When Tigers slugger Miguel Cabrera won the Triple Crown last year by leading the league in batting average, home runs and Runs Batted In, he became the first to do so since Red Sox outfielder Carl Yatrzemski in 1967. It was also the first time the Triple Crown winner was broadly questioned by statistical analysts who now use different statistics to evaluate hitters. It was clearly a memorable event from a historical perspective and traditional Tigers fans were understandably miffed that some seemed to be devaluing Cabrera's accomplishment. Personally, I am a traditional enough fan to have enjoyed the feat when it happened, but there were also some things about it that bothered me.
Many regarded Cabrera's season as extraordinary because he won the Triple Crown, and it was a special season symbolically, but it wasn't a remarkable season for him. He hit for a higher On-Base Percentage plus Slugging Average (OPS) and had more Batting Runs in both 2010 and 2011, two statistics which better measure a player's individual batting contribution that the Triple Crown statistics. He missed out on the Triple Crown those years because other players happened to have great seasons in the triple crown categories at the same time.
Cabrera is off to an even better start this year and there is talk about another Triple Crown. That would make him the first back-to-back triple crown winner in history which would be really cool. Suppose though that he has a monster season which surpasses anything he has ever done this and doesn't win the Triple Crown? He could bat 375 with 45 home runs and 160 RBI, and miss the crown because teammate Prince Fielder hits 46 homers. Does his Triple Crown season remain special?
There is no perfect way to summarize a players batting performance, but the triple crown statistics have become outdated as the ultimate measures of success. Most readers of this blog understand the limitations of the batting average/ home runs/ RBI trio. For anyone who needs a refresher, I discussed them in an earlier post. The Triple Crown idea is still appealing, but it would be more meaningful with a more modern trio of statistics.
Some have proposed that the increasingly popular slash line metrics
(batting average/ on-base percentage/ slugging average) be used as the
new triple crown. This trio provides a good summary of offensive
production combining the ability to hit for average, to get on base and
to hit for power. I don't like this threesome much better than the traditional numbers for the triple
crown though. The problem with the slash line statistics is that they
are all rate statistics which do not address playing time.
The Triple Crown should also exclude summary statistics such as OPS. The purpose of the triple crown is to combine three different batter qualities, rather than have one number which mashes everything together. I also don't want anything which includes estimates such as Weighted On-Base Average (wOBA) even if it weren't a summary metric. This is a good measure of batting talent, but I want something that traditional fans can actual count or calculate.
What is needed is a trio which is comprehensive and
relevant but simple enough so as not to turn away the masses. I'll stay with the slash line theme, but I'll tweak it so that it
incorporates playing time. The counting statistic equivalents to
BA/OBP/SLG are hits/times on base/ total bases which are three basic
enough statistics. To stay parallel with the traditional crown, I'll
use one rate statistic and two counting metrics
I don't like using hits as a counting metric because it is biased in
favor of players who rarely draw walks, which is generally not a
positive attribute. While the hits leader is usually a very good batter,
it's better to stick with batting average. Since there is really
nothing about accumulating times on base and total bases which can be
considered negative, those can be left as counting statistics.
So, that's my Alternative Triple Crown - batting average, times on
base and total bases. It addresses everything that a good hitter does -
hit for average, get on base and hit for power. Unlike the traditional crown, it does not fail to reward walks and extra base hits which are not homers. It considers both
excellence and playing time and it's simple.
It turns out that Cabrera did not win the Alternative Triple Crown last year. He finished first in batting average (.330) and Total Bases (377), but was second in Times On Base to (274 versus 284 for Fielder).
This year, Cabrera is leading the league in all three categories with a .387 batting average, 114 Total Bases and 90 Times on Base.
So, let the Alternative Triple Crown watch begin.
Tuesday, May 21, 2013
Saturday, May 18, 2013
Does Rick Porcello Finally Have a Strikeout Pitch?
After seeing ace Justin Verlander allow eight runs in less than three innings to the powerful Texas Rangers on Thursday, Tigers fans feared the worst when Rick Porcello took the mound last night. Porcello silenced doubters with a strong performance against a tough line-up allowing just one run while striking out six in 5 2/3 innings. This was Porcello's fourth solid game since his first-inning meltdown versus the Angels on April 20. During that span, he has a 3.24 ERA and 24/5 K/BB ratio over 25 innings.
