The Angels and Pythag
by vivaelpujols on Aug 21, 2009 6:11 AM EDT
in Stat-Colored Glasses
56 comments
If you'll head over to Halo's Heaven and search for "Pythag", you'll be greeted with much disdain for the word. The most recent example of that is a FanPost which laments the fact that, once again, the Angels are being called lucky this year.
The author of the FanPost is right; a lot of people consider the Angels to be getting lucky. According to Justin's most recent Power Rankings, the Angels have been playing like a .529 W% team within league, compared to an actual W% of .609. So I wanted to take a look at whether this was a skill, or if the Angels are just getting lucky.
First, how rare is the Angels current feat? To answer I went into Baseball Databank and figured out the disparity between PythagenPat W% and actual W% for each team since 1960 (/random arbitrary date). That's returned a total of 1236 separate teams, which seems like a pretty good sample.
The team that unperformed the most was the 1962 New York Mets, when they won a whopping 40 games and had a .248 W%. PythagenPat thought that they should have had a W% of about .390, which would result in about 62 wins. Conversely, the team that overperformed the most was the 2001 Mariners, winning about 20 games more than their Pythag suggested.
The standard deviation was .039 points of winning percentage, which is about 6.3 games over a full season of play. Than means that 68% of teams with have an actual W% within .039 points of their Pythag, and 95% of teams will have be within .079 points.
UPDATE: Due to my SQL suckage, I screwed the pooch on this one. The actual Stdev is about 3.9 wins.
The Angels spread this year is .08, which is over 2 standard deviations from the mean, and it means that their is only a 1/20 chance of this happening in a given year.
Based on that prior, we would naturally be inclined to dismiss it as simply luck, as the odds of a true skill are almost nil; however, this isn't the first time the Angels have overperformed. From Sky on the Halos Heaven FanPost:
1, 2, 5, 4, 12, 7
Those are the number of games the Angels’ Win total has beaten their Pythag by over the last six years. ’04 and ’05 are nothing. ’06 and ’07 are solid, but nothing crazy. ’08 was crazy. ’09 is on pace to be crazy.
Baring that information, I have two questions for you guys:
- What are the mathematical odds of the Angels having an innate skill to beat their Pythag?
- What could be a possible explanation for the Angels beating their Pythag so much?
The first question probably entails some form of Bayesian math. If we know the prior, which I believe would be the odds that a random team does what the Angels have done, then we just have to incorporate the information that we have about the Angels. With me not being a statistician in any sense of the word, other people would be much better qualified to answer that question.
The second question is obviously open to a large range of possibilities. Possible reasons I have heard include bullpen leveraging, "Mike Scosia is a genius", clutch hitting, aggressive base running, etc.; however, as far as I know, nobody has made a convincing case to support any of those notions.
So I'll ask your guys' help. Are the Angels lucky or good? I've already outlined two possible ways to look at it, and I'm sure there are others as well.
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Very interesting questions
I have wonder quite a bit about what type of team over/under preforms there pythag record. I have a wild hunch that overpreforming teams are ones that succeed in close games. Such a team can pull off two 2-1 victories than drop a game 8-2. While this obviously balances out over 162 games, if a team possessed certain qualities that made it good (or conversely, bad) in those types of games it would be key to out playing their expected record. I don’t know what their record is in games decided by 2 runs or less, but they always have the repuation for winning in those games. Is there something in the Angels model that has a high correlation between success in close games?
by Slugger O'Toole on Aug 21, 2009 9:21 AM EDT reply actions 0 recs
Not close games
They’re 27-24 in games decided by two runs or less (source: THT team page). Mathematically speaking, the main driver is that they haven’t won many blowouts but lost a couple (both in May), 17-3 and 13-1.
FYI, they are 23-9 in games decided by 3/4 runs and 13-2 in games decided by 5/6 runs.
