Since the middle of 2010 we’ve been monitoring the level of Goldstream Creek for the National Weather Service by measuring the distance from the top of our bridge to the surface of the water or ice. In 2012 the Creek flooded and washed the bridge downstream. We eventually raised the bridge logs back up onto the banks and resumed our measurements.

This winter the Creek had been relatively quiet, with the level hovering around eight feet below the bridge. But last Friday, we awoke to more than four feet of water over the ice, and since then it's continued to rise. This morning’s reading had the ice only 3.17 feet below the surface of the bridge.

Water also entered the far side of the slough, and is making it’s way around the loop, melting the snow covering the old surface. Even as the main channel stops rising and freezes, water moves closer to the dog yard from the slough.

One of my longer commutes to work involves riding east on the Goldstream Valley trails, crossing the Creek by Ballaine Road, then riding back toward the house on the north side of the Creek. From there, I can cross Goldstream Creek again where the trail at the end of Miller Hill Road and the Miller Hill Extension trail meet, and ride the trails the rest of the way to work. That crossing is also covered with several feet of water and ice.

Yesterday one of my neighbors sent email with the subject line, “Are we doomed?,” so I took a look at the heigh data from past years. The plot below shows the height of the Creek, as measured from the surface of the bridge (click on the plot to view or download a PDF, R code used to generate the plot appears at the bottom of this post).

The orange region is the region where the Creek is flowing; between my reporting of 0% ice in spring and 100% ice-covered in fall. The data gap in July 2014 was due to the flood washing the bridge downstream. Because the bridge isn’t in the same location, the height measurements before and after the flood aren’t completely comparable, but I don’t have the data for the difference in elevation between the old and new bridge locations, so this is the best we’ve got.

The light blue line across all the plots shows the current height of the Creek (3.17 feet) for all years of data. 2012 is probably the closest year to our current situation where the Creek rose to around five feet below the bridge in early January. But really nothing is completely comparable to the situation we’re in right now. Breakup won’t come for another two or three months, and in most years, the Creek rises several feet between February and breakup.

Time will tell, of course, but here’s why I’m not too worried about it. There’s another bridge crossing several miles downstream, and last Friday there was no water on the surface, and the Creek was easily ten feet below the banks. That means that there is a lot of space within the banks of the Creek downstream that can absorb the melting water as breakup happens. I also think that there is a lot of liquid water trapped beneath the ice on the surface in our neighborhood and that water is likely to slowly drain out downstream, leaving a lot of empty space below the surface ice that can accommodate further overflow as the winter progresses. In past years of walking on the Creek I’ve come across huge areas where the top layer of ice dropped as much as six feet when the water underneath drained away. I’m hoping that this happens here, with a lot of the subsurface water draining downstream.

The Creek is always reminding us of how little we really understand what’s going on and how even a small amount of flowing water can become a huge force when that water accumulates more rapidly than the Creek can handle it. Never a dull moment!

# Code

```
library(readr)
library(dplyr)
library(tidyr)
library(lubridate)
library(ggplot2)
library(scales)
wxcoder <- read_csv("data/wxcoder.csv", na=c("-9999"))
feb_2016_incomplete <- read_csv("data/2016_02_incomplete.csv",
na=c("-9999"))
wxcoder <- rbind(wxcoder, feb_2016_incomplete)
wxcoder <- wxcoder %>%
transmute(dte=as.Date(ymd(DATE)), tmin_f=TN, tmax_f=TX, tobs_f=TA,
tavg_f=(tmin_f+tmax_f)/2.0,
prcp_in=ifelse(PP=='T', 0.005, as.numeric(PP)),
snow_in=ifelse(SF=='T', 0.05, as.numeric(SF)),
snwd_in=SD, below_bridge_ft=HG,
ice_cover_pct=IC)
creek <- wxcoder %>% filter(dte>as.Date(ymd("2010-05-27")))
creek_w_year <- creek %>%
mutate(year=year(dte),
doy=yday(dte))
ice_free_date <- creek_w_year %>%
group_by(year) %>%
filter(ice_cover_pct==0) %>%
summarize(ice_free_dte=min(dte), ice_free_doy=min(doy))
ice_covered_date <- creek_w_year %>%
group_by(year) %>%
filter(ice_cover_pct==100, doy>182) %>%
summarize(ice_covered_dte=min(dte), ice_covered_doy=min(doy))
flowing_creek_dates <- ice_free_date %>%
inner_join(ice_covered_date, by="year") %>%
mutate(ymin=Inf, ymax=-Inf)
latest_obs <- creek_w_year %>%
mutate(rank=rank(desc(dte))) %>%
filter(rank==1)
current_height_df <- data.frame(
year=c(2011, 2012, 2013, 2014, 2015, 2016),
below_bridge_ft=latest_obs$below_bridge_ft)
q <- ggplot(data=creek_w_year %>% filter(year>2010),
aes(x=doy, y=below_bridge_ft)) +
theme_bw() +
geom_rect(data=flowing_creek_dates %>% filter(year>2010),
aes(xmin=ice_free_doy, xmax=ice_covered_doy, ymin=ymin, ymax=ymax),
fill="darkorange", alpha=0.4,
inherit.aes=FALSE) +
# geom_point(size=0.5) +
geom_line() +
geom_hline(data=current_height_df,
aes(yintercept=below_bridge_ft),
colour="darkcyan", alpha=0.4) +
scale_x_continuous(name="",
breaks=c(1,32,60,91,
121,152,182,213,
244,274,305,335,
365),
labels=c("Jan", "Feb", "Mar", "Apr",
"May", "Jun", "Jul", "Aug",
"Sep", "Oct", "Nov", "Dec",
"Jan")) +
scale_y_reverse(name="Creek height, feet below bridge",
breaks=pretty_breaks(n=5)) +
facet_wrap(~ year, ncol=1)
width <- 16
height <- 16
rescale <- 0.75
pdf("creek_heights_2010-2016_by_year.pdf",
width=width*rescale, height=height*rescale)
print(q)
dev.off()
svg("creek_heights_2010-2016_by_year.svg",
width=width*rescale, height=height*rescale)
print(q)
dev.off()
```

# Introduction

While riding to work this morning I figured out a way to disentangle the effects of trail quality and physical conditioning (both of which improve over the season) from temperature, which also tends to increase throughout the season. As you recall in my previous post, I found that days into the season (winter day of year) and minimum temperature were both negatively related with fat bike energy consumption. But because those variables are also related to each other, we can’t make statements about them individually.

