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Talent_Distribution
Thursday, January 26, 2012
By , 04:36 AM
It is generally accepted in the sabermetric community that the AL is a better league than the NL, at least for the last several years. This is evidenced by the fact that the AL has a large advantage in IL games, although at least some of that edge could be something other than overall “talent”, although this is not likely and several people, including myself, have found little or no inherent advantage to the AL in IL games (e.g., the NL teams do not have any DH’s, so they have to juggle their lineup in AL parks, on the other hand, in NL parks, AL teams have to sit their DH’s or juggle their lineup, perhaps putting a bad defender - their DH - in the field, the AL pitchers typically are poorer hitters than the NL pitchers, etc.).
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Monday, November 21, 2011
Clay notes:
In seven of the 24 leagues between 2000-2011, the second wild card actually had the fourth-best record in the league, beating out at least one of the division winners. In two more seasons the WC2 was tied with one of the division winners – so that quite often the “fifth” team has as good a claim to the playoffs as one of the division winners.
So, 9 times out of 24, the play-in team was as good or better than one of the division winners. Remember, a division is simply some artificial construct.
He notes however:
In eight of the last 12 years [in the AL], the new card winner (assuming things played out as before) would have trailed the real winner by 5 or more games, with the 2001 Twins finishing a whopping 17 games behind the “102 win but still just a wild card” A’s.
In order to give that statement some value, I’d like to know what the corresponding number is between the best and worst division winners in each year. Presumably, we’ve had plenty of 99-win teams and 87-win teams being the division winners. Somebody want to do that work?
Friday, November 18, 2011
Nolasco is one of the handful of pitchers that requires sabermetric study (Matt Cain, and a few others as well). As Derek points out, Nolasco’s K rate drops substantially (from 23% to 18%), his BB rate jumps substantially (4% to 6%), and his BABIP jumps a bit (.304 to .315). All of that conspires to make the number of runs allowed by Nolasco to diverge significantly from his peripherals (peripherals that we presume are not disproportionately influenced by the base/out state, any more than the average pitcher).
Andy in The Book noted that there is definitely a skill with men on base (and it could simply be for the reason of going from the full windup to not). Regardless. It’s a real skill that could impact by about 5 wOBA points. Not a whole lot of course. But given that a pitcher sees men on base 45% of the time, it’ll come into play often enough.
And of course, if we know more about the pitcher’s change in mechanics, then we’d be able to come up with a much better estimate. Unlike the clutch skill, this is more like a handedness skill: a real physical change in the environment that the player participates in.
Tuesday, November 15, 2011
Evidence.
The point of a uber-stat is to make sure it’s not biased, as well as being reasonable. Any teenager out there (me included at the time) has attempted to combine various outcome numbers to create a superstat. It’s literally impossible to create a stat where Pujols is not near the top, as long as you are being anything close to reasonable. But, it’s extreme cases, guys who walk a ton, or steal a ton, or are fantastic fielders, or hit a ton of HR, disproportionate from the rest of their outcome lines, that are the issue. Since we don’t get that many kind of extreme players, we end up with significant overlap between Elias rankings and WAR-based rankings.
It’s clear that one source of bias is relief pitchers.
Another way to verify the rankings (after all, why is WAR necessarily better than Elias?), is to create the A and B types based on how much they signed. (Of course, the compensation aspect affects the signing, and that can be adjusted based on Victor’s numbers.)
By the way, I think Elias is just the trustee, and not the creator. So, scorn should be reserved, if deserved, to the creators of the system, and not the messenger.
Monday, November 14, 2011
A reader asked about using plate appearances (PA) instead of innings played (IP) as the playing time component in replacement level.
Notably, leadoff hitters earn more value than a 9th place hitter, even if both are equal as hitters. Since replacement level is roughly .003 wins per plate appearance, and the gap between the number of PA for a 1st and 9th place hitter is 8/9 x 162 = 144 PA, that’s roughly 0.45 wins extra the leadoff hitter gets.
I agree, and PA is being used only because of lack of IP data being available. And general laziness. I think Rally accounts for this rWAR.(*)
(*) By the way, who started calling it bWAR? It’s rWAR.