BTW, if they keep it up, the Angels will have the best five-year Pythagorean run in baseball history.
by studes on Aug 21, 2009 10:08 AM EDT reply actions 0 recs
Good stuff studes, beat me to it.
Here is a link to the article I wrote on it: Link
Jeff Zimmerman - Protecting the world from RBI's and Wins from my mom's guest house.
by Jeff Zimmerman (TucsonRoyal) on Aug 21, 2009 10:36 AM EDT up reply actions 0 recs
Link to site?
At Baseball-Reference The detailed standings show them with a W-L in 1-run games at 22-10. which conversely would put there 2-run game W-L at 3-14.
This team is our extended family, That's why we love them no matter what the record, no matter what the score.
by halofan4life on Aug 21, 2009 11:49 AM EDT up reply actions 0 recs
Here:
http://www.hardballtimes.com/main/teams/
—— | Close
LAA | 27 – 25
@bs_uf15bosox9be The Original Gameday; Learn to use SB Nation
by bs.uf15bosox9bears23 on Aug 24, 2009 2:06 PM EDT up reply actions 0 recs
My guess is baserunning, stolen bases and defense
I would think this at least partly shows up in pythag, though. Check out the situational hitting numbers though, they’re pretty crazy. In every combination of men on base the team OPS is at least .800, except for man on second which is .694, which tells me they expend a lot of outs moving the man to third with no outs, which is at least understandable considering the team OPS is over 1.000 with man on third, less than two outs. They also have a higher GB% than teams with similarly productive offense. They blow away all other teams in BABIP with a pretty staggering .327, I’m guessing there has to be a speed/hustle combo factor in there.
by Daniel Berlyn on Aug 21, 2009 10:23 AM EDT reply actions 0 recs
That makes sense
The question now, is whether or not those things are skills?
Thanks
by vivaelpujols on Aug 21, 2009 10:55 AM EDT up reply actions 0 recs
Sciosca wills it
The Rockies need some oldschool purple/white striped high socks. The team’s problem is it’s lack of swagger. I feel strongly that these socks will provide the swagger necessary to tap the potential that are the Rockies.
by Resolution on Aug 21, 2009 11:09 AM EDT up reply actions 2 recs
I'm going to have to say that yes, they have an advantage in pressure situations for one reason or another
It’s well known that they emphasize looking for your pitch, contact, and efficient baserunning, I can imagine those things become even more useful with men on. I don’t know if that makes a whole lot of sense but I’m sayin’ it anyway.
by Daniel Berlyn on Aug 21, 2009 11:29 AM EDT up reply actions 0 recs
clutch hitting
Clutch hitting. They are batting .333 in high leverage situations, .299 in medium leverage situations and .267 in low leverage situations. That is a remarkable split for a team.
http://www.baseball-reference.com/teams/split.cgi?t=b&team=LAA&year=2009#lever
by studes on Aug 21, 2009 11:15 AM EDT reply actions 0 recs
They had a similar split last year
Thanks
by vivaelpujols on Aug 21, 2009 11:22 AM EDT up reply actions 0 recs
that's cool
Last year’s split trended the same way, but this year’s is much more severe. The difference in BA between low and high was 42 points last year — this year it’s 66.
Still, I wonder how often a team has managed such strong splits two years in a row? Is this a historic event?
by studes on Aug 21, 2009 11:30 AM EDT up reply actions 0 recs
Standard Deviation
I really think we need to know the mathematical chances of any team exceeding run differential significantly in two straight seasons. As you point out above, there is a 1/20 chance of a team doing what the Angels are doing, which means we should see about 3 teams over 2 seasons. I’m not willing to chalk it up to anything other than random fluctuation… yet.
by baserip4 on Aug 21, 2009 1:36 PM EDT reply actions 0 recs
true, but...
