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## Thursday, April 10, 2003

#### Win Values 2002

Did Barry Zito really deserve the Cy Young Award?

Introduction

Last year I introduced a new stat to measure the value that a starting pitcher brought to his team on a game-by-game basis.  In short, win values assigns a number between -1 and +1 to each starting pitcher for each game to reflect how well the pitcher performed given the run support he was provided.  The win value figure is the difference in probabilities that the starting pitcher?s team would have won the game given its offensive run support with the pitcher?s performance compared to if a league average pitcher would have started in his place.

As an example, a pitcher who wins a game 1-0 is earns a very high number of win value points since his team would very likely have lost the game (scoring only 1 run) with league average pitching.  On the other hand, a pitcher who wins a game 10-0 earns only a few win value points since his team would very likely have won the game (scoring ten runs) with league average pitching.  A complete description of the win value methodology and results from previous seasons is available here.

Win Values: A New Method to Evaluate Starting Pitchers

Top AL Starting Pitchers in 2002

Retrosheet just released the play-by-play data for the 2002 season.  Thus, I am now able to calculate the starting pitcher win values for last season.  The following table presents the top ten starting pitcher performances according to win values in the American League.

I wish to thank David Smith, Tom Ruane, Ray Kerby, Tangotiger, and all the Retrosheet volunteers for making available the 2002 season data.

Table 1:  2002 AL Win Value Leaders

 W-L ERA+ Wins Above Average (WAA) Win Value (relative to league avg) Win Value (relative to replacement) Tim Hudson 15-9 156 4.7 4.75 7.30 Barry Zito 23-5 169 5.2 4.40 7.03 Derek Lowe 21-8 171 5.1 4.27 6.67 Pedro Martinez 20-4 196 5.4 4.11 6.36 Bartolo Colon* 20-8 148 4.2 3.99 6.47 Jarrod Washburn 18-6 138 3.2 3.96 6.36 Roy Halladay 19-7 152 4.5 3.63 6.18 Mark Mulder 19-7 134 2.9 3.60 5.85 Kenny Rogers 13-8 128 2.6 2.73 5.21 Jamie Moyer 13-8 127 2.7 2.51 5.06

The entries in the table are the pitcher?s won-loss record, his park-adjusted ERA relative to league, his wins above average (which is based solely upon his ERA+ and number of innings pitched), his win values relative to a league average pitcher, and his win values relative to a replacement level pitcher.  Bartolo Colon?s stats reflect his pitching in both leagues last season; Colon accumulated 2.78 win values relative to league average in the AL and 1.21 win values in the NL.

As you know, Barry Zito won the 2002 AL Cy Young award, largely due to his 23-5 record.  Pedro Martinez finished second in the voting, with Derek Lowe third; the only other pitcher to appear on a ballot was Jarrod Washburn who got a lone third place vote.

Win values suggests that the AL pitcher who contributed the most to his team last season was Tim Hudson, a pitcher who did not even appear on a single Cy Young ballot.  The reason, of course, is that Huddy only went 15-9 and Cy Young voters are enamored with a pitcher?s won-loss record.

A game-by-game look at Hudson?s season reveals why win values tabs it as the best in the AL.