The most encouraging feature of the above statistical line is the high strikeout total. According to Porcello's game logs on Baseball-Reference.com, he has struck out six plus batters in his last three games. This is hardly an impressive feat on a staff which features strikeout artists such as Anibal Sanchez, Max Scherzer and Verlander. However, it is the first such three-game string of Porcello's career.
I wanted to see which pitches the strikeouts came on, so I checked the Game Day results of his last three games at MLB.COM. THey were as follows:
May 2 versus Houston
Change-up swinging
Change-up swinging
four-seam fastball called
Change-up called
Curveball called
Change-up swinging
Four-seam fastball swinging
May 12 versus Cleveland
Change-up swinging
Sinker called
Sinker called
Sinker swinging
Change-up called
Four-seam fastball called
May 17 versus Texas
Four-seam swinging
Change-up swinging
Change-up swinging
Change-up swinging
Curveball swinging
Curveball called
If you count them up, you'll see the following totals:
Change-ups 9
Four-seam fastballs 4
Sinkers 3
Curves 3
So, he is making good use his change-up which is something that Jeff Roberts of Eye on the Tigers noted earlier this week. Roberts used FanGraphs data to show that it has been Porcello's most improved pitch this year in terms of linear weights results.
Porcello has had good stretches before where he prevented runs with good control and lots of ground balls, but his inability to miss bats (only five strikeouts per nine innings for his career) has always come back to haunt him. His annual strikeouts by pitch according to Brooks Baseball.net (plus last night's game) are shown in the table below. (You may notice that the strikeout totals in the bottom row are not quite right in some cases, but I trust that the Brooks Baseball pitch type data are the most accurate available.
Table 1: Rick Porcello's Strikeouts by Pitch Type
Data source: Brooks Baseball.net
The most striking number on the table is the 13 strikeouts on change-ups already in 2013, nine of which came in the last three games. This is remarkable because Porcello has never struck out more than 14 on his change in any season. Some of that is due to increased usage of the pitch which is a good thing if it's working. Time will tell whether he can maintain the effectiveness of his change throughout a full season, but it's encouraging and something to watch in his upcoming starts.
The most encouraging feature of the above statistical line is the high strikeout total. According to Porcello's game logs on Baseball-Reference.com, he has struck out six plus batters in his last three games. This is hardly an impressive feat on a staff which features strikeout artists such as Anibal Sanchez, Max Scherzer and Verlander. However, it is the first such three-game string of Porcello's career.
I wanted to see which pitches the strikeouts came on, so I checked the Game Day results of his last three games at MLB.COM. THey were as follows:
May 2 versus Houston
Change-up swinging
Change-up swinging
four-seam fastball called
Change-up called
Curveball called
Change-up swinging
Four-seam fastball swinging
May 12 versus Cleveland
Change-up swinging
Sinker called
Sinker called
Sinker swinging
Change-up called
Four-seam fastball called
May 17 versus Texas
Four-seam swinging
Change-up swinging
Change-up swinging
Change-up swinging
Curveball swinging
Curveball called
If you count them up, you'll see the following totals:
Change-ups 9
Four-seam fastballs 4
Sinkers 3
Curves 3
So, he is making good use his change-up which is something that Jeff Roberts of Eye on the Tigers noted earlier this week. Roberts used FanGraphs data to show that it has been Porcello's most improved pitch this year in terms of linear weights results.
Porcello has had good stretches before where he prevented runs with good control and lots of ground balls, but his inability to miss bats (only five strikeouts per nine innings for his career) has always come back to haunt him. His annual strikeouts by pitch according to Brooks Baseball.net (plus last night's game) are shown in the table below. (You may notice that the strikeout totals in the bottom row are not quite right in some cases, but I trust that the Brooks Baseball pitch type data are the most accurate available.
Table 1: Rick Porcello's Strikeouts by Pitch Type
|
Pitch type
|
2009
|
2010
|
2011
|
2012
|
2013
|
|
Four-seam fastball
|
25
|
22
|
24
|
17
|
3
|
|
Sinker
|
33
|
30
|
36
|
55
|
7
|
|
Slider
|
11
|
23
|
37
|
17
|
4
|
|
Curveball
|
7
|
1
|
5
|
4
|
4
|
|
Change-up
|
12
|
10
|
14
|
14
|
13
|
|
Totals
|
88
|
86
|
118
|
107
|
27
|
Data source: Brooks Baseball.net
The most striking number on the table is the 13 strikeouts on change-ups already in 2013, nine of which came in the last three games. This is remarkable because Porcello has never struck out more than 14 on his change in any season. Some of that is due to increased usage of the pitch which is a good thing if it's working. Time will tell whether he can maintain the effectiveness of his change throughout a full season, but it's encouraging and something to watch in his upcoming starts.
