One might have thought he looked like this...
Unfortunately, he only looked like this...
My interest in baseball has been fairly low for this season. My semi-beloved Orioles have taken quite a beating on this blog, but currently they expected (Pythagoreanly) to be above 500 for the first time in about a decade. (In fact based on their runs scored and runs against that are the middlest team in baseball. Certainly not awesome but should not be described multiple times as a candidate for the WORST TEAM IN BASEBALL unless that candidate set is 15 teams long).
Coming right at you with eight wins in a row
However, despite scoring more runs than they gave up, the Os are 6 games under 500. For the baseball statistical purist they would be described as underperforming by chance - that their Pythogorean Expectation is somehow a purer method of determining how good they are instead of their win loss, ala last years Cleveland Indians. The Indians won 12 fewer games than they were expected to by runs for and against. The Orioles are on pace to win 6 fewer games. More extremely - the Yankees are currently 9 games under expectation while Arizona is a whopping 10 games OVER expectation.
This reminds me of a conversation I had with GF last year about the Indians. The Pythagorean expectation is all well and good as a general indicator of how well a team should performa. But, there are certain predictors of win loss that is cannot capture. For example, if a team has 4 pitchers, two of whom have an ERA of 0 and two of whom have an ERA of 5 and the team scores exactly 4 runs a game. The team will obviously be a 500 team (the first two pitchers will win every game and the second two lose every game). However, over 160 games, we would expect them to win 102. Their actual performance would be -22 from pyagorean expectation, but we don't REALLY expect them to win 102 games. At some point is a massive deviation from Pythagorean expectation not just an expected possible deviation that could happen to any team, but actually soemthing which could EXPLAIN SOMETHING ABOUT A SPECIFIC TEAM? Thoughts?
"Eureka," says Pythagoras, "the Orioles suck only a little."
9 comments:
The icing on the God Shammgod cake is that he played college ball at Providence.
The Yankees may be this year's clearest case of run differential being a funny figure to read out of context.
In a single given game, the run scoring ceiling is infinitely higher than the basement is low. Naturally, team A with a tendency to explode offensively when they're not slumping can have the same run differential as team B that scores consistently and never slumps for long. In terms of being relevant to victory, (in hindsight anyway), all of team A's extra runs were unneeded. From a GM standpoint, they over-invested in their offense.
In their last twenty games, the Yankees have reached run totals of 21, 17, 16, 14, 13, and 10, scoring 5 or more in 18 of 20 games. Of course many of their 15 wins during that stretch were blowouts, which padded their overall run differential out of proportion to the number of wins they racked up. The Indians of last year were in a similar boat, struggling similarly with pitching but compensating in differential by the odd blowout.
A team with fewer wins than expected, after reading run differential, either had a high number of offensive explosions or won by tossing a high number of shutouts or one-run gems while tending to lose only close games. The latter is not an especially common model in today's game, so the former could probably be assumed.
On the flipside, naturally, teams whose records belie their middling run differentials have won lots of close games in spite of suffering a few routs. Or else they were shut out (or nearly so) repeatedly, while their opponents scored at a normal rate. Again, in today's offensively-charged game, the former is much more likely.
This suggests something that was almost certainly already obvious - that good pitching is more valuable than good hitting, at least if you believe my assumptions about the nature of today's game. Which, I suppose, would then have been obvious even before you considered run differential. But the point is that good pitching will compensate for a lack of good hitting in a way that is not true the other way around. If I were a GM, then, I would invest my $14 million in a half-decent pitcher way before I would bother with a bum like Carlos Beltran, who leads the league in weakness and in being a wiener.
The bottom ten teams in baseball, from worst to best:
1) Pirates (red down arrow of prediction)
2) Reds (r.d.a.)
3) Giants (tied) (r.d.a)
3) Devil Rays (tied) (blue up arrow)
5) Marlins (no arrow)
6) Astros (n.a.)
7) Nationals (n.a.)
8) Rangers (n.a. or maybe b.u.a.)
9) Orioles (n.a. or maybe b.u.a.)
10) Cardinals (n.a.)
I'm not sure I totally followed what you wrote, Simon, but I believe that basically you're right. A team whose W-L deviates widely from its Pythagorean expected W-L may not simply be lucky/unlucky, but may have particular strengths or weaknesses that account for the deviation. In particular, I believe that research has shown that teams with strong bullpens often outperform their expected records and vice versa.
From what I understand though, the simple Pythagorean formula is not really used that much anymore. And instead there are a bunch of more complicated formulas that use a team's opponents' numbers and its strength of schedule to generate (supposedly) more accurate predictions. I am not so good at teh maths anymore so I get pretty lost trying to read about this stuff, but those who are interested can look into it here:
http://www.baseballprospectus.com/article.php?articleid=342
You can also check out those formulas applied to this season on BP's adjusted standings page:
http://www.baseballprospectus.com/statistics/standings.php
Shoot, Blogger messed up the formatting on those links, but if you right-click on the address to highlight the whole thing and c+p into the browser it seems it will still work.
Thanks GF and R'TC.
