-leverage relief situations.)

Judging Oakland's runs scored anomaly is extremely difficult - an approach that evaluates offensive decision-making on a per game basis has to be based on Win Expectation as LEV is. I am not aware of a warehouse for offensive win probability analyses, and I sure as hell wasn't keeping track during the year. So all we really know is the overall offensive philosophies of Oakland and Anaheim.

This brings us back to smallball versus Moneyball, an angle I promised not to take in this article. Oh well: Angel partisans will likely point to smallball techniques as the reason why the Angels won games without scoring very many runs. It seems tempting, but records in one-run games are famously unreliable, and Mike Scioscia's club fared poorly in such contests in 2003 and 2004. Furthermore, the anomaly was in the Angels' runs allowed distribution, not their runs scored. An offensive technique, such as the vaunted smallball, would manifest itself in the runs scored distribution.

Athletics partisans (late disclaimer: such as myself) will want to label it bad luck and add it to four consecutive first-round playoff exits and Kirk Gibson's home run. I absolutely guarantee that some will take the bizarre run distribution as evidence that the A's didn't play enough smallball. I won't say it's not true - although I don't think it is - but I imagine that whoever advances this theory will come armed with anecdotal evidence. Just glancing quickly at the 2004 run distributions for the Athletics, the numerical evidence does not support the proposition that it is the Oakland philosophy that prevented them from scoring runs in line with the Weibull distribution. I also discussed previously the reasons I do not think it is the personnel. So what was it? I won't claim to know the answer, but there is nothing obvious in roster construction or game-management that tells me that the A's offense was destined to be a feast-or-famine unit.

So are run distributions just dumb luck, bound to change every year? From a runs allowed perspective, I think that optimal bullpen usage (not talent) can help, although not guarantee, that a team beat its Weibull distribution and therefore its Pythagorean projection. From a runs-scored perspective, I'm stumped. There are a number of possible explanations that I won't present here since they rely on anecdote, conjecture, and small-sample size data, if any. The truth may be obscured in the Jamesian fog, and until we know any better, I would think that the run distributions of the Angels of Anaheim and the Oakland Athletics are likely to change next year while continuing to exhibit some inexplicable features next year. Given how evenly-matched the teams were this year - and barring any major additions or subtractions - the AL West is going to be a two-team dogfight again in 2006. The loser can blame Waloddi Weibull.

Special thanks to Professor Steven J. Miller for his helpful discussions