The only issue is what to do with PH and DH. What you can do for them (and for all of them) is to look at fractions of PA for the lineup slot they are in. So, if they have 4 PA for the day, and their lineup slot came to the plate 5 times, then you give them 80% of a game.
Of course, we should do the same for innings played, so if they played 8 innings out of 9, that’s 89% of a game.
Generally speaking, a non-pitcher’s value is generally about 62.5% offense and 37.5% fielding. So in the above case, I’d credit the player with 83% of a game.
So, if you care about every 0.1 or 0.2 wins to give out, use this method instead.
Thursday, November 03, 2011
A few years ago, I asked what is the breakeven point if you don’t consider two 3-WAR players to be equal to one 6-WAR player.
Rally responded with:
From that formula, a 5.3 WAR player is equal to:
2 3.0 players
3 2.25 players
4 1.9 players
5 1.7 players
Which, I think, is a reasonable viewpoint among those people who give value to scarcity. I responded as follows:
Good stuff Rally, just the basis for discussion I was looking for.
Ok, if for trade purposes:
5.3 = 3.0 + 3.0
Then what would be the equivalent here:
x + 0.7 = 3.0 + 3.0
And once you do that, then answer these as well:
y + 1.7 = 3.0 + 3.0
z + 2.7 = 3.0 + 3.0
Give me your answers for x, y, z.
This trade proposal from Dave had spurred some interest in the comments and elsewhere.
***
Now, I do NOT want to talk about Dave’s plan specifically, not the least of which is because it involves the Mariners. But, we can talk about something along those lines. Let’s consider a 1-1 trade proposal (so we don’t waste time talking about the value of roster spots). And we’ll talk about Joey Votto, one of the best players in baseball, and Matt Moore, perhaps the best pitching prospect in baseball.
Here are my questions: you have Joey Votto for two years, and you are going to get two compensation picks in the draft once you let him go. What you are willing to pay for two years of Votto and access to those two picks? 70MM$? Give me a range too. Imagine that in the second half of 2011, he tanked, or that in the second half of 2011, he Bondsed-out. Now what are you willing to pay for him? 40MM$ to 80MM$? Something like that?
Now, what of Matt Moore? Highly rated entering 2011, Minor League Pitcher of the Year for 2011, tantalizing end-of-season start to his career (including playoffs). You get him for six years (and let’s say you get one comp pick for him). What are you willing to pay for him? If the stars align, maybe you give him what Sabathia and Lee and Jered Weaver get, so 130MM$. Of course, there’s always a certain level of uncertainty with guys with limited to no experience, not to mention he’s a pitcher. What’s the downside for him? 30MM$? So, maybe you’d realistically pay 70MM$ for him?
Let’s say this is where we are at: you are willing to pay Joey Votto 40MM$ - 80MM$ (average of 70MM$), and you are willing to pay Matt Moore 30MM$ - 130MM$ (average of 70MM$).
Now, let’s say that Joey Votto WANTS 26.5MM$ for those two years, and Matt Moore WANTS 26.5MM for those six years. Take as an assumption of fact everything I have said above.
Which of the two do you sign for 26.5MM$? Votto for 2 years, or Matt Moore for 6 years?
Monday, October 31, 2011
Dave Cameron, using Fangraphs’ latest feature, gives us his list.
Wednesday, September 14, 2011
Rob Neyer points out that you don’t even have to worry about wins and losses when it comes to divisional standings: just look at runs scored and allowed differential over the entire season. Because you get the exact same order for 28 of the teams (within the division anyway), with one little swap for the other 2 teams. Indeed, even for the Wild Card, you get a very strong ordinal ranking match. In the AL, you swap two teams (Cleveland and some other team). In the NL, it’s not so clean, notably because of the Padres (only -29 runs, yet 2nd to last in the league).
I’m sure you can look at other leagues, and get the same result. This is the big thing that is sold to the public: look at each game as if you are starting from scratch. The reality is that you don’t even have to start the game from scratch, because just keeping a running total of runs scored and allowed will give you the same answer.