Thursday, May 16, 2013
Verlander's Worst Game Ever?
Tonight's pitching duel between aces Yu Darvish and Justin Velander did not live up to its' advance billing as Darvish was mediocre and Verlander was awful. So, instead of admiring a masterpiece, Tigers fan discussed on Twitter whether this was Verlander's worst game ever. Everybody had their own opinion on Verlander's worst game, but this game was certainly among them.
One way to measure the strength of a game by a pitcher is by Bill James' Game Score metric. It is computed as follows:
Prior to today's game, Verlander's 2013 game scores ranged from 43 to 80 with an average of 62. Today, he allowed 8 runs on 6 hits and 2 walks in just 2 2/3 innings and ended with a Game Score of 15. According to Baseball-Reference, that was tied for his worst game score ever. The others are listed in Table 1 below.
Table 1: Justin Verlander's Worst Game Scores Ever
Data source: Baseball-Reference
Verlander's worst games ever included seven runs in 2 1/3 innings versus the Indians during his rookie year in 2006. He failed to get though two innings allowing 8 runs (5 earned) against the Yankees in September, 2008. He also allowed 8 runs in 3 2/3 innings on opening day in Toronto in 2009.
Verlander was just as bad tonight, but it could have been worse. Tigers right hander Scott Sanders once had a game score of -15 (Negative 15) in a game in 1998 where he gave up 11 runs on 16 hits in 4 innings.
One way to measure the strength of a game by a pitcher is by Bill James' Game Score metric. It is computed as follows:
- Start at 50 points.
- Add one point for each out recorded.
- Add two for each inning pitched after the fourth.
- Add one for each strikeout.
- Subtract two for each hit.
- Subtract four for each earned run.
- Subtract two for each unearned run.
- Subtract one for each walk
Prior to today's game, Verlander's 2013 game scores ranged from 43 to 80 with an average of 62. Today, he allowed 8 runs on 6 hits and 2 walks in just 2 2/3 innings and ended with a Game Score of 15. According to Baseball-Reference, that was tied for his worst game score ever. The others are listed in Table 1 below.
Table 1: Justin Verlander's Worst Game Scores Ever
Date
|
Opponent
|
IP
|
H
|
R
|
ER
|
BB
|
K
|
GS
|
04/13/2006
|
CLE
|
2 1/3
|
7
|
7
|
7
|
1
|
0
|
15
|
09/01/2008
|
NYY
|
1 2/3
|
7
|
8
|
5
|
2
|
2
|
15
|
04/06/2009
|
@ TOR
|
3 2/3
|
8
|
8
|
8
|
2
|
4
|
15
|
05/16/2013
|
@TEX
|
2 2/3
|
6
|
8
|
8
|
2
|
3
|
15
|
Verlander's worst games ever included seven runs in 2 1/3 innings versus the Indians during his rookie year in 2006. He failed to get though two innings allowing 8 runs (5 earned) against the Yankees in September, 2008. He also allowed 8 runs in 3 2/3 innings on opening day in Toronto in 2009.
Verlander was just as bad tonight, but it could have been worse. Tigers right hander Scott Sanders once had a game score of -15 (Negative 15) in a game in 1998 where he gave up 11 runs on 16 hits in 4 innings.
Wednesday, May 15, 2013
Anibal Sanchez Among Early Pitching Leaders
Today, I'll take my first look at some of my favorite sabermetrics pitching leaders. Most readers
of this blog are aware of the limitations of ERA in evaluating pitcher
performance. Two of the biggest issues are:
Because they are based on things that pitchers essentially control, the DIPS metrics are said to be better measures of true talent than ERA. As a result, they are also better than ERA at predicting future performance. However, they only measure a portion of a pitcher's talent and should be used as complements to ERA rather than as replacements.