But what if we look at pairs of trips that are within two days of each other and look at the difference in temperature between those trips and the difference in energy consumption? We’ll only pair trips going the same direction (to or from work), and we’ll restrict the pairings to two days or less. That eliminates seasonality from the data because we’re always comparing two trips from the same few days.

# Data

For this analysis, I’m using SQL to filter the data because I’m better at window functions and filtering in SQL than R. Here’s the code to grab the data from the database. (The CSV file and RMarkdown script is on my GitHub repo for this analysis). The trick here is to categorize trips as being to work (“north”) or from work (“south”) and then include this field in the partition statement of the window function so I’m only getting the next trip that matches direction.

```
library(dplyr)
library(ggplot2)
library(scales)
exercise_db <- src_postgres(host="example.com", dbname="exercise_data")
diffs <- tbl(exercise_db,
build_sql(
"WITH all_to_work AS (
SELECT *,
CASE WHEN extract(hour from start_time) < 11
THEN 'north' ELSE 'south' END AS direction
FROM track_stats
WHERE type = 'Fat Biking'
AND miles between 4 and 4.3
), with_next AS (
SELECT track_id, start_time, direction, kcal, miles, min_temp,
lead(direction) OVER w AS next_direction,
lead(start_time) OVER w AS next_start_time,
lead(kcal) OVER w AS next_kcal,
lead(miles) OVER w AS next_miles,
lead(min_temp) OVER w AS next_min_temp
FROM all_to_work
WINDOW w AS (PARTITION BY direction ORDER BY start_time)
)
SELECT start_time, next_start_time, direction,
min_temp, next_min_temp,
kcal / miles AS kcal_per_mile,
next_kcal / next_miles as next_kcal_per_mile,
next_min_temp - min_temp AS temp_diff,
(next_kcal / next_miles) - (kcal / miles) AS kcal_per_mile_diff
FROM with_next
WHERE next_start_time - start_time < '60 hours'
ORDER BY start_time")) %>% collect()
write.csv(diffs, file="fat_biking_trip_diffs.csv", quote=TRUE,
row.names=FALSE)
kable(head(diffs))
```

start time | next start time | temp diff | kcal / mile diff |
---|---|---|---|

2013-12-03 06:21:49 | 2013-12-05 06:31:54 | 3.0 | -13.843866 |

2013-12-03 15:41:48 | 2013-12-05 15:24:10 | 3.7 | -8.823329 |

2013-12-05 06:31:54 | 2013-12-06 06:39:04 | 23.4 | -22.510564 |

2013-12-05 15:24:10 | 2013-12-06 16:38:31 | 13.6 | -5.505662 |

2013-12-09 06:41:07 | 2013-12-11 06:15:32 | -27.7 | -10.227048 |

2013-12-09 13:44:59 | 2013-12-11 16:00:11 | -25.4 | -1.034789 |

Out of a total of 123 trips, 70 took place within 2 days of each other. We still don’t have a measure of trail quality, so pairs where the trail is smooth and hard one day and covered with fresh snow the next won’t be particularly good data points.

Let’s look at a plot of the data.

```
s = ggplot(data=diffs,
aes(x=temp_diff, y=kcal_per_mile_diff)) +
geom_point() +
geom_smooth(method="lm", se=FALSE) +
scale_x_continuous(name="Temperature difference between paired trips (degrees F)",
breaks=pretty_breaks(n=10)) +
scale_y_continuous(name="Energy consumption difference (kcal / mile)",
breaks=pretty_breaks(n=10)) +
theme_bw() +
ggtitle("Paired fat bike trips to and from work within 2 days of each other")
print(s)
```

This shows that when the temperature difference between two paired trips is negative (the second trip is colder than the first), additional energy is required for the second (colder) trip. This matches the pattern we saw in my earlier post where minimum temperature and winter day of year were negatively associated with energy consumption. But because we’ve used differences to remove seasonal effects, we can actually determine how large of an effect temperature has.

There are quite a few outliers here. Those that are in the region with very little difference in temperature are likey due to snowfall changing the trail conditions from one trip to the next. I’m not sure why there is so much scatter among the points on the left side of the graph, but I don’t see any particular pattern among those points that might explain the higher than normal variation, and we don’t see the same variation in the points with a large positive difference in temperature, so I think this is just normal variation in the data not explained by temperature.

## Results

Here’s the linear regression results for this data.

```
summary(lm(data=diffs, kcal_per_mile_diff ~ temp_diff))
```

## ## Call: ## lm(formula = kcal_per_mile_diff ~ temp_diff, data = diffs) ## ## Residuals: ## Min 1Q Median 3Q Max ## -40.839 -4.584 -0.169 3.740 47.063 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -2.1696 1.5253 -1.422 0.159 ## temp_diff -0.7778 0.1434 -5.424 8.37e-07 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 12.76 on 68 degrees of freedom ## Multiple R-squared: 0.302, Adjusted R-squared: 0.2917 ## F-statistic: 29.42 on 1 and 68 DF, p-value: 8.367e-07

The model and coefficient are both highly signficant, and as we might expect, the intercept in the model is not significantly different from zero (if there wasn’t a difference in temperature between two trips there shouldn’t be a difference in energy consumption either, on average). Temperature alone explains 30% of the variation in energy consumption, and the coefficient tells us the scale of the effect: each degree drop in temperature results in an increase in energy consumption of 0.78 kcalories per mile. So for a 4 mile commute like mine, the difference between a trip at 10°F vs −20°F is an additional 93 kilocalories (30 × 0.7778 × 4 = 93.34) on the colder trip. That might not sound like much in the context of the calories in food (93 kilocalories is about the energy in a large orange or a light beer), but my average energy consumption across all fat bike trips to and from work is 377 kilocalories so 93 represents a large portion of the total.