The same applies for tennis, I am sure (and NHL, NBA, NFL, etc, though NFL has the advantage of having only 16 games). Basically, sell the public that there’s a winner or loser every game, when in reality, what we have are running totals of runs, points, or goals for the entire season.
Tuesday, September 13, 2011
By , 03:22 AM
I know there has been similar research published on the web, but I am too lazy to look it up right now. I took the 1998-2010 draft list from BA and looked at how the various pitchers did in the major leagues, breaking the rounds down into various buckets. It was a quick study and I just matched names from the draft lists with my major league databases. I probably missed 3-5% of the players because the names, especially first names, did not match up exactly.
First I looked at the rookie years for all pitchers in each draft round 1-3+, for a total of 4 buckets. Each round included the supplemental rounds, so, the first round actually has 60 picks in most years. The rest of the rounds pretty much have 30 picks each. Perhaps I should consider the first 30 picks of the 1st round as the 1st round and then the next 30 picks in the 1st round supplement as the 2nd round, etc.
Does anyone know if there is anything special about the supplemental round after the first 30 picks or is it just the next 30 best players and then the second round is 61-90 best players?
For each pitcher, I looked at whether their primary role in their rookie major league season was as a starter (S), a reliever (R), or mixed (N).
The currency I used was my normalized, component ERA (nERC), which is an “ERA” based on a pitcher’s raw stats (s, d, t, hr, nibb, hp, outs, and wp) adjusted for park, opponent, and defense, and normalized to his own league, where the average pitcher in each league, weighted by TBF, is 4.00. I weighted the aggregate nERC in each bucket by each pitcher’s IP. If I used the simple average of all the pitchers (weighting each pitcher exactly the same regardless of how many IP they threw), the numbers would be much higher, as the pitchers who had the worst true talent generally had the fewest IP.
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Friday, September 09, 2011
The primary reason something stabilizes is based on the spread of true rate of whatever entities are involved.
As an example, hitter K/PA stabilizes very fast because there is a wide range in talent in terms of striking out.
The reason you find the wide range in talent is if a player is selected based on that component.
For a nonpitcher, having a high or low K/PA is not that important, because there’s tons other things a nonpitcher brings to the table to counteract the negative effects of a high K/PA. So, by not selecting specifically on that, we see a wide range in talent.
For a pitcher, having a high or low K/PA is important, because there’s comparatively little else he can do. And that’s because most pitcher’s have a small spread in talent on balls in play: they’ve been selected to make sure that the 75% of the time that they pitch to contact, that they don’t get blown away. So, they’ve already been selected based on BABIP, so they don’t necessarily selected based on K/PA.
This is why GB rates for pitchers stabilize very fast: pitchers are not selected based on being GB or FB pitchers.
(Of course, there are other things that you aren’t selected for, that doesn’t stabilize: that’s because it has very little value.)
Goalies in hockey are very tight in their save percentages because that’s the ONLY thing they can do. So, you have no choice but to see a tight range (on a per shot basis). However, since they face some 1500 shots per season, what is hidden on a rate basis is more visible on a volume basis.
***
Inspired by this article.
Monday, August 29, 2011
Of all the sports that could start its own league, it’s basketball.
Hockey would have a bit of a tough time, for one big reason: The Stanley Cup. The Cup is actually not owned by the NHL, seeing that it predates the NHL itself. Instead, it has trustees appointed. There was some “transfer” or “delegation” that occurred that makes the NHL defacto “owner”, but until a court actually rules on that, the ownership thing is in limbo. Nonetheless, players play for the Stanley Cup, and anything else will be considered second fiddle.
Setting that aside, then hockey and baseball would face similar challenges: venues and tradition. The NHL did face competition from WHA in the 1970s, and the WHA was able to compete for talent based on salary, and they did attract star player, notably the older Bobby Hull and Gordie Howe (but still very talented). And the NHL has a draft age of 20 (!), so they also attracted “underaged” players like Wayne Gretzky (well, there was no one like him, but they got him and all the underaged players).
And NFL has done a great job of making football about the “team” and not about players. It doesn’t take much for a Packers fan to turn its back on Brett Favre. What counts is the uniform, just like college football.
