I heard that postage rates are probably going to increase in January, 2011, from 44 cents to 46 cents for letters up to one ounce.
I still think that's a small price to pay to send a letter anywhere in the country in just a couple of days. I also think the USPS provides a great service. Many people like to complain about the service, but I think those complaints are mostly unfounded.
The first postage rates were 6 cents in 1863. In 1914, the price to mail a letter had actually decreased down to 2 cents! www.inflationdata.com only has inflation rates since 1914. 2 cents in 1914 is equivalent to 44 cents in 2010 dollars. That means that compared to 1914, it's basically the same price to mail a letter now than it was then.
I haven't researched this issue at all, but I have some random thoughts about it. I assume that postage rates decreased over the first 50 years because using the mail became more popular and technology evolved. It became cheaper to process mail and the demand grew - causing prices to drop.
Inflation took off in the early 70's and postage rates increased to match inflation. So even though it seems as though postage has been going crazy lately, it hasn't made much of a change in terms of real dollars over the last century.
Here's a graph showing the price of postage since 1863:
Tuesday, December 28, 2010
Wednesday, September 1, 2010
Can Brandon Marshall Succeed in Miami?
A couple of months ago on the BS Report, Bill Simmons and Matthew Berry were discussing the 2010 fantasy prospects of Brandon Marshall. Simmons made a comment that he didn't think WR's who changed teams usually did very well, with the exception of Randy Moss. He repeated this theory this week with Mike Lombardi. At first glance, this seems fairly accurate. Guys like Carl Pickens and Alvin Harper jump to mind as guys who did very little after changing teams.
But how many players really compare to Brandon Marshall? Marshall has played for 4 seasons and 2010 will be his age 26 season. Marshall has over 100 receptions and 1,000 yards in each of the past 3 seasons. It's not often that a player with as much success, and still as young as Marshall, changes teams. There have been 36 players to gain 500+ receiving yards at age 25 or younger and then change teams the following season. If we stretch that out to include guys who were 26 or younger, the count increases to 77 players.
Of those 77 players, eight of them had 1,000+ receiving yards before changing teams, and all eight of them had fewer receiving yards with their new team:
Out of the 77 players who changed teams, only 16 had more yards in the first year with their new team than they had in the last year with their old team. The most successful of these was Santana Moss who had 1,483 yards receiving for Washington at age 26 - which was 645 yards better than his previous season with the Jets. On average, these players had 225 yards fewer with their new team than they had with their old team. If we expand the pool to include all players with 500+ yards, regardless of age, we have a pool of 249 players, and the average only increases to a 258-yard dropoff in production. In all, 47 of the 249 receivers had better seasons with their new teams.
Because of regression to the mean we know that most players who have a good season, will naturally follow those up with less successful seasons. So how did the guys do who had 500+ yards and stayed with the same team? First, let's take a look at the young guys. There have been 922 receivers to catch 500+ yards in a season, and play for the same team the following year. 326 of those had a yardage increase in year N+1 with an average decrease of 111 yards. Once again, the old guys were a little less successful. Disregarding age, there were 1,971 receivers with 500+ yards who stayed with the same team. 593 of them increased their yardage total, with an average decrease of 149 yards.
In summary:
These numbers reflect what we would think intuitively: younger receivers are more likely to improve on a good (500+ receiving yards) season and players who stay with their team are more likely to improve on a good season. This is because the team that has the receiver on a team knows him best and knows if he still has more good seasons left in him. Also, if a player stays with his team, he and his teammates are more familiar with each other.
But this still doesn't tell us a whole lot about whether Brandon Marshall will have success in Miami or not. Marshall has had a much better start to his career than the average receiver. Let's see if we can narrow down some comparable situations to Marshall. Marshall has averaged over 1,200 yards per season over the past 3 seasons. There are 109 other receivers who have averaged over 1,000 yards during at least one 3-year span in their careers. Only 46 of those achieved that feat by their age 26 season. There are only 2 players besides Marshall to meet this criteria and then play for a different team the following season: David Boston and Buddy Dial.
David Boston had 1,156 yards at age 22, 1,598 yards at age 23 and then 512 yards in just 8 games at age 24. Then he went to San Diego at age 25 and gained 880 yards in 14 games and that was basically the end of his career. Boston had injury problems, and was never the same player again.