# Introduction

I’ve had a fat bike since late November 2013, mostly using it to commute the 4.1 miles to and from work on the Goldstream Valley trail system. I used to classic ski exclusively, but that’s not particularly pleasant once the temperatures are below 0°F because I can’t keep my hands and feet warm enough, and the amount of glide you get on skis declines as the temperature goes down.

However, it’s also true that fat biking gets much harder the colder it gets. I think this is partly due to biking while wearing lots of extra layers, but also because of increased friction between the large tires and tubes in a fat bike. In this post I will look at how temperature and other variables affect the performance of a fat bike (and it’s rider).

The code and data for this post is available on GitHub.

# Data

I log all my commutes (and other exercise) using the RunKeeper app, which uses the phone’s GPS to keep track of distance and speed, and connects to my heart rate monitor to track heart rate. I had been using a Polar HR chest strap, but after about a year it became flaky and I replaced it with a Scosche Rhythm+ arm band monitor. The data from RunKeeper is exported into GPX files, which I process and insert into a PostgreSQL database.

From the heart rate data, I estimate energy consumption (in kilocalories, or what appears on food labels as calories) using a formula from Keytel LR, et al. 2005, which I talk about in this blog post.

Let’s take a look at the data:

```
library(dplyr)
library(ggplot2)
library(scales)
library(lubridate)
library(munsell)
fat_bike <- read.csv("fat_bike.csv", stringsAsFactors=FALSE, header=TRUE) %>%
tbl_df() %>%
mutate(start_time=ymd_hms(start_time, tz="US/Alaska"))
kable(head(fat_bike))
```

start_time | miles | time | hours | mph | hr | kcal | min_temp | max_temp |
---|---|---|---|---|---|---|---|---|

2013-11-27 06:22:13 | 4.17 | 0:35:11 | 0.59 | 7.12 | 157.8 | 518.4 | -1.1 | 1.0 |

2013-11-27 15:27:01 | 4.11 | 0:35:49 | 0.60 | 6.89 | 156.0 | 513.6 | 1.1 | 2.2 |

2013-12-01 12:29:27 | 4.79 | 0:55:08 | 0.92 | 5.21 | 172.6 | 951.5 | -25.9 | -23.9 |

2013-12-03 06:21:49 | 4.19 | 0:39:16 | 0.65 | 6.40 | 148.4 | 526.8 | -4.6 | -2.1 |

2013-12-03 15:41:48 | 4.22 | 0:30:56 | 0.52 | 8.19 | 154.6 | 434.5 | 6.0 | 7.9 |

2013-12-05 06:31:54 | 4.14 | 0:32:14 | 0.54 | 7.71 | 155.8 | 463.2 | -1.6 | 2.9 |

There are a few things we need to do to the raw data before analyzing it. First, we want to restrict the data to just my commutes to and from work, and we want to categorize them as being one or the other. That way we can analyze trips to ABR and home separately, and we’ll reduce the variation within each analysis. If we were to analyze all fat biking trips together, we’d be lumping short and long trips, as well as those with a different proportion of hills or more challenging conditions. To get just trips to and from work, I’m restricting the distance to trips between 4.0 and 4.3 miles, and only those activities where there were two of them in a single day (to work and home from work). To categorize them into commutes to work and home, I filter based on the time of day.

I’m also calculating energy per mile, and adding a “winter day of year”
variable (`wdoy`), which is a measure of how far into the winter
season the trip took place. We can’t just use day of year because that
starts over on January 1st, so we subtract the number of days between
January and May from the date and get day of year from that. Finally, we
split the data into trips to work and home.

I’m also excluding the really early season data from 2015 because the trail was in really poor condition.

```
fat_bike_commute <- fat_bike %>%
filter(miles>4, miles<4.3) %>%
mutate(direction=ifelse(hour(start_time)<10, 'north', 'south'),
date=as.Date(start_time, tz='US/Alaska'),
wdoy=yday(date-days(120)),
kcal_per_mile=kcal/miles) %>%
group_by(date) %>%
mutate(n=n()) %>%
ungroup() %>%
filter(n>1)
to_abr <- fat_bike_commute %>% filter(direction=='north',
wdoy>210)
to_home <- fat_bike_commute %>% filter(direction=='south',
wdoy>210)
kable(head(to_home %>% select(-date, -kcal, -n)))
```

start_time | miles | time | hours | mph | hr | min_temp | max_temp | direction | wdoy | kcal_per_mile |
---|---|---|---|---|---|---|---|---|---|---|

2013-11-27 15:27:01 | 4.11 | 0:35:49 | 0.60 | 6.89 | 156.0 | 1.1 | 2.2 | south | 211 | 124.96350 |

2013-12-03 15:41:48 | 4.22 | 0:30:56 | 0.52 | 8.19 | 154.6 | 6.0 | 7.9 | south | 217 | 102.96209 |

2013-12-05 15:24:10 | 4.18 | 0:29:07 | 0.49 | 8.60 | 150.7 | 9.7 | 12.0 | south | 219 | 94.13876 |

2013-12-06 16:38:31 | 4.17 | 0:26:04 | 0.43 | 9.60 | 154.3 | 23.3 | 24.7 | south | 220 | 88.63309 |

2013-12-09 13:44:59 | 4.11 | 0:32:06 | 0.54 | 7.69 | 161.3 | 27.5 | 28.5 | south | 223 | 119.19708 |

2013-12-11 16:00:11 | 4.19 | 0:33:48 | 0.56 | 7.44 | 157.6 | 2.1 | 4.5 | south | 225 | 118.16229 |