But basketball? You don’t have 20 or 25 or 45 man rosters. You’ve got 12 guys. And, the superstar has a far larger impact in basketball than the other sports. So, you can easily create a 12-team league made up of superstars. You don’t have the same sense of history and tradition that you do with NHL and MLB. You don’t have the same live-and-die attitude as you do with football.
And forcing players to get less than they think they deserve is just what led to the NHL/WHA competition for talent. There’s a certain level below which players will revolt.
***
Related article: Forbes.
Lacob reportedly paid $ 450 million for the Warriors. That franchise price only makes sense if LeBron James, Dwight Howard, Kobe Bryant, etc… come play his Warriors. If these players are all in a new league, Lacob will stand to lose much of his investment in the Warriors. And the same story will be repeated for the other 29 owners. Faced with potential loss of the one thing fans are willing to pay to see (i.e. elite basketball talent), one suspects the stand the owners are currently taking will crumble.
And when that happens… well, I still think the players and cities should form their own league. Either way, though, fans will once again get to see basketball played at the highest level in the world.
Thursday, August 25, 2011
Ozzie Guillen believes it’s Peter Bourjos. Others might think it’s Brett Gardner. The first white guy to break 10 seconds is Marian Woronin of Poland in 1984. The two other white guys to break 10 seconds are Patrick Johnson (Australia) in 2003 and Christophe Lemaitre of France last year and this year. Koji Ito of Japan hit 10 seconds on the dot (though, the dot would be 2 or 3 decimal places).
The only good thing about pointing out that Bourjos is fast and white is that it shines a light on the accomplishments of others, and on the statistical oddity of it all. If that’s what it’s limited to, then I don’t have a problem with Ozzie’s declaration.
There was a time as recently as the 1980s where white boxers would be labelled “The Great White Hope”, which, today, seems outrageously racist and ridiculous to say, but back then, not many batted an eye.
Tuesday, August 23, 2011
My article at Fangraphs. This is good for those who want to see replacement level discussed in a somewhat different manner.
Thursday, August 18, 2011
In response to a query:
Whether it’s FIP or ERA or any rate stat, the way to “scale” them the same when you have differing opportunities (IP or plate appearances, etc) is the same:
value = (metric minus baseline) x opportunity
In your case, with FIP (or ERA), we’d like to establish the baseline as something like 1 or 1.25 runs above the league average. So, if the league average is an ERA of 4.00, then our baseline is 5.00 or 5.25. In other words, we create the baseline as the “minimum acceptable level” of performance. Think of a bullpen guy getting a spot start, or a last minute AAA callup, etc.
For opportunity, you use IP, but let’s use IP/9 so that it’s in the form of “games”. This is especially useful since FIP and ERA are also in the form of games (runs per 9 IP).
So, as an example, let’s say you have one guy with a FIP of 3.50 and 180 innings, and you have someone else with a FIP of 2.50 and only 108 innings. What are their values?
We’ll presume a baseline of 5.00.
value = (5.00 - 3.50) x 180/9 = 30
It may not be readily obvious, but the unit here is runs, so we have a pitcher who provided 30 runs of value above the minimum acceptable level (what we normally call the replacement level, or readily available talent level).
For the other guy:
value = (5.00 - 2.50) x 108/9 = 30
As you can see, these two pitchers are equivalent.
Such is life when dealing with uncertainty levels. When we say Jeff Francoeur is a replacement-level player, we don’t know for certain that he is. It’s just our estimate that he is. According to fWAR, he was close to 0 wins from 2008-2010. According to rWAR, he was below 0 wins. In the three seasons from 2005-2007, fWAR had him at 8 wins and rWAR at 6 wins.
When you make your estimate, you have to use all his data, not just his last three seasons. Of course, the further back in time you go, the less weight you give. Roughly speaking, the last three years should get double the weight to the three seasons preceding those. For most players, you can just look at the last three years, and get on with it, because you’ll get a similar answer. But with some guys, like Frenchy, who shows an 8 win gap between the current 3 years and preceding 3 years, you need to consider it.