If they maintain their seven-game edge this year, they will have posted the best five-year pythagorean record in baseball history.
by studes on Aug 21, 2009 1:53 PM EDT up reply actions 0 recs
standard deviation
I looked at all teams with 160 or more games played in baseball history. The standard deviation for the pythagorean variance was four.
by studes on Aug 21, 2009 1:56 PM EDT up reply actions 0 recs
I do the same thing and come up with 3.92. Restrict it to only teams 1993+ and I get 3.97. (I’d post the SQL I used, but the comments here strip out too many characters.
by cwyers on Aug 21, 2009 10:04 PM EDT up reply actions 0 recs
Looking at 1993+ with 160+ games, the StDev of Win% with PythWin% is 0.024, or 3.88 games after 162 games.
by cwyers on Aug 21, 2009 10:25 PM EDT up reply actions 0 recs
How about if you use the tag?
Beyond the Boxscore Not a member? Sign up.
by Sky Kalkman on Aug 23, 2009 7:09 AM EDT up reply actions 0 recs
Why has Atlanta so underperformed?
Over the last 4 years, Atlanta has rountinely underperformed their Pythag by 2-7 games. What are the odds of that? Why does no one discuss this?
Or is it, given 30 teams and 100+ years of seasons, this is just predictibly random over and underperforming of one team we are in the middle of? Given your stats above, we can discount 04 and 05 and 1 or 2 games are inconsequential when trying to evaluate whether a team has a skill at outperforming their Pythag. So looking at 06 and on, you can expect any given year a team will have a 32% chance of outperforming their Pythag by 6 games, and a 5 % chance at outperforming by 12 or 13 games.
Over the last 4 years:
06 – 5 about 32% (less, but I’m shortcutting this)
07 – 4 about 32%
08 – 12 about 5%
09 – 7 about 32%
The odds that one team will do that over any 4 consecutive years is calculated at .32*.32*.05*.32 = .001638, which is 1.6 times in 1,000 seasons of playing.
30 teams play 1,000 seasons in about 33 years total. We would expect one team to outperform their Pythag thusly once every 2 decades or so, without anything unusual at all. Why wouldn’t it be the Angels right now?
"It's not the size of the dog in the fight, it's the size of the fight in the dog." - Bear Bryant
by NJBammer on Aug 21, 2009 2:35 PM EDT reply actions 0 recs
Correction:
I meant the odds are more than 32%, not less. My 1 in 20 years back of the envelope math is therefore overestimating how unlikely this is. Sorry for the mis-labeling.
"It's not the size of the dog in the fight, it's the size of the fight in the dog." - Bear Bryant
by NJBammer on Aug 21, 2009 2:37 PM EDT up reply actions 0 recs
source?
Not sure where you’re getting your stats from, but twelve has been reached only four times in 1,115 team seasons of 160 and more games. That’s less than one percent.
I believe there has been a trend toward more teams outperforming their Pythagorean projection in the last couple of decades, particularly the last one, and I think the cause is greater use of the bullpen. It’s hard to quantify this, however, because the nature of the math is that total wins always equal total losses, and total runs scored always equal total runs allowed.
But five of the top six seasons (of 160 games or more) in positive Pythagorean variance occurred in the 2000’s. The bottom of the list is more random.
by studes on Aug 21, 2009 3:00 PM EDT up reply actions 0 recs
I was relying..
on the post above, which stated that one std dev was 6.3 wins.
The standard deviation was .039 points of winning percentage, which is about 6.3 games over a full season of play.
If that was wrong, sorry I was just relying on that. The rest was just math.
"It's not the size of the dog in the fight, it's the size of the fight in the dog." - Bear Bryant
by NJBammer on Aug 21, 2009 3:03 PM EDT up reply actions 0 recs
Trend...
If there is a trend of more teams outperforming, there would theoretically be more teams underperforming as well (runs scored = runs allowed for the league as a whole). So what you’re saying is that the SD would be increasing (I don’t know if there is any evidence for this or not), which would make what the Angels are doing more likely, thus increasing the chance it is just randomness.
by baserip4 on Aug 21, 2009 3:08 PM EDT up reply actions 0 recs
If the SD is increasing
Doesn’t that suggest that teams are doing something differently, and whatever they are doing has an effect on how they do against pythag? That doesn’t sound random at all.