# Analysis

Here a plot of the data. We’re plotting all trips with winter day of year on the x-axis and energy per mile on the y-axis. The color of the points indicates the minimum temperature and the straight line shows the trend of the relationship.

```
s <- ggplot(data=fat_bike_commute %>% filter(wdoy>210), aes(x=wdoy, y=kcal_per_mile, colour=min_temp)) +
geom_smooth(method="lm", se=FALSE, colour=mnsl("10B 7/10", fix=TRUE)) +
geom_point(size=3) +
scale_x_continuous(name=NULL,
breaks=c(215, 246, 277, 305, 336),
labels=c('1-Dec', '1-Jan', '1-Feb', '1-Mar', '1-Apr')) +
scale_y_continuous(name="Energy (kcal)", breaks=pretty_breaks(n=10)) +
scale_colour_continuous(low=mnsl("7.5B 5/12", fix=TRUE), high=mnsl("7.5R 5/12", fix=TRUE),
breaks=pretty_breaks(n=5),
guide=guide_colourbar(title="Min temp (°F)", reverse=FALSE, barheight=8)) +
ggtitle("All fat bike trips") +
theme_bw()
print(s)
```

Across all trips, we can see that as the winter progresses, I consume less energy per mile. This is hopefully because my physical condition improves the more I ride, and also because the trail conditions also improve as the snow pack develops and the trail gets harder with use. You can also see a pattern in the color of the dots, with the bluer (and colder) points near the top and the warmer temperature trips near the bottom.

Let’s look at the temperature relationship:

```
s <- ggplot(data=fat_bike_commute %>% filter(wdoy>210), aes(x=min_temp, y=kcal_per_mile, colour=wdoy)) +
geom_smooth(method="lm", se=FALSE, colour=mnsl("10B 7/10", fix=TRUE)) +
geom_point(size=3) +
scale_x_continuous(name="Minimum temperature (degrees F)", breaks=pretty_breaks(n=10)) +
scale_y_continuous(name="Energy (kcal)", breaks=pretty_breaks(n=10)) +
scale_colour_continuous(low=mnsl("7.5PB 2/12", fix=TRUE), high=mnsl("7.5PB 8/12", fix=TRUE),
breaks=c(215, 246, 277, 305, 336),
labels=c('1-Dec', '1-Jan', '1-Feb', '1-Mar', '1-Apr'),
guide=guide_colourbar(title=NULL, reverse=TRUE, barheight=8)) +
ggtitle("All fat bike trips") +
theme_bw()
print(s)
```

A similar pattern. As the temperature drops, it takes more energy to go the same distance. And the color of the points also shows the relationship from the earlier plot where trips taken later in the season require less energy.

There is also be a correlation between winter day of year and temperature. Since the winter fat biking season essentially begins in December, it tends to warm up throughout.

# Results

The relationship between winter day of year and temperature means that we’ve got multicollinearity in any model that includes both of them. This doesn’t mean we shouldn’t include them, nor that the significance or predictive power of the model is reduced. All it means is that we can’t use the individual regression coefficients to make predictions.

Here are the linear models for trips to work, and home:

```
to_abr_lm <- lm(data=to_abr, kcal_per_mile ~ min_temp + wdoy)
print(summary(to_abr_lm))
```

## ## Call: ## lm(formula = kcal_per_mile ~ min_temp + wdoy, data = to_abr) ## ## Residuals: ## Min 1Q Median 3Q Max ## -27.845 -6.964 -3.186 3.609 53.697 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 170.81359 15.54834 10.986 1.07e-14 *** ## min_temp -0.45694 0.18368 -2.488 0.0164 * ## wdoy -0.29974 0.05913 -5.069 6.36e-06 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 15.9 on 48 degrees of freedom ## Multiple R-squared: 0.4069, Adjusted R-squared: 0.3822 ## F-statistic: 16.46 on 2 and 48 DF, p-value: 3.595e-06

```
to_home_lm <- lm(data=to_home, kcal_per_mile ~ min_temp + wdoy)
print(summary(to_home_lm))
```

## ## Call: ## lm(formula = kcal_per_mile ~ min_temp + wdoy, data = to_home) ## ## Residuals: ## Min 1Q Median 3Q Max ## -21.615 -10.200 -1.068 3.741 39.005 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 144.16615 18.55826 7.768 4.94e-10 *** ## min_temp -0.47659 0.16466 -2.894 0.00570 ** ## wdoy -0.20581 0.07502 -2.743 0.00852 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 13.49 on 48 degrees of freedom ## Multiple R-squared: 0.5637, Adjusted R-squared: 0.5455 ## F-statistic: 31.01 on 2 and 48 DF, p-value: 2.261e-09

The models confirm what we saw in the plots. Both regression coefficients are negative, which means that as the temperature rises (and as the winter goes on) I consume less energy per mile. The models themselves are significant as are the coefficients, although less so in the trips to work. The amount of variation in kcal/mile explained by minimum temperature and winter day of year is 41% for trips to work and 56% for trips home.

What accounts for the rest of the variation? My guess is that trail conditions are the missing factor here; specifically fresh snow, or a trail churned up by snowmachiners. I think that’s also why the results are better on trips home than to work. On days when we get snow overnight, I am almost certainly riding on an pristine snow-covered trail, but by the time I leave work, the trail will be smoother and harder due to all the traffic it’s seen over the course of the day.

# Conclusions

We didn’t really find anything surprising here: it is significantly harder to ride a fat bike when it’s colder. Because of conditioning, improved trail conditions, as well as the tendency for warmer weather later in the season, it also gets easier to ride as the winter goes on.

# Introduction

Often when I’m watching Major League Baseball games a player will come up to bat or pitch and I’ll comment “former Oakland Athletic” and the player’s name. It seems like there’s always one or two players on the roster of every team that used to be an Athletic.

Let’s find out. We’ll use the Retrosheet database again, this time using the roster lists from 1990 through 2014 and comparing it against the 40-man rosters of current teams. That data will have to be scraped off the web, since Retrosheet data doesn’t exist for the current season and rosters change frequently during the season.

# Methods

As usual, I’ll use R for the analysis, and rmarkdown to produce this post.

```
library(plyr)
library(dplyr)
library(rvest)
options(stringsAsFactors=FALSE)
```

We’re using `plyr` and `dplyr` for most of the data manipulation and
`rvest` to grab the 40-man rosters for each team from the MLB website.
Setting `stringsAsFactors` to false prevents various base R packages
from converting everything to factors. We're not doing any statistics
with this data, so factors aren't necessary and make comparisons and
joins between data frames more difficult.