Table 2:  Tim Hudson?s 2002 Game-by-Game Win Values

 Date Opponent IP* Score when left game** Final Score Hudson W/L/ND Oakland W or L Win Value 4/2 TEX 7 2-1 3-2 ND W .370 4/7 at SEA 6 3-1 6-5 W W .211 4/12 at ANA 7 3-1 5-1 W W .315 4/17 SEA 7 3-4 4-7 L L -.105 4/23 NYA 9 1-2 1-2 L L .219 4/28 CHA 8 10-0 10-0 W W .206 5/4 at CHA 7 2-10 2-10 L L -.341 5/9 BOS 7 1-4 1-5 L L -.128 5/14 at BOS 6 1-6 2-6 L L -.269 5/19 at TOR 7 0-5 0-11 L L -.173 5/24 TBA 6 6-6 9-8 ND W -.276 5/30 at TBA 7 2-1 3-4 ND L .354 6/4 SEA 7 2-2 3-2 ND W .186 6/9 HOU 7 6-1 7-6 ND W .284 6/14 at SFN 7 3-1 3-2 W W .290 6/20 at PIT 8 5-2 5-3 W W .317 6/25 at SEA 6 1-4 1-7 L L -.167 6/30 SFN 9 7-0 7-0 W W .339 7/5 KCA 7 1-1 4-3 ND W .336 7/12 at BAL 8 1-0 1-0 W W .574 7/17 ANA 6 3-5 4-10 L L -.232 7/24 at ANA 7 1-5 1-5 L L -.208 7/29 CLE 7 6-8 6-8 ND L -.480 8/3 DET 7 6-3 8-4 W W .149 8/9 at NYA 7 0-0 3-2 ND W .442 8/14 TOR 8 4-2 4-2 W W .308 8/19 at CLE 9 8-1 8-1 W W .266 8/24 at DET 9 12-3 12-3 W W .081 8/30 MIN 7 4-2 4-2 W W .258 9/4 KCA 7 11-5 12-11 ND W -.014 9/9 at ANA 8 2-1 2-1 W W .406 9/14 SEA 9 1-0 1-0 W W .716 9/19 ANA 8 5-3 5-3 W W .203 9/25 at SEA 7 2-1 2-3 ND L .312

*  Last inning Tim Hudson appeared in (partial innings, including facing one or more batters without recording an out, count as a full inning).

** The score at the conclusion of both halves of the last inning Hudson appeared in; Oakland?s score is given first.

Let me describe Hudson?s first game to make sure the reader understands what is being reported in the table.  The first row indicates that Hudson?s first start of the season was at home against Texas on April 2.  Hudson pitched into the 7th inning, and the score at the conclusion of the 7th inning was 2-1 in favor of Oakland.  The A?s won the game 3-2 (details below).  Hudson got a no-decision in the game.  Hudson?s performance was worth .370 win value points.  That is, Hudson put the A?s into a position (leading 2-1) in which his team had a .370 higher probability of winning the game after 7 innings than if a league average pitcher had started that day for Oakland.

You will see that Hudson?s hard luck stayed with him for the entire season.  Games in which Hudson pitched very well but came up without a victory include the following.

• Left April 2 game vs Texas leading 2-1.  Closer Billy Koch gave up the tying run in the top of the ninth and Oakland won with one run in the bottom of the ninth.

• Complete game 2-1 loss vs the Yankees on April 23.

• Left May 30 game at Tampa Bay leading 2-1; Jim Mecir gave up tying run (then Koch blew another save after Oakland re-took the lead).

• Left June 9 game leading 6-1 vs Houston; after Hudson was removed Mecir immediately proceeded to give up 5 runs without getting an out (ouch).

• Left July 5 game tied 1-1 after which Mecir gave up two runs in the top of the ninth, and then the A?s scored three in the bottom of the ninth to give Mecir the win (in the olden days Hudson would have been credited with the win as he was by far the best A?s pitcher that day).

• Left August 9 game vs Yankees leading 2-0 (the A?s scored two runs in the top of the eighth after the score was tied 0-0 after 7 innings).  Chad Bradford immediately gave up the tying runs, costing Hudson another victory.

• Left September 4 game at Kansas City leading 11-5.  Bradford, Jeff Tam, and Koch managed to give up six runs in two innings (Koch vultured yet another win when the A?s won in the bottom of ninth).

• Finally, in Hudson?s last start of the season, he left the September 25 game at Seattle leading 2-1.  Our old friend Jim Mecir gave up two runs in the bottom of the eighth to cost Hudson yet another victory.

By my count, if neither team had scored any more runs after Hudson left each of his starts, he would have gone 21-9 (with four ties).  Since he actually went 15-9, it is clear that Hudson?s bullpen mates cost him several victories.  In short, Hudson?s W-L record does not do justice to how great a season he actually had.