A couple of comments:
The use of Poisson distributions in the thing that Greg linked to SHOULD capture exactly what Ben suggested and more - that the number of runs in a ball game have to be integers greater than or equal to zero. I did get a little lost in the argument of the article OTHER than it was slightly better data fitting. That being said, the benefit of the more precise article is minor and the Yankees still are under-performing and the Diamondbacks are still over-performing based on this statistic. Because of the modifications mean a slightly better fit - but still could not predict such serious outliers - I am going to stick with the simpler formula for now.
I would add one point to Ben's claim about teams with fewer wins than expected - which is SOME of this has to be attributed to chance. I can't quite figure out how much, but it seems like EVEN a deviation like the Indians last year might not have been so unexpected (that it was nothing about the Indians - just that at some point with so many teams, some teams is going to deviate that much from expectation). It would have to be an enormous deviation (i guess) for it really to reflect on the team.
In terms of the strong bullpen idea that Greg brought up - I would have to think more about that.
Finally - I can live with the Orioles being the 9th worst team in baseball - but I demand a blue-up-arrow.
There's that old baseball saw about the journeyman who hits .275 with 500 at-bats one year (I think I'm paraphrasing Ball Four here but I can't remember). He looks at his statistics in the off-season, and realizes that if he'd gotten just 12 more hits over the course of an entire season, he could hit .300 and maybe be an All-Star candidate.
That's 12 hits divided by 162 games - one hit every three series is the difference between a .275 and a .300 hitter.
I think the punchline is that he ends up hitting .250. But the point is that, yes, the long season and the relatively minimal statistical difference between success and failure (both for individuals and teams) means that outcomes over long periods frequently hinge on something like random chance.
I would guess that most teams play about ten games a year that really could go either way. These include scoreless pitchers' duels, late-extra inning games where both bullpens are almost completely spent, 14-13 slugfests, etc. Let's say that these games go beyond what any manager or GM could reasonably plan for by having a deep bench or a good bullpen or whatever, since they stretch the limits of the rosters much further than anyone on either team made provisions for - and yet they have to end decisively.
If a thoroughly mediocre team goes 5-5 in such games, then they finish 81-81 - but if they have very good luck, they could win 84 or 85, which is good enough for playoff contention - or they could win 77, which would make them look a lot worse than they might be. In any case, these tossups have little bearing on run differential, while at the same time certain conceivable deviations can and do affect the season as a whole.
This is not even to mention the incidental effect that a couple of lucky outcomes can have. If a team is 43-39 at the break rather than 41-41, this might make the difference between buying and selling at the deadline, and might well motivate the players to better performance if they feel like they're in contention. Look at how fast Johan Santana shut up after the Twins won a few in a row coincident with the Tigers and Indians losing streaks. Of course the power of motivation and the difference between fortune and well-deserved success can't easily be quantified, but one assumes they exist.
So in conclusion, it's likely that random chance - as well as its nonrandom impact - have a bearing on under and overachievement.
I almost totally agree with Ben except:
(1) I think the 0.275 stuff comes from Moneyball
(2) While 10 games are IDENTIFIABLE as going either way (50-50) other games are ALSO dictated by random processes, but are more like 40-60 or so. For these games, the runs allowed/runs scored can give an indication of the underlying likelihoods that wins-losses cannot (that is a little confusing, but somehow correct).
Things I agree with wholeheartedly.
Random chance leads has nonrandom consequences. It you imagine a team which will have exactly a 50-50 chance going into each game - there is a 37% chance that after 81 games they are at least 43-39 and very much in contention and a 20% chance they are at most 37-45 and very much out of contention. These teams are fundamentally as good as each other - but the rest of the season will play out very differently for each team.
Finally - the thing that Baseball has going for it in this regard is the length of the season. If you imagine two teams - team A which has a 50% chance of winning each game and team B which has a 60% chance of winning - the likelihood that team A will have won as many or more games than team B after 162 games is only ~4%.
In a football season - the likelihood that team A has the same or better winning % as team B is 34%.
In blasketball - team A >= team b is ~11%.
Conclusion, there may be more randomness in baseball than other sports - but over the course of 162 games IT IS VERY LIKELY (but not necessary) that the best team will win.
As a side note, the tendency for baseball teams to fall between .400 and .600 seems to be not only due to the statistical fact of the long season, but of its physical toll. Over the last 10 games, for example, the vast majority of teams (21 out of 30) were either 4-6, 5-5, or 6-4. Only three were 8-2 or 2-8, and none had more extreme L10s than that.
By contrast, last season in the NFL after ten games, 14 out of 31 teams were 7-3 or better or 3-7 or worse. Seven teams were 8-2 or better or 2-8 or worse.
Although an inferior football team may be more likely, statistically, to sneak ahead of their betters in the standings, there is quite naturally a recognition that each game counts more, and therefore that superiority must be established from game to game, at any cost, as opposed to from series to series in baseball, or over an even longer stretch. For a baseball team to put as much effort into a given game as a football team would be exhausting and ultimately impossible. This of course explains the trend toward specialization, a kind of detente so that pitchers can have longer careers, and the impossibility of fielding an entire team of top-tier specialists perhaps explains the tendency for good teams to nevertheless lose a lot.
Post a Comment