Buddy Dial came into the league in 1959 with the Pittsburgh Steelers. From 1960 through 1963 while playing with Bobby Layne he had yardage totals of 972, 1,047, 981 and 1295 before being traded to the Dallas Cowboys in 1964. He played just 3 more seasons in the NFL and due to injuries never topped 283 yards in a season.
Like Marshall, there are 3 players who met these criteria for the first time last season. These are Santonio Holmes, Greg Jennings and Calvin Johnson. I'm going to remove them from the analysis. Also, Braylon Edwards, Andre Johnson and Larry Fitzgerald have yet to play their age 29 season, so I am going to remove them also. Edwards was traded to the Jets during his age 26 season after averaging 1,000+ yards his previous 3 seasons - only one of which went over 1,000 yards.
We now have a list of 39 players who had sustained success at WR prior to age 27, and have already played their age 29 season (or have retired). These 39 players went on to average 863 yards per season for their age 27 through 29 seasons. 12 of them averaged over 1,000 yards per season over that span.
The full list:
Name Yards
Torry Holt 1,466
Chad Johnson 1,414
Jerry Rice 1,397
Michael Irvin 1,391
Sterling Sharpe 1,285
James Lofton 1,271
Isaac Bruce 1,247
Gary Clark 1,227
Herman Moore 1,191
Lance Alworth 1,108
Art Powell 1,062
Hines Ward 1,047
Anquan Boldin 972
Plaxico Burress 967
Laveranues Coles 964
Andre Reed 960
Antonio Freeman 935
Steve Largent 930
Tony Hill 926
Santana Moss 881
Mark Clayton 849
Bob Hayes 825
Carl Pickens 818
Andre Rison 794
Dwight Clark 793
Randy Moss 775
Mike Quick 746
Stanley Morgan 719
Al Toon 677
Darrell Jackson 645
Mark Carrier 630
Frank Sanders 589
Cris Collinsworth 582
Joey Galloway 481
John Jefferson 400
Harlon Hill 242
Buddy Dial 238
George Sauer 170
David Boston 27
Conclusion: Obviously, there is no way to predict how things will turn out for Brandon Marshall. There haven't been many other players with similar success to Brandon Marshall who changed teams during his successful run. The closest comps are David Boston, Buddy Dial and Braylon Edwards. Boston and Dial were derailed by injuries, and Braylon Edwards who has played enough to use as a predictor for Marshall. When comparing Marshall to other players who came off 500+ yard seasons we see that generally those players will decrease productivity the following season. But when we compare Marshall to other receivers who had sustained success at a young age, we see that these players generally continued to play well through their 20's and is a who's who list of the best WR's in NFL history.
But how many players really compare to Brandon Marshall? Marshall has played for 4 seasons and 2010 will be his age 26 season. Marshall has over 100 receptions and 1,000 yards in each of the past 3 seasons. It's not often that a player with as much success, and still as young as Marshall, changes teams. There have been 36 players to gain 500+ receiving yards at age 25 or younger and then change teams the following season. If we stretch that out to include guys who were 26 or younger, the count increases to 77 players.
Of those 77 players, eight of them had 1,000+ receiving yards before changing teams, and all eight of them had fewer receiving yards with their new team:
| Player | Year | Age | Team | Yards | N+1 Yards |
| John Jefferson | 1980 | 24 | SD | 1340 | 632 |
| Jeff Graham | 1995 | 26 | Pit | 1301 | 788 |
| Laveranues Coles | 2002 | 25 | Was | 1264 | 1204 |
| Peerless Price | 2002 | 26 | Buf | 1252 | 838 |
| Harold Jackson | 1972 | 26 | Phi | 1048 | 874 |
| Rob Moore | 1994 | 26 | NYJ | 1010 | 907 |
| Derrick Alexander | 1998 | 26 | Bal | 1009 | 992 |
| Antonio Bryant | 2005 | 24 | Cle | 1009 | 733 |
Out of the 77 players who changed teams, only 16 had more yards in the first year with their new team than they had in the last year with their old team. The most successful of these was Santana Moss who had 1,483 yards receiving for Washington at age 26 - which was 645 yards better than his previous season with the Jets. On average, these players had 225 yards fewer with their new team than they had with their old team. If we expand the pool to include all players with 500+ yards, regardless of age, we have a pool of 249 players, and the average only increases to a 258-yard dropoff in production. In all, 47 of the 249 receivers had better seasons with their new teams.