Barry Zito, Pedro Martinez, and Derek Lowe each had better ERA+ and better W-L records than did Hudson.  So how can their win value be lower?

Seasonal averages can mask a myriad of issues that a detailed game-by-game analysis can take into account.  Zito pitched very well last year but there were several games in which his team did not need him to pitch so great.  For example, here are the scores in six of Zito?s starts when he left the games: 10-3, 11-1, 9-3, 7-0, 7-1, and 8-1.  Even with a league average pitcher, the A?s would likely have won these games, and accordingly Zito is given little credit for winning these games.

Similarly, in five of Derek Lowe?s starts the Red Sox outscored the opposition 49-0 when Lowe was the pitcher of record (10-0, 9-0, 9-0, 10-0, and 11-0).  Obviously Lowe pitched great in these games but receives little win value credit since his run support was so high in each of these games.  This is an illustration that win values is a "value" stat (backward looking) rather than an "ability" stat (forward looking).

Pedro Martinez had another outstanding season in 2002.  The main reason why he doesn?t finish higher on the win value ladder is that Pedro only started 30 games last season.  Contrast that to Zito?s 35 and Hudson?s 34.  I am confident had Pedro started 34 or 35 games, he would have had the league?s highest win value total.  The Red Sox rightfully protect their franchise pitcher?s arm, so I am not suggesting that they pitch Pedro more; I am merely pointing out why he finished fourth in win values.

Martinez and Lowe illustrate another issue related to how win values are calculated.  In the win value system, as in WAA, Pete Palmer?s TPI, and Michael Wolverton?s SNW, the pitcher is given total credit for run prevention, be it via the strikeout or the groundout.  Thus, Pedro receives no additional credit for being such a dominating strikeout pitcher (nor do Clemens, Johnson, Seaver, et al.).

Barry Zito, Pedro Martinez, and Derek Lowe all had outstanding seasons in 2002.  However, according to win values, none contributed more to his team winning (in a probabilistic sense) than did Tim Hudson.

Top NL Starting Pitchers in 2002

Table 3 presents the top ten National League starting pitchers according to win values.

Table 3:  2002 NL Win Value Leaders

 W-L ERA+ Wins Above Average (WAA) Win Value (relative to league avg) Win Value (relative to replacement) Randy Johnson 24-5 190 6.8 5.22 7.85 Greg Maddux 16-6 157 4.0 4.15 6.70 Curt Schilling 23-7 136 3.8 3.90 6.55 Roy Oswalt 19-9 142 3.8 3.62 6.20 Odalis Perez 15-10 126 2.5 2.95 5.35 Randy Wolf 11-9 118 1.8 2.92 5.25 Kevin Millwood 18-8 127 2.6 2.89 5.47 Wade Miller 15-4 130 2.1 2.70 4.65 Tom Glavine 18-11 139 3.5 2.42 5.12 A.J. Burnett 12-9 121 2.0 2.31 4.54

Randy Johnson dominated the NL once again in 2002 (especially in light of Curt Schilling?s late-season slide) and unanimously won his 4th consecutive and 5th overall Cy Young award.  Schilling was a near-unanimous second place finisher.  John Smoltz and his 55 saves came in third for the Cy Young.  Roy Oswalt tied Eric Gagne for fourth.

We don?t need to spend a lot of time discussing the NL.  Any evaluation tool that claims someone other that Randy Johnson was the best starting pitcher in the NL last season is highly suspect.  However, it is worth noting that Curt Schilling and Randy Johnson were virtually tied in win values after Schilling?s September 15 start.  That night Byung-Hyun Kim blew a save in the ninth or else Schilling would have gone to 24-5 (Johnson was 22-5 at the time).  Johnson closed out the season with two great victories whereas Schilling?s last two starts were both struggling losses.

Greg Maddux had another great season last year and, due to Schilling?s late season fade, actually finished second in win values in 2002.  In the next section of the article, I will update Johnson, Maddux and the other top active pitchers? career win value totals to include the 2002 figures.