## Players by team for previous years

Load the roster data:

```
retrosheet_db <- src_postgres(host="localhost", port=5438,
dbname="retrosheet", user="cswingley")
rosters <- tbl(retrosheet_db, "rosters")
all_recent_players <-
rosters %>%
filter(year>1989) %>%
collect() %>%
mutate(player=paste(first_name, last_name),
team=team_id) %>%
select(player, team, year)
save(all_recent_players, file="all_recent_players.rdata", compress="gzip")
```

The Retrosheet database lives in PostgreSQL on my computer, but one of
the advantages of using `dplyr` for retrieval is it would be easy to
change the source statement to connect to another sort of database
(SQLite, MySQL, etc.) and the rest of the commands would be the same.

We only grab data since 1990 and we combine the first and last names into a single field because that’s how player names are listed on the 40-man roster pages on the web.

Now we filter the list down to Oakland Athletic players, combine the rows for each Oakland player, summarizing the years they played for the A’s into a single column.

```
oakland_players <- all_recent_players %>%
filter(team=='OAK') %>%
group_by(player) %>%
summarise(years=paste(year, collapse=', '))
```

Here’s what that looks like:

```
kable(head(oakland_players))
```

player | years |
---|---|

A.J. Griffin | 2012, 2013 |

A.J. Hinch | 1998, 1999, 2000 |

Aaron Cunningham | 2008, 2009 |

Aaron Harang | 2002, 2003 |

Aaron Small | 1996, 1997, 1998 |

Adam Dunn | 2014 |

... | ... |

## Current 40-man rosters

Major League Baseball has the 40-man rosters for each team on their
site. In order to extract them, we create a list of the team identifiers
(`oak`, `sf`, etc.), then loop over this list, grabbing the team
name and all the player names. We also set up lists for the team names
(“Athletics”, “Giants”, etc.) so we can replace the short identifiers
with real names later.

```
teams=c("ana", "ari", "atl", "bal", "bos", "cws", "chc", "cin", "cle", "col",
"det", "mia", "hou", "kc", "la", "mil", "min", "nyy", "nym", "oak",
"phi", "pit", "sd", "sea", "sf", "stl", "tb", "tex", "tor", "was")
team_names = c("Angels", "Diamondbacks", "Braves", "Orioles", "Red Sox",
"White Sox", "Cubs", "Reds", "Indians", "Rockies", "Tigers",
"Marlins", "Astros", "Royals", "Dodgers", "Brewers", "Twins",
"Yankees", "Mets", "Athletics", "Phillies", "Pirates",
"Padres", "Mariners", "Giants", "Cardinals", "Rays", "Rangers",
"Blue Jays", "Nationals")
get_players <- function(team) {
# reads the 40-man roster data for a team, returns a data frame
roster_html <- html(paste("http://www.mlb.com/team/roster_40man.jsp?c_id=",
team,
sep=''))
players <- roster_html %>%
html_nodes("#roster_40_man a") %>%
html_text()
data.frame(team=team, player=players)
}
current_rosters <- ldply(teams, get_players)
save(current_rosters, file="current_rosters.rdata", compress="gzip")
```

Here’s what that data looks like:

```
kable(head(current_rosters))
```

team | player |
---|---|

ana | Jose Alvarez |

ana | Cam Bedrosian |

ana | Andrew Heaney |

ana | Jeremy McBryde |

ana | Mike Morin |

ana | Vinnie Pestano |

... | ... |

# Combine the data

To find out how many players on each Major League team used to play for the A’s we combine the former A’s players with the current rosters using player name. This may not be perfect due to differences in spelling (accented characters being the most likely issue), but the results look pretty good.

```
roster_with_oakland_time <- current_rosters %>%
left_join(oakland_players, by="player") %>%
filter(!is.na(years))
kable(head(roster_with_oakland_time))
```

team | player | years |
---|---|---|

ana | Huston Street | 2005, 2006, 2007, 2008 |

ana | Grant Green | 2013 |

ana | Collin Cowgill | 2012 |

ari | Brad Ziegler | 2008, 2009, 2010, 2011 |

ari | Cliff Pennington | 2008, 2009, 2010, 2011, 2012 |

atl | Trevor Cahill | 2009, 2010, 2011 |

... | ... | ... |

You can see from this table (just the first six rows of the results) that the Angels have three players that were Athletics.

Let’s do the math and find out how many former A’s are on each team’s roster.

```
n_former_players_by_team <-
roster_with_oakland_time %>%
group_by(team) %>%
arrange(player) %>%
summarise(number_of_players=n(),
players=paste(player, collapse=", ")) %>%
arrange(desc(number_of_players)) %>%
inner_join(data.frame(team=teams, team_name=team_names),
by="team") %>%
select(team_name, number_of_players, players)
names(n_former_players_by_team) <- c('Team', 'Number',
'Former Oakland Athletics')
kable(n_former_players_by_team,
align=c('l', 'r', 'r'))
```

Team | Number | Former Oakland Athletics |
---|---|---|

Athletics | 22 | A.J. Griffin, Andy Parrino, Billy Burns, Coco Crisp, Craig Gentry, Dan Otero, Drew Pomeranz, Eric O'Flaherty, Eric Sogard, Evan Scribner, Fernando Abad, Fernando Rodriguez, Jarrod Parker, Jesse Chavez, Josh Reddick, Nate Freiman, Ryan Cook, Sam Fuld, Scott Kazmir, Sean Doolittle, Sonny Gray, Stephen Vogt |