The HK-47 hitting droid is the finest line drive machine ever built
by RallyMonkey5 on Aug 21, 2009 3:55 PM EDT up reply actions 0 recs
Without looking at the numbers or the real situation
Having a very bad 5th starter and long man could seriously mess up a Pythagorean. If you get occasionally just blown out the water with huge loses. Like 10 to 1 losses. On the other end having a true shut down closer seems like a good way to have more wins than your Pythag would say. I would be curious to see how a team like the Twins do in regards to their Pythag wins.
by FlimtotheFlam on Aug 21, 2009 2:50 PM EDT reply actions 0 recs
math?
Viva, how did you get your math? I get a different result for the 1962 Mets than you do (I have them nine games under), and 6.3 games sounds like a very high standard deviation.
The exponent I get for the 1962 Mets is 1.92. They scored 617 runs and allowed 948. That results in a .304 pythagorean winning percentage and 49 wins (instead of their actual of 40).
by studes on Aug 21, 2009 4:42 PM EDT reply actions 0 recs
B-Ref
Has those Mets at 50-110 pythag. And the 2001 Mariners 7 over, with 109 wins.
The HK-47 hitting droid is the finest line drive machine ever built
by RallyMonkey5 on Aug 21, 2009 11:17 PM EDT up reply actions 0 recs
My database check
Has the 1993 Mets the worst, -14 games. The top 3 are the 2005 Diamondbacks, 2004 Yankees, and 1984 Mets, +12 each.
The HK-47 hitting droid is the finest line drive machine ever built
by RallyMonkey5 on Aug 21, 2009 11:29 PM EDT up reply actions 0 recs
Hmmm...
Here is my query:
SELECT (R^(((R+RA)/G)^.287)/(R^(((R+RA)/G)^.287) + RA^(((R+RA)/G)^.287))) – (W/G) as Dif, teamid, yearid
FROM teams
WHERE yearID > ‘1960’
ORDER by Dif desc;
The first result was the 1962 Mets, who had a “Dif” of .141. Multiply that by 162 and you get about 23 games. Then I just pasted the entire table into excel, and did “STDEV”. The result was .0394.
I see that Colin also got a different answer. I trust that he is much better at this stuff than I am. What did I do wrong?
At any rate, if you guys are correct, the Angels feat is even more impressive.
Thanks
by vivaelpujols on Aug 22, 2009 12:46 AM EDT up reply actions 0 recs
You'll note that a lot of the query got junked by SBN's comment filtering.
Anyway, the problem is that ^ in SQL does not signify an exponent; it signifies something called a “bitwise XOR” (I could try to explain what it means but I really don’t know and you really don’t care, so we’ll skip it).
In order to do an exponent, you have to do:
POWER[value,exponent]
Where the brackets are standing in for parenthesis (Sky, someone, can you beg the guys at SBN for a code tag that lets us actually post SQL in comments?).
Now what you’re doing COULD be considered a standard deviation, but since you’re comparing an estimator to true it’s also a root mean square error. You can do this without bothering with Excel, and it’s pretty simple (so much simpler than trying to mess with correlation in SQL, at least for me but I do things the roundabout way). Anyway.
Here’s the code I used, set up for your criteria.
by cwyers on Aug 22, 2009 1:07 AM EDT up reply actions 0 recs
Aah, thanks Colin
I should really get more acquainted with SQL before I try to do stuff.
The wierd thing is that my “SD” of .039 matched up perfectly with the SE you would find if you used a Binomial distribution on a major league team. Is that just random, or is it something in the ^ sign that I used.