Because of regression to the mean we know that most players who have a good season, will naturally follow those up with less successful seasons. So how did the guys do who had 500+ yards and stayed with the same team? First, let's take a look at the young guys. There have been 922 receivers to catch 500+ yards in a season, and play for the same team the following year. 326 of those had a yardage increase in year N+1 with an average decrease of 111 yards. Once again, the old guys were a little less successful. Disregarding age, there were 1,971 receivers with 500+ yards who stayed with the same team. 593 of them increased their yardage total, with an average decrease of 149 yards.
In summary:
| Type | Number | Number Improved | Pct Improved | Average Improvement |
| Changed Teams - All Ages | 249 | 47 | 18.9% | -258 yards |
| Change Teams - 27 or younger | 77 | 16 | 20.8% | -225 yards |
| Same Team - All Ages | 1971 | 593 | 30.1% | -149 yards |
| Same Team - 27 or younger | 922 | 326 | 35.4% | -111 yards |
These numbers reflect what we would think intuitively: younger receivers are more likely to improve on a good (500+ receiving yards) season and players who stay with their team are more likely to improve on a good season. This is because the team that has the receiver on a team knows him best and knows if he still has more good seasons left in him. Also, if a player stays with his team, he and his teammates are more familiar with each other.
But this still doesn't tell us a whole lot about whether Brandon Marshall will have success in Miami or not. Marshall has had a much better start to his career than the average receiver. Let's see if we can narrow down some comparable situations to Marshall. Marshall has averaged over 1,200 yards per season over the past 3 seasons. There are 109 other receivers who have averaged over 1,000 yards during at least one 3-year span in their careers. Only 46 of those achieved that feat by their age 26 season. There are only 2 players besides Marshall to meet this criteria and then play for a different team the following season: David Boston and Buddy Dial.
David Boston had 1,156 yards at age 22, 1,598 yards at age 23 and then 512 yards in just 8 games at age 24. Then he went to San Diego at age 25 and gained 880 yards in 14 games and that was basically the end of his career. Boston had injury problems, and was never the same player again.
Buddy Dial came into the league in 1959 with the Pittsburgh Steelers. From 1960 through 1963 while playing with Bobby Layne he had yardage totals of 972, 1,047, 981 and 1295 before being traded to the Dallas Cowboys in 1964. He played just 3 more seasons in the NFL and due to injuries never topped 283 yards in a season.
Like Marshall, there are 3 players who met these criteria for the first time last season. These are Santonio Holmes, Greg Jennings and Calvin Johnson. I'm going to remove them from the analysis. Also, Braylon Edwards, Andre Johnson and Larry Fitzgerald have yet to play their age 29 season, so I am going to remove them also. Edwards was traded to the Jets during his age 26 season after averaging 1,000+ yards his previous 3 seasons - only one of which went over 1,000 yards.
We now have a list of 39 players who had sustained success at WR prior to age 27, and have already played their age 29 season (or have retired). These 39 players went on to average 863 yards per season for their age 27 through 29 seasons. 12 of them averaged over 1,000 yards per season over that span.
The full list:
Name Yards
Torry Holt 1,466
Chad Johnson 1,414
Jerry Rice 1,397
Michael Irvin 1,391
Sterling Sharpe 1,285
James Lofton 1,271
Isaac Bruce 1,247
Gary Clark 1,227
Herman Moore 1,191
Lance Alworth 1,108
Art Powell 1,062
Hines Ward 1,047
Anquan Boldin 972
Plaxico Burress 967
Laveranues Coles 964
Andre Reed 960
Antonio Freeman 935
Steve Largent 930
Tony Hill 926
Santana Moss 881
Mark Clayton 849
Bob Hayes 825
Carl Pickens 818
Andre Rison 794
Dwight Clark 793
Randy Moss 775
Mike Quick 746
Stanley Morgan 719
Al Toon 677
Darrell Jackson 645
Mark Carrier 630
Frank Sanders 589
Cris Collinsworth 582
Joey Galloway 481
John Jefferson 400
Harlon Hill 242
Buddy Dial 238
George Sauer 170
David Boston 27
Conclusion: Obviously, there is no way to predict how things will turn out for Brandon Marshall. There haven't been many other players with similar success to Brandon Marshall who changed teams during his successful run. The closest comps are David Boston, Buddy Dial and Braylon Edwards. Boston and Dial were derailed by injuries, and Braylon Edwards who has played enough to use as a predictor for Marshall. When comparing Marshall to other players who came off 500+ yard seasons we see that generally those players will decrease productivity the following season. But when we compare Marshall to other receivers who had sustained success at a young age, we see that these players generally continued to play well through their 20's and is a who's who list of the best WR's in NFL history.