It is not known exactly how much control pitchers have on the results of balls in play, but recent research tells us that some pitchers are better than others at preventing hits on balls in play. For example, Mike Fast, formerly of Baseball Prospectus and now a MLB sabermetrician, used Sportsvision's hit f/x data to show how pitchers varied on the speed of balls off the bat.
So, rather than making the big leap from ERA to FIP, it might be a good idea meet half way. Instead of removing hit prevention and sequencing in one step, it might be better to remove one factor at a time. Bill James did that with his Component ERA (ERC). Applying the runs created methodology to pitchers, he determined what a pitcher's ERA should have been based on walks, hit batsmen, strikeouts, homers AND hits allowed. I'm going to look at some similar statistics here based on more modern measures such as linear weights and Base Runs.
We often use Weighted On-Base Average (wOBA) to measure overall hitting performance and it can also be used for pitchers. The American League wOBA Against (wOBAA) leaders are shown in Table 1 below. Hishashi Iwakuma of the Mariners currently leads the league with a .208 wOBAA. The top Tiger is Anibal Sanchez, sixth in the AL at .251. Max Scherzer was 11th prior at .267 prior to today, but likely dropped down the list quite a bit with today's performance. Justin Verlander (.267) and Doug Fister (.287) are 12th and 18th respectively.
Table 1: AL wOBA Against Leaders
Data source: Baseball-Reference
It's generally a good to convert to runs allowed when trying to evaluate pitchers, so I'll do that next. The Base Runs measure was created by David Smythe in the early 1990s. It is based on the idea that we can estimate team runs scored if we know the number of base runners, total bases, home runs and the typical score rate (the score rate is the percentage of base runners that score on average). Base Runs also works well for individual pitchers. The complete formula can be found here.
Sanchez has 16 Base Runs Against in 52 2/3 innings so far this year. This means that he should have allowed an estimated 16 runs based on the number of base runners, total bases and home runs he has allowed. He has allowed 14 actual runs, so runs are scoring against him at a slightly lower rate than you would expect so far. That could possibly be due to good defense, unfortunate timing or just bad luck on locations of batted balls.
Sanchez has 10 Base Runs Above Average (RAA) which means that he has saved the Tigers an estimated 10 runs compared to the average pitcher in the same number of innings. Table 2 shows that he is ninth in the league on that metric. Iwakuma is the league leader at 14. Other Tigers among the leaders include Verlander and Fister, both with 8.
Table 2: AL Runs Saved Leaders
Data source: Baseball-Reference
Finally, Table 3 shows that Sanchez has allowed 2.69 Base Runs per nine innings. About 93% of runs are earned, so multiply this result by .93. to put it on the same scale as ERA. The final result is a weighted component ERA. Although, I am not using linear weights here, I call it WERC because others have said they like the name. It's really not a novel idea though. Patriot of Walk Like a Saber has been using Base Runs to evaluate pitchers for a while but prefers to not convert to the ERA scale.
Getting back to the example, Sanchez has a 2.50 WERC which places him seventh in the league. Once again, Iwakuma (1.85) is the AL leader.
Table 3: AL WERC Leaders
Data source: Baseball-Reference
Some may have noticed that the Tigers rank lower on WERC than FIP which had their big four starters - Sanchez, Verlander, Scherzer and Fister - all in the top eight entering today. The FIP metric, of course does not involve hits allowed. The Tigers starters have been allowing a lot of hits on balls in play as all four have BABIPs of .312 or greater. You could blame this on poor fielding or bad luck, but we don't know to what extent that's true. Therefore, it's useful to see where they stand if hits are taken into account.
I would guess that the Tigers FIPs and WERCs will move closer together as the season progresses. I'll update these numbers again when we have a larger sample size.
- ERA gives pitchers full credit/blame for results of batted balls in play despite the fact that they share that responsibility with fielders. For example, a pitcher with a strong defense behind him will tend to give up fewer hits (and thus fewer runs) than if he has a poor defense behind him.
- ERA gives pitchers full responsibility for sequencing or timing of events, that is, it assumes that they can control when they give up hits and walks. For example, if a pitcher pitches extraordinarily well with runners in scoring position in a given year, he will have a lower ERA than if he had a typical year in those situations. Additionally, a pitcher who tends to bunch base runners together in single innings will have a higher ERA than if he had a typical year distributing base runners more evenly.