At any rate, this only makes the Angels feat more impressive. For that last 2 years, they have been around 3 SD’s above the mean, which I got to think tilts it towards being a skill.
Thanks
by vivaelpujols on Aug 22, 2009 1:21 AM EDT up reply actions 0 recs
Not necessarily.
We have four years where we’re within our 95% confidence range that are really messing with folks here. Yes, they all trend in the same direction, but I’d be willing to bet that if you took ONLY teams that were above .500 you’d see a similiar bias in the DIRECTION in which Pythag is in error. (Remember, the spread of Pythag Win% is smaller than the spread of observed Win%.)
So we really only have two years where the Pythag is appreciably in error, and to be quite frank we’re not certain about the extent to which ’09 is an outlier yet (the Angels still have roughly 40 games in which to regress a bit to the mean – this year is already below 2 SDs by my reckoning, and will probably creep in a little closer still.)
But even if we have two back to back years of +2 SD performance, we have to realize that there are a lot of major league teams that play in back to back year, and we have to look at the odds of ALL teams with a +2 SD team putting up a +2 SD performance in the following year, and see how many actually have. It may simply be a fluke (I know people don’t like hearing that but quite frankly I’m not too worried about that).
by cwyers on Aug 22, 2009 1:32 AM EDT up reply actions 0 recs
Okay, let me clarify a point there.
The SD among teams for Pythag% is .067, while the SD among teams for Win% is .071.
In other words, for teams farther away from .500, their Pythag is ALWAYS more likely to be closer to the mean (it – yes! – regresses that direction) than it is to be farther away. So we should expect to see teams with high Win% (like the Angels) outperform their Pythag more often than they underperform it.
by cwyers on Aug 22, 2009 1:37 AM EDT up reply actions 0 recs
So this is like the same thing with FIP and ERA right?
Pythag is more linear than actualy performance, thus it isn’t a great model for teams who are towards the extremes?
Thanks
by vivaelpujols on Aug 22, 2009 1:50 AM EDT up reply actions 0 recs
I'd say it differently
No, it’s different. It’s regression to the mean, not a difference in the “model.” The best and the worst teams become the best and worst thanks to a little extra push from Pythagoras.
Actually, most of the difference between FIP and ERA is regression to the mean, too. Colin’s post at THT significantly overstated the impact of the difference in the two models.
by studes on Aug 22, 2009 9:19 AM EDT up reply actions 0 recs
I'm working on a follow-up to that.
One of my computers’ hard drives went down recently, which is slowing down some of those projects. Short version – studes is right, it is because of regression to the mean. (Which, still, means that subtracting FIP from ERA doesn’t equal the effect of defense.)
And Pythag is definately non-linear.
The smaller spread isn’t a bug but a feature when you want to predict teams. (Of course, the same is true of FIP.) And I’m not saying that Pythag is less ACCURATE for those teams – observed RMSE should be about the same.
I’m just staring at those years where the observed error was 4 and 5 and I can’t say for sure that those aren’t really within 1 SD – if RMSE stays the same, you end up with an off-centered distribution, and this is where my math chops fall off a bit. Lemme see if I can whip something up here.
by cwyers on Aug 22, 2009 10:54 AM EDT up reply actions 0 recs
Did a quick look -
Of the 301 teams from 1960 on with a .550 WinPct or higher, 88 of those had a Pythag higher than their observed WinPct, while 213 had a Pythag below observed WinPct.
There’s probably still some more stuff to be found digging, but it turns out the best way to beat Pythag for a number of years in a row is simply to have a WinPct .500 or greater.
by cwyers on Aug 22, 2009 11:25 AM EDT up reply actions 0 recs
For teams with a .550 WinPct...
…RMSE jumps from .024 to .026, or a diffference of about a third of a win per season. That’s not meaningful, I would say.
But doing some really crude figuring I come up with an observed range of 1 SD = -0.0285 to 0.0204, or in 162 games from -4.6 to 3.3.