Thursday, January 7, 2010
NFL Parity
(Originally posted 10/21/09)
It seems like every year - especially early in the season - you hear lots of people talking about parity in the NFL. Some years the talk is about how even all the teams are (high parity) and some years the talk is about how many bad teams there are (low parity). This year seems to be a year where there is quite a bit of talk about how parity has disappeared.
After just 6 weeks (some teams have only played 5 games), it is really not reasonable to make a determination about parity. The apparent parity (or lack thereof) this early in the season is going to be strongly related to the NFL schedule. For instance, the New York Giants have played 2/3 of their games against some of the worst teams in the league (Was, TB, KC and Oak) - so their 5-1 record might make the Giants look like a better team than they really are.
So I thought I would take a quick look and see how parity this year compares to other years. I only looked at NFL seasons since the AFL-NFL merger in 1970.
For simplicity's sake, I calculated parity by determining the average games over .500 that each NFL team finished in a given year. For instance, if one team finished 12-4, they were 8 games away from .500. If another team finished 7-9, they were 2 games away from .500. I did this for every team, added them up and then divided by the number of teams. I also normalized the values to a 16-game season for all seasons in which fewer than 16 games were played.
Here are the all-time parity rankings. 1975 comes in as the year with the least amount of parity. In 1975 there were 26 teams in the league and they each played a 14 game schedule. 19 of the 26 teams either won or lost 10+ games that year. There were 3 other teams that either won or lost 9 games (meaning if they played a 16-game schedule that year, there was a decent chance that 22 of the 26 teams would have won or lost 10+ games!).
Here is a graph of the parity trend over time:
Click the image for a larger version.
Now the question is: How does 2009 (so far) compare? If I use the same method to calculate parity for 2009, I will get a parity rating of 7.2 through Week 6, which would tie the 1975 rating. But that's not a fair rating. Right now the NFL sports 9 teams that are either undefeated or winless. A straight extrapolation of records to 16 games means we'd end the season with 9 teams undefeated or winless - we know that won't happen. Instead, I calculated each team's pythagorean record through 16 games to come up with an expected W-L record for each team. A perfect-parity season would be if every team finished 8-8, and the parity rating would be 0. A perfect un-parity season would be if half the teams finished 16-0 and half finished 0-16 (which could probably never happen due to the schedule) and that provide a parity rating of 16.
At the top of the standings, Pythagorus says that the Saints will win 14 games, while the Colts and Broncos will win 13. It also says that the Rams will go 1-15 and the Titans, Browns and Raiders will go 2-14. These seem like reasonable approximations of what could happen - though I'd guess that there will be fewer than 4 teams that win fewer than 3 games.
Using these figures, I come up with a parity rating of 6.3 for 2009 through Week 6, which would be the 4th most un-parity season of all time. It wouldn't surprise me if the actual parity rating for 2009 is fairly high (remember, high rating means low parity), but I suspect it won't be as high as 6.3.
Updates:
Update:
With a full season of data, 2009 finishes with an actual rating of 5.0 (using actual W-L instead of Pythag. The Pythag rating was 5.1) That puts 2009 approximately in the center of the all-time rankings. Also, the all-time average is a parity rating of 5.1 which means that 2009 ends up finishing with a less varied league than average.
Even if the Colts had gone on to a 16-0 season, that would have only bumped 2009 up to 5.1 - right at the all-time average.
So in conclusion, the early-season perception that the league had lots of really bad teams and lots of really good teams was not accurate. It probably had more to do with the way the schedule worked out early on, and maybe a higher than usual number of hot and/or cold teams early.
It seems like every year - especially early in the season - you hear lots of people talking about parity in the NFL. Some years the talk is about how even all the teams are (high parity) and some years the talk is about how many bad teams there are (low parity). This year seems to be a year where there is quite a bit of talk about how parity has disappeared.
After just 6 weeks (some teams have only played 5 games), it is really not reasonable to make a determination about parity. The apparent parity (or lack thereof) this early in the season is going to be strongly related to the NFL schedule. For instance, the New York Giants have played 2/3 of their games against some of the worst teams in the league (Was, TB, KC and Oak) - so their 5-1 record might make the Giants look like a better team than they really are.