Astros | 5 | Chris Carter, Dan Straily, Jed Lowrie, Luke Gregerson, Pat Neshek |

Braves | 4 | Jim Johnson, Jonny Gomes, Josh Outman, Trevor Cahill |

Rangers | 4 | Adam Rosales, Colby Lewis, Kyle Blanks, Michael Choice |

Angels | 3 | Collin Cowgill, Grant Green, Huston Street |

Cubs | 3 | Chris Denorfia, Jason Hammel, Jon Lester |

Dodgers | 3 | Alberto Callaspo, Brandon McCarthy, Brett Anderson |

Mets | 3 | Anthony Recker, Bartolo Colon, Jerry Blevins |

Yankees | 3 | Chris Young, Gregorio Petit, Stephen Drew |

Rays | 3 | David DeJesus, Erasmo Ramirez, John Jaso |

Diamondbacks | 2 | Brad Ziegler, Cliff Pennington |

Indians | 2 | Brandon Moss, Nick Swisher |

White Sox | 2 | Geovany Soto, Jeff Samardzija |

Tigers | 2 | Rajai Davis, Yoenis Cespedes |

Royals | 2 | Chris Young, Joe Blanton |

Marlins | 2 | Dan Haren, Vin Mazzaro |

Padres | 2 | Derek Norris, Tyson Ross |

Giants | 2 | Santiago Casilla, Tim Hudson |

Nationals | 2 | Gio Gonzalez, Michael Taylor |

Red Sox | 1 | Craig Breslow |

Rockies | 1 | Carlos Gonzalez |

Brewers | 1 | Shane Peterson |

Twins | 1 | Kurt Suzuki |

Phillies | 1 | Aaron Harang |

Mariners | 1 | Seth Smith |

Cardinals | 1 | Matt Holliday |

Blue Jays | 1 | Josh Donaldson |

Pretty cool. I do notice one problem: there are actually two Chris Young’s playing in baseball today. Chris Young the outfielder played for the A’s in 2013 and now plays for the Yankees. There’s also a pitcher named Chris Young who shows up on our list as a former A’s player who now plays for the Royals. This Chris Young never actually played for the A’s. The Retrosheet roster data includes which hand (left and/or right) a player bats and throws with, and it’s possible this could be used with the MLB 40-man roster data to eliminate incorrect joins like this, but even with that enhancement, we still have the problem that we’re joining on things that aren’t guaranteed to uniquely identify a player. That’s the nature of attempting to combine data from different sources.

One other interesting thing. I kept the A’s in the list because the
number of former A’s currently playing for the A’s is a measure of how
much turnover there is within an organization. Of the 40 players on the
current A’s roster, only 22 of them have ever played for the A’s. That
means that 18 came from other teams or are promotions from the minors
that haven’t played for *any* Major League teams yet.

# All teams

## Teams with players on other teams

Now that we’ve looked at how many A’s players have played for other teams, let’s see how the number of players playing for other teams is related to team. My gut feeling is that the A’s will be at the top of this list as a small market, low budget team who is forced to turn players over regularly in order to try and stay competitive.

We already have the data for this, but need to manipulate it in a different way to get the result.

```
teams <- c("ANA", "ARI", "ATL", "BAL", "BOS", "CAL", "CHA", "CHN", "CIN",
"CLE", "COL", "DET", "FLO", "HOU", "KCA", "LAN", "MIA", "MIL",
"MIN", "MON", "NYA", "NYN", "OAK", "PHI", "PIT", "SDN", "SEA",
"SFN", "SLN", "TBA", "TEX", "TOR", "WAS")
team_names <- c("Angels", "Diamondbacks", "Braves", "Orioles", "Red Sox",
"Angels", "White Sox", "Cubs", "Reds", "Indians", "Rockies",
"Tigers", "Marlins", "Astros", "Royals", "Dodgers", "Marlins",
"Brewers", "Twins", "Expos", "Yankees", "Mets", "Athletics",
"Phillies", "Pirates", "Padres", "Mariners", "Giants",
"Cardinals", "Rays", "Rangers", "Blue Jays", "Nationals")
players_on_other_teams <- all_recent_players %>%
group_by(player, team) %>%
summarise(years=paste(year, collapse=", ")) %>%
inner_join(current_rosters, by="player") %>%
mutate(current_team=team.y, former_team=team.x) %>%
select(player, current_team, former_team, years) %>%
inner_join(data.frame(former_team=teams, former_team_name=team_names),
by="former_team") %>%
group_by(former_team_name, current_team) %>%
summarise(n=n()) %>%
group_by(former_team_name) %>%
arrange(desc(n)) %>%
mutate(rank=row_number()) %>%
filter(rank!=1) %>%
summarise(n=sum(n)) %>%
arrange(desc(n))
```

This is a pretty complicated set of operations. The main trick (and possible flaw in the analysis) is to get a list similar to the one we got for the A’s earlier, and eliminate the first row (the number of players on a team who played for that same team in the past) before counting the total players who have played for other teams. It would probably be better to eliminate that case using team name, but the team codes vary between Retrosheet and the MLB roster data.

Here are the results:

```
names(players_on_other_teams) <- c('Former Team', 'Number of players')
kable(players_on_other_teams)
```

Former Team | Number of players |
---|---|

Athletics | 57 |

Padres | 57 |

Marlins | 56 |

Rangers | 55 |

Diamondbacks | 51 |

Braves | 50 |

Yankees | 50 |

Angels | 49 |

Red Sox | 47 |

Pirates | 46 |

Royals | 44 |

Dodgers | 43 |

Mariners | 42 |

Rockies | 42 |

Cubs | 40 |

Tigers | 40 |

Astros | 38 |

Blue Jays | 38 |

Rays | 38 |

White Sox | 38 |

Indians | 35 |

Mets | 35 |

Twins | 33 |

Cardinals | 31 |

Nationals | 31 |

Orioles | 31 |

Reds | 28 |

Brewers | 26 |

Phillies | 25 |

Giants | 24 |

Expos | 4 |

The A’s are indeed on the top of the list, but surprisingly, the Padres are also at the top. I had no idea the Padres had so much turnover. At the bottom of the list are teams like the Giants and Phillies that have been on recent winning streaks and aren’t trading their players to other teams.