Updating Top Active Pitchers? Career Win Values

In my previous article, I presented a table of the greatest starting pitchers of the last thirty years, the seasons for which Retrosheet has made available the play-by-play data, according to win values.

Win Values: Updated for 1969, 1974-77

Below, I update the active pitchers included in that table to incorporate their 2002 seasons.  Note that the table is sorted by career win values relative to replacement level, though win values relative to league average are also presented.

Table 4:  Win Values for Top Starters of Last 30 Years

 W-L ERA+ Career Starts Career Reliefs Win Value relative to League Avg Win Value relative to Replacement Roger Clemens (a) 293-151 142 573 1 67.4 110.4 Tom Seaver 311-205 127 647 9 54.9 103.7 Greg Maddux (a) 273-152 146 535 4 61.0 101.3 Gaylord Perry 314-265 117 690 87 37.3 91.3 Nolan Ryan 324-292 112 773 34 31.1 89.9 Bert Blyleven 287-250 118 685 7 38.1 89.7 Steve Carlton 329-244 115 709 32 35.0 89.0 Phil Niekro 318-274 115 716 148 30.6 88.0 Don Sutton 324-256 108 756 18 28.2 85.4 Jim Palmer 268-152 125 521 37 44.9 84.9 Tommy John 288-231 110 700 60 26.7 80.7 Fergie Jenkins 284-226 115 594 70 33.6 79.9 Randy Johnson (a) 224-106 144 426 10 47.6 79.8 Tom Glavine (a) 242-143 126 505 0 32.9 70.8 Rick Reuschel 214-191 114 529 28 22.9 63.2 Luis Tiant 229-172 114 484 89 24.5 63.0 Kevin Brown (a) 183-122 129 409 10 29.6 60.5 Pedro Martinez (a) 152-63 171 259 67 39.2 60.3 Chuck Finley (a) 200-173 115 467 57 23.5 59.9 Mike Mussina (a) 182-102 129 355 0 33.0 59.7 Dennis Martinez 245-193 106 562 130 14.2 59.6 David Cone (a) 193-123 119 415 30 27.5 59.3 Jack Morris 254-186 105 527 22 18.8 58.9 Frank Tanana 240-236 106 616 22 11.4 58.2 Jerry Koosman 222-209 110 527 85 16.5 58.1 Orel Hershiser 204-150 111 466 44 21.2 57.3 Bret Saberhagen 167-117 125 371 28 28.3 56.8 Kevin Appier (a) 161-127 124 377 12 27.9 56.5 Jimmy Key 186-117 122 389 81 25.3 56.5 Curt Schilling (a) 155-108 127 314 112 29.0 55.4 Vida Blue 209-161 108 473 29 18.6 54.8 Dave Stieb 176-137 122 412 31 22.8 54.5 Bob Welch 211-146 106 462 44 17.8 53.6 Charlie Hough 216-216 106 440 418 9.2 52.7 John Smoltz (a) 163-118 122 361 106 22.7 52.5 Dwight Gooden 194-112 110 410 20 18.6 49.9 Ron Guidry 170-91 119 323 45 24.3 49.6 Frank Viola 176-150 112 420 1 17.1 48.7 David Wells (a) 185-121 111 356 170 14.8 45.8 Doyle Alexander 194-174 103 464 97 7.4 44.6 Catfish Hunter 224-166 104 476 24 7.5 43.8 Jerry Reuss 220-191 100 547 81 -0.5 42.6 Joe Niekro 221-204 97 500 202 -2.9 39.7 Dave Stewart 168-129 100 348 175 7.8 38.3 Mike Torrez 185-160 97 458 36 1.3 36.6

Roger Clemens is deemed to be the greatest starting pitcher in the last 30 years, both in win values relative to replacement level and in win values relative to league average.  At this point in his career, Clemens is treading water, so he?ll likely not add much to his totals.

Greg Maddux is still one of the best pitchers in the majors, and has a good shot of surpassing Clemens in the next two seasons.