So I thought I would take a quick look and see how parity this year compares to other years. I only looked at NFL seasons since the AFL-NFL merger in 1970.
For simplicity's sake, I calculated parity by determining the average games over .500 that each NFL team finished in a given year. For instance, if one team finished 12-4, they were 8 games away from .500. If another team finished 7-9, they were 2 games away from .500. I did this for every team, added them up and then divided by the number of teams. I also normalized the values to a 16-game season for all seasons in which fewer than 16 games were played.
Here are the all-time parity rankings. 1975 comes in as the year with the least amount of parity. In 1975 there were 26 teams in the league and they each played a 14 game schedule. 19 of the 26 teams either won or lost 10+ games that year. There were 3 other teams that either won or lost 9 games (meaning if they played a 16-game schedule that year, there was a decent chance that 22 of the 26 teams would have won or lost 10+ games!).
| Year | Average |
| 1975 | 7.2 |
| 1976 | 7 |
| 1973 | 6.4 |
| 2005 | 6 |
| 1972 | 5.9 |
| 1977 | 5.7 |
| 1991 | 5.7 |
| 1992 | 5.7 |
| 1970 | 5.6 |
| 1986 | 5.6 |
| 1982 | 5.5 |
| 1998 | 5.5 |
| 1990 | 5.4 |
| 2003 | 5.4 |
| 1984 | 5.3 |
| 2000 | 5.3 |
| 2001 | 5.3 |
| 2008 | 5.2 |
| 1971 | 5.1 |
| 2007 | 5.1 |
| 1980 | 5 |
| 1985 | 5 |
| 1974 | 4.9 |
| 2004 | 4.9 |
| 1997 | 4.8 |
| 1979 | 4.6 |
| 1988 | 4.6 |
| 1987 | 4.5 |
| 1996 | 4.5 |
| 1989 | 4.4 |
| 1994 | 4.4 |
| 1999 | 4.4 |
| 1978 | 4.3 |
| 1981 | 4.3 |
| 2002 | 4.3 |
| 2006 | 4.3 |
| 1993 | 4.1 |
| 1983 | 3.9 |
| 1995 | 3.9 |
Here is a graph of the parity trend over time:
Now the question is: How does 2009 (so far) compare? If I use the same method to calculate parity for 2009, I will get a parity rating of 7.2 through Week 6, which would tie the 1975 rating. But that's not a fair rating. Right now the NFL sports 9 teams that are either undefeated or winless. A straight extrapolation of records to 16 games means we'd end the season with 9 teams undefeated or winless - we know that won't happen. Instead, I calculated each team's pythagorean record through 16 games to come up with an expected W-L record for each team. A perfect-parity season would be if every team finished 8-8, and the parity rating would be 0. A perfect un-parity season would be if half the teams finished 16-0 and half finished 0-16 (which could probably never happen due to the schedule) and that provide a parity rating of 16.
At the top of the standings, Pythagorus says that the Saints will win 14 games, while the Colts and Broncos will win 13. It also says that the Rams will go 1-15 and the Titans, Browns and Raiders will go 2-14. These seem like reasonable approximations of what could happen - though I'd guess that there will be fewer than 4 teams that win fewer than 3 games.
Using these figures, I come up with a parity rating of 6.3 for 2009 through Week 6, which would be the 4th most un-parity season of all time. It wouldn't surprise me if the actual parity rating for 2009 is fairly high (remember, high rating means low parity), but I suspect it won't be as high as 6.3.
Updates:
| Through | W-L | Pythag |
| Week 7 | 7.3 | 6.9 |
Update:
With a full season of data, 2009 finishes with an actual rating of 5.0 (using actual W-L instead of Pythag. The Pythag rating was 5.1) That puts 2009 approximately in the center of the all-time rankings. Also, the all-time average is a parity rating of 5.1 which means that 2009 ends up finishing with a less varied league than average.
Even if the Colts had gone on to a 16-0 season, that would have only bumped 2009 up to 5.1 - right at the all-time average.
So in conclusion, the early-season perception that the league had lots of really bad teams and lots of really good teams was not accurate. It probably had more to do with the way the schedule worked out early on, and maybe a higher than usual number of hot and/or cold teams early.
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