## Current players on the same team

We can look at the reverse situation: how many players on the current
roster played for that same team in past years. Instead of removing the
current × former team combination with the highest number, we include
*only* that combination, which is almost certainly the combination where
the former and current team is the same.

```
players_on_same_team <- all_recent_players %>%
group_by(player, team) %>%
summarise(years=paste(year, collapse=", ")) %>%
inner_join(current_rosters, by="player") %>%
mutate(current_team=team.y, former_team=team.x) %>%
select(player, current_team, former_team, years) %>%
inner_join(data.frame(former_team=teams, former_team_name=team_names),
by="former_team") %>%
group_by(former_team_name, current_team) %>%
summarise(n=n()) %>%
group_by(former_team_name) %>%
arrange(desc(n)) %>%
mutate(rank=row_number()) %>%
filter(rank==1,
former_team_name!="Expos") %>%
summarise(n=sum(n)) %>%
arrange(desc(n))
names(players_on_same_team) <- c('Team', 'Number of players')
kable(players_on_same_team)
```

Team | Number of players |
---|---|

Rangers | 31 |

Rockies | 31 |

Twins | 30 |

Giants | 29 |

Indians | 29 |

Cardinals | 28 |

Mets | 28 |

Orioles | 28 |

Tigers | 28 |

Brewers | 27 |

Diamondbacks | 27 |

Mariners | 27 |

Phillies | 27 |

Reds | 26 |

Royals | 26 |

Angels | 25 |

Astros | 25 |

Cubs | 25 |

Nationals | 25 |

Pirates | 25 |

Rays | 25 |

Red Sox | 24 |

Blue Jays | 23 |

Athletics | 22 |

Marlins | 22 |

Padres | 22 |

Yankees | 22 |

Dodgers | 21 |

White Sox | 20 |

Braves | 13 |

The A’s are near the bottom of this list, along with other teams that
have been retooling because of a lack of recent success such as the
Yankees and Dodgers. You would think there would be an inverse relationship
between this table and the previous one (if a lot of your former players are
currently playing on other teams they’re not playing on *your* team), but this
isn’t always the case. The White Sox, for example, only have 20 players on
their roster that were Sox in the past, and there aren’t very many of them
playing on other teams either. Their current roster must have been developed
from their own farm system or international signings, rather than by exchanging
players with other teams.

# Introduction

One of the best sources of weather data in the United States comes from the National Weather Service's Cooperative Observer Network (COOP), which is available from NCDC. It's daily data, collected by volunteers at more than 10,000 locations. We participate in this program at our house (station id DW1454 / GHCND:USC00503368), collecting daily minimum and maximum temperature, liquid precipitation, snowfall and snow depth. We also collect river heights for Goldstream Creek as part of the Alaska Pacific River Forecast Center (station GSCA2). Traditionally, daily temperature measurements were collecting using a minimum maximum thermometer, which meant that the only way to calculate average daily temperature was by averaging the minimum and maximum temperature. Even though COOP observers typically have an electronic instrument that could calculate average daily temperature from continuous observations, the daily minimum and maximum data is still what is reported.

In an earlier post we looked at methods used to calculate average daily temperature, and if there are any biases present in the way the National Weather Service calculates this using the average of the minimum and maximum daily temperature. We looked at five years of data collected at my house every five minutes, comparing the average of these temperatures against the average of the daily minimum and maximum. Here, we will be repeating this analysis using data from the Climate Reference Network stations in the United States.

The US Climate Reference Network is a collection of 132 weather stations that are properly sited, maintained, and include multiple redundant measures of temperature and precipitation. Data is available from http://www1.ncdc.noaa.gov/pub/data/uscrn/products/ and includes monthly, daily, and hourly statistics, and sub-hourly (5-minute) observations. We’ll be focusing on the sub-hourly data, since it closely matches the data collected at my weather station.

A similar analysis using daily and hourly CRN data appears here.

# Getting the raw data

I downloaded all the data using the following Unix commands:

```
$ wget http://www1.ncdc.noaa.gov/pub/data/uscrn/products/stations.tsv
$ wget -np -m http://www1.ncdc.noaa.gov/pub/data/uscrn/products/subhourly01/
$ find www1.ncdc.noaa.gov/ -type f -name 'CRN*.txt' -exec gzip {} \;
```

The code to insert all of this data into a database can be found
here.
Once inserted, I have a table named `crn_stations` that has the
station data, and one named `crn_subhourly` with the five minute
observation data.

# Methods

Once again, we’ll use R to read the data, process it, and produce plots.

## Libraries

Load the libraries we need:

```
library(dplyr)
library(lubridate)
library(ggplot2)
library(scales)
library(grid)
```

Connect to the database and load the data tables.

```
noaa_db <- src_postgres(dbname="noaa", host="mason")
crn_stations <- tbl(noaa_db, "crn_stations") %>%
collect()
crn_subhourly <- tbl(noaa_db, "crn_subhourly")
```

Remove observations without temperature data, group by station and date, calculate average daily temperature using the two methods, remove any daily data without a full set of data, and collect the results into an R data frame. This looks very similar to the code used to analyze the data from my weather station.

```
crn_daily <-
crn_subhourly %>%
filter(!is.na(air_temperature)) %>%
mutate(date=date(timestamp)) %>%
group_by(wbanno, date) %>%
summarize(t_mean=mean(air_temperature),
t_minmax_avg=(min(air_temperature)+
max(air_temperature))/2.0,
n=n()) %>%
filter(n==24*12) %>%
mutate(anomaly=t_minmax_avg-t_mean) %>%
select(wbanno, date, t_mean, t_minmax_avg, anomaly) %>%
collect()
```

The two types of daily average temperatures are calculated in this step:

```
summarize(t_mean=mean(air_temperature),
t_minmax_avg=(min(air_temperature)+
max(air_temperature))/2.0)
```

Where `t_mean` is the value calculated from all 288 five minute
observations, and `t_minmax_avg` is the value from the daily minimum
and maximum.

Now we join the observation data with the station data. This attaches station information such as the name and latitude of the station to each record.

```
crn_daily_stations <-
crn_daily %>%
inner_join(crn_stations, by="wbanno") %>%
select(wbanno, date, state, location, latitude, longitude,
t_mean, t_minmax_avg, anomaly)
```

Finally, save the data so we don’t have to do these steps again.

```
save(crn_daily_stations, file="crn_daily_averages.rdata")
```

# Results

Here are the overall results of the analysis.

```
summary(crn_daily_stations$anomaly)
```

## Min. 1st Qu. Median Mean 3rd Qu. Max. ## -11.9000 -0.1028 0.4441 0.4641 1.0190 10.7900

The average anomaly across all stations and all dates is 0.44 degrees Celsius (0.79 degrees Farenheit). That’s a pretty significant error. Half the data is between −0.1 and 1.0°C (−0.23 and +1.8°F) and the full range is −11.9 to +10.8°C (−21.4 to +19.4°F).