Although Randy Johnson has not yet cracked the top ten in win values relative to replacement, he is currently fourth in win values relative to league average, and may well eclipse Tom Seaver to move into third place in this measure before he retires.

Pedro Martinez is the other member of this modern quartet (sure-fire Hall of Famers).  Pedro is still in mid-career, so he hasn?t yet accumulated a ton of win values relative to replacement, at least compared to pitchers who pitched for 20 years.  On the other hand, the meteoric first-half of Pedro?s career (highest ERA+ in history) yields the sixth highest win values relative to league average, behind only Clemens, Maddux, Seaver, Johnson, and Palmer.

Other active pitchers who are making inroads on the list of the best modern starters include Tom Glavine, Kevin Brown, Chuck Finley, Mike Mussina, the recently revived David Cone, Kevin Appier, Curt Schilling, John Smoltz (now a closer), and David Wells.  Conventional wisdom puts Glavine into the Hall of Fame, and none of the other guys as of now, though Mussina will likely have a solid case before he ultimately retires.

Concluding Remarks

In this article I have presented updated results of my new win value system that evaluates starting pitchers.  Thanks to the wonderful volunteers at Retrosheet, the required data for the 2002 season recently became available.  Thus, I have calculated win values for each league for last season.

We saw that Randy Johnson contributed the most among NL starting pitchers to his team in 2002, and deservedly won his 4th consecutive and 5th overall Cy Young award.  In the AL, on the other hand, win values suggests that Tim Hudson, a pitcher who did not appear on a single Cy Young ballot, contributed the most among AL starting pitchers.  As always, Cy Young voters and the general public place too much emphasis on a pitcher?s won-loss record.

Many sophisticated analysts disregard a pitcher?s W-L record altogether and instead focus entirely upon ERA (ERA+).  I have found that there may be valuable information in a pitcher?s W-L record, especially looking backward.  Accordingly, I developed the win values system to be the best integration of W-L and ERA+ data when attempting to determine how much the pitcher contributed to his team.  In my system, run prevention is critical but its value in helping a team win must be measured in the context of the number of runs the team?s offense scores.

Comments on the method or the 2002 results are encouraged.

Rob Wood Posted: April 10, 2003 at 05:00 AM | 22 comment(s) Login to Bookmark
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1. Dolf Lucky Posted: April 10, 2003 at 12:56 AM (#610311)
I'm with Kostya. This doesn't tell me that Tim Hudson is my best option to win any given ballgame, it tells me that Tim Hudson was the most underrated by his W-L record, I think.
2. Joe Morgan Posted: April 10, 2003 at 12:56 AM (#610312)
What this doesn't factor in, is that Tim Hudson just doesn't know how to win like Pedro and Zito do.
3. Jason Posted: April 10, 2003 at 12:56 AM (#610314)
"Roger Clemens is deemed to be the greatest starting pitcher in the last 30 years, both in win values relative to replacement level and in win values relative to league average. At this point in his career, Clemens is treading water, so he?ll likely not add much to his totals.

Greg Maddux is still one of the best pitchers in the majors, and has a good shot of surpassing Clemens in the next two seasons."

Really?

Even forgetting the small sample so far this season (Clemens good, Maddux dreadful), Clemens' xERA compared to AL avg. was better than Maddux's compared to the NL average. The only reason their actual ERAs were reversed (drastically so) was that Clemens was about the most unlucky pitcher in the AL (over 30% BIP for hits) while Maddux managed to give up bunches of hits while avoiding giving up earned runs (many unearned runs plus luck of timing). Given Clemens' K rate of over 1 per inning last season and Maddux's declining K rate, I'd guess that Maddux is much closer to losing his effectiveness than is the Rocket.