So, entering 2011, rather than thinking he is a replacement-level player, you’d see he averaged around 0 wins in the last three seasons, and a bit over 3 wins per 162 games in the three seasons preceding those (using fWAR). Now, his average is a bit over 1 wins. Furthermore, seeing that he’s young, his true talent is on an upward slope. Finally, given that he was given so much playing time, regression toward the mean demands that he be compared to a more select group of players. All of a sudden, a guy who can be reasonably considered a replacement-level players under one perspective can then be considered at least a 1 win player, if not 1.5 wins, entering 2011.
Now, with Frenchy’s above average season this year, that (enhanced) estimate entering 2011 will be even higher entering 2012.
If we consider the entirety of his career, weighting each successive season at 25% higher than the preceding one, then Frenchy is at 5.3 WAR in 2236 weighted PA, or 1.66 WAR per 700 PA. We bump that up a bit because of regression toward the mean (10% toward 2.25 league average, or, if you want to be fair, something like 2.5 or 2.75 toward guys who play all the time like Frenchy). So, he gets an extra 0.1 WAR, to put him at 1.76 WAR. And then a bump of his past performance because of his age, which would be say another 0.1 WAR. We’ve got him now at 1.86 WAR. We give him 85% playing time, and now our new official estimate of Frenchy’s talent level entering 2012 is 1.6 wins. And for 2013, it’s going to be say 1.4 wins.
So, 2012-2013 is 3 wins of value, which at 4.5MM$ per win is 13.5MM$. And that’s what Frenchy’s next extension was signed at. Congratulations to Frenchy and the Royals for signing a fair deal.
Well, fair, as best as our uncertainty level allows us to say.
Tuesday, August 16, 2011
Or: how much is 26 games worth in wins?
If you follow wins above average, then 26 games is worth a bit less than 1 win.
If you follow wins above replacement, then 26 games is worth a bit more than 1 win.
(The gap between the above two is 0.36 wins.)
If you believe that missing a game means that you should get zero credit for your replacement player, then 26 games is worth 2 wins.
My guess is that most people don’t really believe the replacement-level model. I think most people think of it that if you don’t play, then it’s like you are leaving your team shorthanded. And I think that’s why the games played is going to be a huge penalty against Victorino.
To be more clear: the replacement-level model essentially means that you are being given credit for the performance of a replacement-level-kind of player.
Friday, August 12, 2011
These are all the pitchers born since 1952 (i.e., after Blyleven), with at least 60 starts, through age 27. They are ordered by ERA+ from worst to… uh, not-worst. The general rule is that if you’ve been given 60 starts, you are not going to get many more. The more non-worst you are, the more chances you are given. That’s why you see near the non-worst point, guys with over 100 starts. Kyle Davies stands out as someone who has been given an enormous number of starts at such a poor performance level. You’ll also note that a good portion of the players were given a fair number of games in the bullpen. Basically: it’s not working out here, let’s try you over there. Kyle Davies stands out as someone who was kept in the starting rotation. At some point, scouting has to give in to empirical data: as much as a scout may say that Kyle Davies is a decent pitcher, we have to accept that maybe he’s not that good.
Of course, right behind Davies is Mike Scott. You kids may not remember him, but he was one of the best pitchers of his era (at some point in his career).
Let’s look at the top 10 in this list, and see what they did in the 4 years after their age 27 season. How much hope can we possibly give the Kyle Davies of the world? (I had to exclude pitchers who are still to young, so I went down to the #15 on the list below to get my top 10.)
Here we go:
Van Poppel: 282 IP, 108 ERA+ (almost all in relief)
Bowen: out of MLB
Mike Scott: 796 IP, 106 ERA+ (almost all as starter), and then continued on for a few more excellent seasons)
Knapp: out of MLB
Snyder: out of MLB
Scudder: out of MLB
Walk: 530 IP, 115 ERA+ (half games as starter), and continued his career beyond
Rupe: 10 more innings then out of MLB
Wright: out of MLB
Codiroli (*): 122 IP, 75 ERA+
(*) I followed MLB intently when I was a kid, knowing every player on every team (easier done when you collect baseball cards, and are in fantasy leagues). I do not remember this guy at all.