Because they are based on things that pitchers essentially control, the DIPS metrics are said to be better measures of true talent than ERA. As a result, they are also better than ERA at predicting future performance. However, they only measure a portion of a pitcher's talent and should be used as complements to ERA rather than as replacements.
It is not known exactly how much control pitchers have on the results of balls in play, but recent research tells us that some pitchers are better than others at preventing hits on balls in play. For example, Mike Fast, formerly of Baseball Prospectus and now a MLB sabermetrician, used Sportsvision's hit f/x data to show how pitchers varied on the speed of balls off the bat.
So, rather than making the big leap from ERA to FIP, it might be a good idea meet half way. Instead of removing hit prevention and sequencing in one step, it might be better to remove one factor at a time. Bill James did that with his Component ERA (ERC). Applying the runs created methodology to pitchers, he determined what a pitcher's ERA should have been based on walks, hit batsmen, strikeouts, homers AND hits allowed. I'm going to look at some similar statistics here based on more modern measures such as linear weights and Base Runs.
We often use Weighted On-Base Average (wOBA) to measure overall hitting performance and it can also be used for pitchers. The American League wOBA Against (wOBAA) leaders are shown in Table 1 below. Hishashi Iwakuma of the Mariners currently leads the league with a .208 wOBAA. The top Tiger is Anibal Sanchez, sixth in the AL at .251. Max Scherzer was 11th prior at .267 prior to today, but likely dropped down the list quite a bit with today's performance. Justin Verlander (.267) and Doug Fister (.287) are 12th and 18th respectively.
Table 1: AL wOBA Against Leaders
Team
|
G
|
IP
|
wOBAA
|
|
Hisashi
Iwakuma
|
SEA
|
8
|
51.2
|
.208
|
Yu
Darvish
|
TEX
|
8
|
52.2
|
.240
|
Clay
Buchholz
|
BOS
|
8
|
58.2
|
.244
|
Felix
Hernandez
|
SEA
|
9
|
64.2
|
.246
|
James
Shields
|
KCR
|
8
|
58.0
|
.247
|
Anibal
Sanchez
|
DET
|
8
|
52.2
|
.251
|
Jon
Lester*
|
BOS
|
8
|
52.2
|
.252
|
Chris
Sale*
|
CHW
|
8
|
56.1
|
.258
|
Hiroki
Kuroda
|
NYY
|
8
|
50.2
|
.259
|
Derek
Holland*
|
TEX
|
8
|
55.1
|
.261
|
Max
Scherzer
|
DET
|
7
|
47.1
|
.267
|
Justin
Verlander
|
DET
|
8
|
51.1
|
.268
|
Matt
Moore*
|
TBR
|
8
|
48.0
|
.275
|
Justin
Masterson
|
CLE
|
9
|
63.0
|
.277
|
Ervin
Santana
|
KCR
|
7
|
48.1
|
.284
|
Jake
Peavy
|
CHW
|
7
|
45.2
|
.285
|
Doug
Fister
|
DET
|
8
|
50.0
|
.287
|
Zach
McAllister
|
CLE
|
7
|
43.2
|
.291
|
Wei-Yin Chen*
|
BAL
|
8
|
47.1
|
.292
|
A.J.
Griffin
|
OAK
|
8
|
51.2
|
.300
|
Data source: Baseball-Reference
It's generally a good to convert to runs allowed when trying to evaluate pitchers, so I'll do that next. The Base Runs measure was created by David Smythe in the early 1990s. It is based on the idea that we can estimate team runs scored if we know the number of base runners, total bases, home runs and the typical score rate (the score rate is the percentage of base runners that score on average). Base Runs also works well for individual pitchers. The complete formula can be found here.
Sanchez has 16 Base Runs Against in 52 2/3 innings so far this year. This means that he should have allowed an estimated 16 runs based on the number of base runners, total bases and home runs he has allowed. He has allowed 14 actual runs, so runs are scoring against him at a slightly lower rate than you would expect so far. That could possibly be due to good defense, unfortunate timing or just bad luck on locations of batted balls.
Sanchez has 10 Base Runs Above Average (RAA) which means that he has saved the Tigers an estimated 10 runs compared to the average pitcher in the same number of innings. Table 2 shows that he is ninth in the league on that metric. Iwakuma is the league leader at 14. Other Tigers among the leaders include Verlander and Fister, both with 8.