# Plots

Let’s look at some plots.

## Raw data by latitude

To start, we’ll look at all the anomalies by station latitude. The plot only shows one percent of the actual anomalies because plotting 512,460 points would take a long time and the general pattern is clear from the reduced data set.

```
set.seed(43)
p <- ggplot(data=crn_daily_stations %>% sample_frac(0.01),
aes(x=latitude, y=anomaly)) +
geom_point(position="jitter", alpha="0.2") +
geom_smooth(method="lm", se=FALSE) +
theme_bw() +
scale_x_continuous(name="Station latitude", breaks=pretty_breaks(n=10)) +
scale_y_continuous(name="Temperature anomaly (degrees C)",
breaks=pretty_breaks(n=10))
print(p)
```

The clouds of points show the differences between the min/max daily average and the actual daily average temperature, where numbers above zero represent cases where the min/max calculation overestimates daily average temperature. The blue line is the fit of a linear model relating latitude with temperature anomaly. We can see that the anomaly is always positive, averaging around half a degree at lower latitudes and drops somewhat as we proceed northward. You also get a sense from the actual data of how variable the anomaly is, and at what latitudes most of the stations are found.

Here are the regression results:

```
summary(lm(anomaly ~ latitude, data=crn_daily_stations))
```

## ## Call: ## lm(formula = anomaly ~ latitude, data = crn_daily_stations) ## ## Residuals: ## Min 1Q Median 3Q Max ## -12.3738 -0.5625 -0.0199 0.5499 10.3485 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 0.7403021 0.0070381 105.19 <2e-16 *** ## latitude -0.0071276 0.0001783 -39.98 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.9632 on 512458 degrees of freedom ## Multiple R-squared: 0.00311, Adjusted R-squared: 0.003108 ## F-statistic: 1599 on 1 and 512458 DF, p-value: < 2.2e-16

The overall model and coefficients are highly significant, and show a slight decrease in the positive anomaly as we move farther north. Perhaps this is part of the reason why the analysis of my station (at a latitude of 64.89) showed an average anomaly close to zero (−0.07°C / −0.13°F).

## Anomalies by month and latitude

One of the results of our earlier analysis was a seasonal pattern in the anomalies at our station. Since we also know there is a latitudinal pattern, in the data, let’s combine the two, plotting anomaly by month, and faceting by latitude.

Station latitude are binned into groups for plotting, and the plots themselves show the range that cover half of all anomalies for that latitude category × month. Including the full range of anomalies in each group tends to obscure the overall pattern, and the plot of the raw data didn’t show an obvious skew to the rarer anomalies.

Here’s how we set up the data frames for the plot.

```
crn_daily_by_month <-
crn_daily_stations %>%
mutate(month=month(date),
lat_bin=factor(ifelse(latitude<30, '<30',
ifelse(latitude>60, '>60',
paste(floor(latitude/10)*10,
(floor(latitude/10)+1)*10,
sep='-'))),
levels=c('<30', '30-40', '40-50',
'50-60', '>60')))
summary_stats <- function(l) {
s <- summary(l)
data.frame(min=s['Min.'],
first=s['1st Qu.'],
median=s['Median'],
mean=s['Mean'],
third=s['3rd Qu.'],
max=s['Max.'])
}
crn_by_month_lat_bin <-
crn_daily_by_month %>%
group_by(month, lat_bin) %>%
do(summary_stats(.$anomaly)) %>%
ungroup()
station_years <-
crn_daily_by_month %>%
mutate(year=year(date)) %>%
group_by(wbanno, lat_bin) %>%
summarize() %>%
group_by(lat_bin) %>%
summarize(station_years=n())
```

And the plot itself. At the end, we’re using a function called
`facet_adjust`, which adds x-axis tick labels to the facet on the
right that wouldn't ordinarily have them. The code comes from this
stack overflow
post.

```
p <- ggplot(data=crn_by_month_lat_bin,
aes(x=month, ymin=first, ymax=third, y=mean)) +
geom_hline(yintercept=0, alpha=0.2) +
geom_hline(data=crn_by_month_lat_bin %>%
group_by(lat_bin) %>%
summarize(mean=mean(mean)),
aes(yintercept=mean), colour="darkorange", alpha=0.5) +
geom_pointrange() +
facet_wrap(~ lat_bin, ncol=3) +
geom_text(data=station_years, size=4,
aes(x=2.25, y=-0.5, ymin=0, ymax=0,
label=paste('n =', station_years))) +
scale_y_continuous(name="Range including 50% of temperature anomalies") +
scale_x_discrete(breaks=1:12,
labels=c('Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun',
'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec')) +
theme_bw() +
theme(axis.text.x=element_text(angle=45, hjust=1, vjust=1.25),
axis.title.x=element_blank())
facet_adjust(p)
```

Each plot shows the range of anomalies from the first to the third quartile (50% of the observed anomalies) by month, with the dot near the middle of the line at the mean anomaly. The orange horizontal line shows the overall mean anomaly for that latitude category, and the count at the bottom of the plot indicates the number of “station years” for that latitude category.

It’s clear that there are seasonal patterns in the differences between the mean daily temperature and the min/max estimate. But each plot looks so different from the next that it’s not clear if the patterns we are seeing in each latitude category are real or artificial. It is also problematic that three of our latitude categories have very little data compared with the other two. It may be worth performing this analysis in a few years when the lower and higher latitude stations have a bit more data.

# Conclusion

This analysis shows that there is a clear bias in using the average of minimum and maximum daily temperature to estimate average daily temperature. Across all of the CRN stations, the min/max estimator overestimates daily average temperature by almost a half a degree Celsius (0.8°F).

We also found that this error is larger at lower latitudes, and that there are seasonal patterns to the anomalies, although the seasonal patterns don’t seem to have clear transitions moving from lower to higher latitudes.

The current length of the CRN record is quite short, especially for the sub-hourly data used here, so the patterns may not be representative of the true situation.