So, that’s what you have here: 20% chance of good success, 10% chance of being useful as back of the bullpen guy, and 70% chance of being out of MLB.
Note: replacement level is ERA+ of 75-80 as a starter, and 95 as a reliever.
Glove-slap: Eric.
Source Baseball-Reference.com:
Tuesday, August 09, 2011
The Detroit Tigers are 61-53. The Tampa Rays are one game back, at 60-54.
When the NHL expanded from six to twelve teams, the NHL new that to give the expansion team a fighting chance, they’d have to put all six expansion teams in the same division. By letting the original six and expansion six have limited games against each other, it guaranteed that the expansion division would “look” competitive. But, in terms of head-to-head, the original six decimated the expansion six.
MLB, while nowhere near to this extent, has this kind of issue with the AL East. That is, since the Rays play against slightly tougher competition than the Tigers, it makes it harder for the Rays to pile up wins.
One way to show this is to look at “common opponents”, and in the same proportion. For example, since the Tigers never played the Reds, Marlins, Astros, Brewers, and Cardinals, we throw out all those 21 games from the Rays. So, gone are the Rays’ 12-9 record from those games. At the same time, the Tigers never played the DBacks, Rox, Dodgers, Mets, Pirates, and Giants. So, out goes their 7-11 record.
So, against common opponents, we are now at 54-42 for Tigers and 48-45 for Rays.
However, the Rays faced the Orioles 12 times, while the Tigers faced them only three times. So, what we do is pro-rate the record of the Rays against the Orioles down to 3 games. So, instead of being 6-6 against the Orioles, we make them 1.5-1.5. We repeat this with all the common opponents.
With 75 “matching” games (out of the 114 they played), the Tigers end up with 41 wins, and the Rays end up with 37 wins.
When I started this, I expected the Rays to be ahead of the Tigers, reasoning that the Rays had the tougher opponents. As it stands, they did have slightly tougher common opponents. But the two things that conspire against the Rays:
a. among the teams that only one of them played against, the Rays did much better, but all those games get thrown out
b. when the Tigers and Rays went head-to-head, the Tigers won all three games
Now, obviously, we don’t want or need to throw games out. We would simply do a strength of schedule adjustment with all the teams. Once you do that though, you are doing an indirect approach. You are comparing the Rays against NL Central with the other teams (not Tigers) also against the NL Central. And then you are comparing the Tigers against the NL West with the other teams (not Rays) also against the NL West. With those common baselines now in place (i.e., rest of league against NL West and NL Central), we presume that we can fairly compare the Rays and Tigers indirectly.
We could do that. But I’m not doing that here. In the process I’ve laid out here, we’re doing a direct comparison. And under the direct comparison, the Tigers are 4 games ahead of the Rays.
(Glove-slap to Max for inspiring this.)
Note: as an example of why it’s unfair to ignore the indirect methodology: the Rays could have been 21-0 against the NL and the Tigers could have been 0-18 against the NL, and under the direct methodology, all those games would get thrown out.
Wednesday, June 29, 2011
This gives you the number of pitchers and nonpitchers that were on each team for each year. I counted any nonpitcher who had as many plate appearances as there were team games (so, these days, that means at least 162 PA). For pitchers, I counted anyone with at least 0.23 innings per team game (so, these days, that means at least 37 innings).
We see that since the new run environment (1993-present), the % of roster spots allocated to pitchers is almost exactly 50%.
The jump started occurring in 1990, likely due to specialization of relievers. Prior to then, the number of relievers used topped off at 11.3 per team. From 1951-1984, the number of pitchers used hovered from 9.7 to 10.9 per team.