4.  Posted: April 10, 2003 at 12:56 AM (#610317)
I didn't look at the methodology, so this may be answered there, nor did I look up Hudson's 9/14 game that you list as a 9IP 1-0 win, but provided he did pitch a complete game 1-0 victory and didn't leave prior to the third out of the 9th, I am concerned that he only receives .716 win value. Shouldn't it be tied to the likelihood of a team's victory in the situation? I would expect it to be closer to 98% or higher, resulting in a .98x win value. Maybe not being a math guy I need a little more explantion of why that's not worth close to the full 1.0.
5. Depot Posted: April 10, 2003 at 12:56 AM (#610321)
I really like the idea of going game-by-game for pitchers and I think that's the great thing about this procedure. However, I agree that the rest of the procedure factors in run support too heavily. Why can't this metric simply look at how often the average offense scores 0 runs in a game, 1 run in a game, etc.? Then, you can calculate the number of shares a pitcher should receive if he gives up 3 in 7 innings or 6 runs in 2 innings (or whatever). Basically, use probabilities of different "states" that a league-average offense would induce. So then you have the following info: (1) the pitcher gave up X runs in Y innings; (2) a league-average offense has a P1 prob of scoring R1 runs in Y innings, a P2 prob of scoring R2 runs in Y innings, etc. Then you could use the rest of the procedure - if you're up by so many runs with so many innings left, what's the prob of winning?

I think this eliminates a lot of the context problems. The ones that remain are (a) defense and (b) assuming that a pitcher's team offense has no effect on how he pitches (quality/runs AND innings).
6. Rob Wood Posted: April 10, 2003 at 12:56 AM (#610324)
Me invent new stat. Me smart!
7. gps Posted: April 10, 2003 at 12:56 AM (#610330)
How does hudson get the win?

I assume that after Hudson left, his team scored 3 more runs, making it 6-1...then the pen let up 4 runs making it 6-5. The lead was never let up, so it was always his decision.

(Or something along those lines)
8. Damon Rutherford Posted: April 10, 2003 at 12:56 AM (#610331)
compared to if a league average pitcher would have started in his place.

Does this factor in the hitting quality of the opponent?
9. tangotiger Posted: April 11, 2003 at 12:56 AM (#610341)
What I want to know is, for example, whether Robin Ventura helped win more games than Mike Piazza in 1999, or whether pitcher X helped win more games than pitcher Y. There is no metric that tells me that.

There is. It's called Player Win Averages, from the Mills Brothers, developed over 30 years ago. It did not consider fielding. It is based on play-by-play analysis.

I do something similar for relievers, with Leveraged Index.

Tom Ruane ran something similar based on base/out states (and not inning/score), for 1980-1997. You can look for that on baseballstuff.com

10. Rob Wood Posted: April 12, 2003 at 12:56 AM (#610347)
I'll try to respond to some of the comments. Many of the other comments are not worthy of response since they reflect a lack of understanding what the win value system is all about. Should these posters really be interested in learning more, I encourage them to read the original articles.

The 2002 update was written before the 2003 season got under way, so I stand by my Clemens-Maddux comments. There is nobody who is a bigger Roger Clemens fan than I am. I have written extensively on Clemens. I consider him the 3rd greatest pitcher of all time, and gladly sponsor his page over at Baseball-Reference.com. I am no fan of Greg Maddux, though Maddux is also one of the all-time greats. The win value system considers them that way too.

The reason why Tim Hudson's 6/20 start had a slightly higher win value than his 8/14 start is due to the park factors. I cannot emphasize enough that the win value system does not consider what happens after the pitcher leaves the game (actually after the full inning).

Depot's proposed a different system that does not consider the pitcher's specific run support in the game but instead uses the league distribution of runs scored. In fact, this is what Michael Wolverton does in his Support Neutral Win system. See my original article for a discussion of why I chose to go in another direction than SNW.

The win value system is another way of looking at pitchers. It was not intended to replace SNW or ERA or anything like that. As someone posted, it was designed in a similar vein to Bill James' win shares in which he attempts to allocate credit for team winning. James does this on an aggregate seasonal basis whereas I am able to do this for pitchers on a game-by-game basis. Again, it is purely a backward-looking evaluation system (value) rather than forward-looking (ability).