Table 2: AL Runs Saved Leaders
Player
|
Team
|
G
|
IP
|
Base
Runs
|
RAA
|
Hisashi
Iwakuma
|
SEA
|
8
|
51.2
|
11
|
14
|
Clay
Buchholz
|
BOS
|
8
|
58.2
|
15
|
13
|
Felix
Hernandez
|
SEA
|
9
|
64.2
|
18
|
13
|
James
Shields
|
KCR
|
8
|
58.0
|
16
|
13
|
Yu
Darvish
|
TEX
|
8
|
52.2
|
14
|
11
|
Chris
Sale*
|
CHW
|
8
|
56.1
|
17
|
10
|
Justin
Masterson
|
CLE
|
9
|
63.0
|
21
|
10
|
Jon
Lester*
|
BOS
|
8
|
52.2
|
15
|
10
|
Anibal
Sanchez
|
DET
|
8
|
52.2
|
16
|
10
|
Derek
Holland*
|
TEX
|
8
|
55.1
|
18
|
9
|
Hiroki
Kuroda
|
NYY
|
8
|
50.2
|
15
|
9
|
Justin
Verlander
|
DET
|
8
|
51.1
|
17
|
8
|
Doug
Fister
|
DET
|
8
|
50.0
|
17
|
8
|
Max
Scherzer
|
DET
|
7
|
47.1
|
16
|
7
|
Wei-Yin
Chen*
|
BAL
|
8
|
47.1
|
18
|
5
|
Finally, Table 3 shows that Sanchez has allowed 2.69 Base Runs per nine innings. About 93% of runs are earned, so multiply this result by .93. to put it on the same scale as ERA. The final result is a weighted component ERA. Although, I am not using linear weights here, I call it WERC because others have said they like the name. It's really not a novel idea though. Patriot of Walk Like a Saber has been using Base Runs to evaluate pitchers for a while but prefers to not convert to the ERA scale.
Getting back to the example, Sanchez has a 2.50 WERC which places him seventh in the league. Once again, Iwakuma (1.85) is the AL leader.
Table 3: AL WERC Leaders
Player
|
Team
|
G
|
IP
|
Base
Runs/9 IP
|
WERC
|
Hisashi
Iwakuma
|
SEA
|
8
|
51.2
|
1.99
|
1.85
|
Clay
Buchholz
|
BOS
|
8
|
58.2
|
2.33
|
2.17
|
James
Shields
|
KCR
|
8
|
58.0
|
2.42
|
2.25
|
Yu
Darvish
|
TEX
|
8
|
52.2
|
2.43
|
2.26
|
Felix
Hernandez
|
SEA
|
9
|
64.2
|
2.55
|
2.37
|
Jon
Lester*
|
BOS
|
8
|
52.2
|
2.65
|
2.47
|
Anibal
Sanchez
|
DET
|
8
|
52.2
|
2.69
|
2.50
|
Chris
Sale*
|
CHW
|
8
|
56.1
|
2.72
|
2.53
|
Hiroki
Kuroda
|
NYY
|
8
|
50.2
|
2.76
|
2.57
|
Derek
Holland*
|
TEX
|
8
|
55.1
|
2.89
|
2.69
|
Justin
Masterson
|
CLE
|
9
|
63.0
|
2.93
|
2.73
|
Justin
Verlander
|
DET
|
8
|
51.1
|
2.96
|
2.75
|
Max
Scherzer
|
DET
|
7
|
47.1
|
2.96
|
2.76
|
Doug
Fister
|
DET
|
8
|
50.0
|
3.03
|
2.82
|
Wei-Yin
Chen*
|
BAL
|
8
|
47.1
|
3.35
|
3.12
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Data source: Baseball-Reference
Some may have noticed that the Tigers rank lower on WERC than FIP which had their big four starters - Sanchez, Verlander, Scherzer and Fister - all in the top eight entering today. The FIP metric, of course does not involve hits allowed. The Tigers starters have been allowing a lot of hits on balls in play as all four have BABIPs of .312 or greater. You could blame this on poor fielding or bad luck, but we don't know to what extent that's true. Therefore, it's useful to see where they stand if hits are taken into account.
I would guess that the Tigers FIPs and WERCs will move closer together as the season progresses. I'll update these numbers again when we have a larger sample size.
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