As for nonpitchers, it’s been holding quite steady since 1973 (DH?). Since then, we’ve had 12.5 nonpitchers per team. Prior to that, since 1922, it was 11.7 nonpitchers.
year Pitchers NonPitchers Players % Pitchers
1916 8.1 11.1 19.2 42%
1917 7.4 10.9 18.3 41%
1918 7.6 10.9 18.6 41%
1919 7.6 10.6 18.2 42%
1920 7.4 10.8 18.3 41%
1921 7.8 10.9 18.8 42%
1922 7.9 11.3 19.2 41%
1923 7.8 11.3 19.1 41%
1924 8.4 11.6 20.0 42%
1925 8.4 12.3 20.7 41%
1926 8.4 11.5 19.9 42%
1927 8.3 11.7 20.0 42%
1928 8.6 11.7 20.3 42%
1929 8.5 11.2 19.7 43%
1930 8.4 11.9 20.3 42%
1931 8.6 11.8 20.4 42%
1932 8.4 11.3 19.8 43%
1933 8.9 10.8 19.8 45%
1934 8.5 11.6 20.1 42%
1935 8.8 11.5 20.3 43%
1936 8.8 10.8 19.6 45%
1937 8.9 11.1 19.9 45%
1938 8.9 11.0 19.9 45%
1939 9.1 12.0 21.1 43%
1940 9.4 11.1 20.4 46%
1941 9.5 11.5 21.0 45%
1942 9.6 11.6 21.1 45%
1943 9.3 11.4 20.8 45%
1944 8.9 11.6 20.6 43%
1945 9.7 12.0 21.7 45%
1946 10.3 12.6 22.8 45%
1947 9.9 11.6 21.5 46%
1948 9.5 12.1 21.6 44%
1949 9.3 12.6 21.9 43%
1950 9.4 11.6 21.0 45%
1951 9.7 12.4 22.1 44%
1952 10.2 11.5 21.7 47%
1953 9.8 11.4 21.3 46%
1954 9.8 11.4 21.3 46%
1955 10.4 11.8 22.3 47%
1956 10.1 11.7 21.8 46%
1957 10.2 12.1 22.3 46%
1958 10.2 12.3 22.4 45%
1959 9.7 11.9 21.6 45%
1960 10.1 11.8 21.9 46%
1961 10.0 11.8 21.8 46%
1962 10.6 11.4 22.0 48%
1963 10.1 12.1 22.2 45%
1964 10.4 11.8 22.2 47%
1965 10.3 12.0 22.3 46%
1966 10.6 11.7 22.3 47%
1967 10.8 11.7 22.5 48%
1968 10.2 12.1 22.3 46%
1969 10.2 12.1 22.3 46%
1970 10.2 11.8 22.0 46%
1971 10.1 12.0 22.1 46%
1972 9.9 11.5 21.4 46%
1973 9.8 12.2 21.9 44%
1974 9.9 12.2 22.1 45%
1975 10.2 12.5 22.7 45%
1976 10.1 12.5 22.6 45%
1977 10.2 12.2 22.3 46%
1978 10.2 12.2 22.4 46%
1979 10.7 12.2 22.9 47%
1980 10.2 12.9 23.2 44%
1981 10.7 11.7 22.3 48%
1982 10.6 12.2 22.7 47%
1983 10.8 12.3 23.1 47%
1984 10.9 12.5 23.4 47%
1985 11.3 12.4 23.7 48%
1986 11.0 12.9 23.9 46%
1987 11.0 12.7 23.7 47%
1988 10.7 12.3 22.9 46%
1989 11.3 12.9 24.2 47%
1990 11.8 12.6 24.4 48%
1991 11.7 13.0 24.6 47%
1992 12.1 12.8 24.9 49%
1993 12.2 12.7 24.9 49%
1994 12.0 12.5 24.5 49%
1995 12.1 12.9 25.0 48%
1996 12.3 12.3 24.6 50%
1997 12.4 12.8 25.1 49%
1998 12.2 12.7 24.9 49%
1999 12.5 12.6 25.1 50%
2000 12.3 12.9 25.2 49%
2001 12.5 12.3 24.8 50%
2002 12.4 12.6 25.1 50%
2003 12.5 12.5 25.1 50%
2004 12.3 12.6 24.9 49%
2005 12.2 12.4 24.6 50%
2006 13.0 12.5 25.5 51%
2007 13.1 12.7 25.8 51%
2008 13.1 12.5 25.6 51%
2009 13.3 12.5 25.8 51%
2010 12.5 12.7 25.2 50%
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Complete Archive – By Date