(That’s of WinPct-PythWinPct – so a typical team with a .550 or better WinPct would expect to have a Pythag within that range.)
So at that point our 5-win-differential season is still outside of 1 SD, but not by much. (This is real back of the envelope stuff, mind.)
That makes me very comfortable ignoring ‘04-’07 when it comes to asking if the Angels have a significant talent for beating Pythag. And we don’t have the final data for ‘09 yet (remember, you can’t figure SDs based on a 162-game season and then apply those to partial seasons – okay, you can, but I don’t think it’s correct.)
by cwyers on Aug 22, 2009 11:45 AM EDT up reply actions 0 recs
BTW, that's a beatiful looking query
Thanks
by vivaelpujols on Aug 22, 2009 1:26 AM EDT up reply actions 0 recs
Hey Colin
Do you have the answer to the first question? That’s the one I was most interested in, and I’d like to see what you think.
Thanks
by vivaelpujols on Aug 22, 2009 12:48 AM EDT up reply actions 0 recs
doesn't make a difference
The standard deviation is virtually the same between the two methods. I used population because I had included all games since 1900 in my analysis.
by studes on Aug 22, 2009 9:20 AM EDT up reply actions 0 recs
They have perfected the art of the bloop single.
You got slurved!
I for one welcome our sexy* moderating overlords.
by Slurvey on Aug 22, 2009 1:10 AM EDT reply actions 0 recs
So true.
The 2009 Texas Rangers offense: sigh...
by Kinslerhomer on Aug 22, 2009 2:45 PM EDT up reply actions 0 recs
The Angels are 19th in the Majors in LD%. That’s a better mark than the Cardinals.
I would have believed you more if you said the Angels have perfected the art of the bunt single and infield hit. Not the bloop single, though.
Hard to believe all those bloop singles gave the Angels the second best OPS in the American League, as well.
http://twitter.com/FlyByKnite
by FlyByKnight on Aug 23, 2009 3:54 PM EDT up reply actions 0 recs
Ever watch an Angels game?
The 2009 Texas Rangers offense: sigh...
by Kinslerhomer on Aug 23, 2009 5:02 PM EDT up reply actions 0 recs
Is that a joke? I’m an Angels fan living in Southern California.
http://twitter.com/FlyByKnite
by FlyByKnight on Aug 23, 2009 5:30 PM EDT up reply actions 0 recs
He was being completely serious
Thanks
by vivaelpujols on Aug 24, 2009 3:25 AM EDT up reply actions 0 recs
Line drives
If the Angels are 19th in line drive%, I question the consistency of the data. They seem to have had a ton of games with line drive after line drive. Could be some of these are coded as flies instead. I think I saw something about fewer line drives being coded in Anaheim than most other places, though I think Minnesota was even more extreme.
I look forward to hit f/x implementation, so we can systematically code these instead of relying on coders thousands of miles apart, who may have different thresholds for what counts as a line or fly.
The HK-47 hitting droid is the finest line drive machine ever built
by RallyMonkey5 on Aug 24, 2009 12:12 PM EDT up reply actions 0 recs
Agreed. Like you, I do remember games where they were just taxing the ball on a rope. And it wasn’t just one guy, it was all of them. The one reason I know that LD% cannot be truly accurate is because Erick Aybar is at 19.9% this season. Anyone who has watched him this season knows damn well that he’s hit more line drives than anyone else on the Angels this season. It seems like every time he’s up, he either smashes a line drive or hits a sharp grounder.
http://twitter.com/FlyByKnite
by FlyByKnight on Aug 24, 2009 5:07 PM EDT up reply actions 0 recs
I think Angels stadium has one of the lowest LD Park Factor
Brian Cartwirght took a look at it a while ago on FanGraphs, and found that Angel’s stadium has like a .85 LD park factor.
Thanks
by vivaelpujols on Aug 24, 2009 7:01 PM EDT up reply actions 0 recs
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