Yes, this same approach I take for pitchers can be applied to hitters. It is akin to Win Probabilty Added and other "value-added" measures. I cannot fathom the backlash my system seems to have caused since it is in a long line of methods which sophisticated analysts have embraced for many years.

Finally, the system does not currently take into account the strength of the opposition (strength of schedule). However, I recently developed a system to estimate the strength of opposition a starting pitcher faces and wrote this up in a separate article. My goal is to incorporate this aspect into the next version of the win value system.
11. Damon Rutherford Posted: April 12, 2003 at 12:56 AM (#610348)
My goal is to incorporate this aspect into the next version of the win value system.

Awesome! Thanks, Rob.

...Bill James' win shares in which he attempts to allocate credit for team winning. James does this on an aggregate seasonal basis whereas I am able to do this for pitchers on a game-by-game basis.

Do you find there is a significant difference between the win shares rankings and the win value rankings? Significant enough to be worth the cost of looking at game-by-game instead of total season, assuming there even is a cost (in time and effort) to compute Win Value over Win Shares?
12. Rob Wood Posted: April 13, 2003 at 12:57 AM (#610353)
I have not compared and contrasted my win value figures with Bill James' win shares for starting pitchers. However, I have thus far published the top ten win values in each league from 1974-2002, so someone can do the comparison fairly easily. In addition, I'd be happy to send anyone who is interested an Excel file with all pitchers' win values for these years.

I appreciate David's point though I think it may overlook two of the key aspects of the win value system. First, seasonal data consists of a hodgepodge of game-by-game data, and game-by-game data is the most useful, especially for pitchers. For example, a pitcher's average run support can be misleading since run support is notoriously lumpy (non-normally distributed). Same would be true, probably even moreso, for any measure of bullpen support.

Second, I really think there is room in our analysis toolkit for a value stat for starting pitchers. That is, a stat that attempts to ascribe credit or blame for winning or losing each game, especially with regard to the starting pitchers. We have many useful pitching stats that are great for measuring ability (forward looking). But, as far as I knew when I developed win values, there were no value stats (backward looking) for starting pitchers.
13. tangotiger Posted: April 13, 2003 at 12:57 AM (#610356)
Think about it, your system gives a pitcher more credit for a 1-0 score when leaving the game than a 10-0 score when leaving the game...

It's been several months since I read Rob's Win Values, but from what I remember, this is not a true statement. It doesn't matter what the score is when he leaves the game, but just what the final score of the game was.

For Cy Young, unlike the MVP, pitchers are recognized for their performance in isolation of their teammates contributions (or so the theory goes). To award a Cy Young, you shouldn't care what the team run support is.
14. tangotiger Posted: April 14, 2003 at 12:57 AM (#610369)
Since there seems to be some confusion as to what Rob is actually doing, check out the above link for his original article. Here's a cut/paste of the relevant information

==========
Consider a team that scores 7 runs in a 9-inning game. Suppose I find a team that scores 7 runs in a game will have scored 5 runs at the conclusion of the 6th inning 10% of the time. I also know the distribution of final scores of every team that scored 5 runs at the conclusion of the 6th inning. Say they wind up with 5 runs 12% of the time, 6 runs 20% of the time, 7 runs 25% of the time, ?, and 15 runs 1% of the time.

I can calculate this bootstrapped distribution of final scores for every possible number of runs scored at the conclusion of the 6th inning. To find the ultimate ?could have been? distribution of final scores, I would then weight these probability distributions of each possible runs scored outcome by the respective probability of having that many runs scored at the conclusion of the 6th inning (10% in the case for starting with 5 runs in the example above).

The result is a ?smearing? of the run support provided in a game. For example, this method may find that a team that actually scored 7 runs ?could have? scored runs with the following probabilities: 0 runs (1%), 1 run (2%), 2 runs (4%), 3 runs (6%), 4 runs (7%), 5 runs (9%), 6 runs (12%), 7 runs (15%), 8 runs (10%), 9 runs (8%), 10 runs (7%), 11 runs (6%), 12 runs (5%), 13 runs (4%), 14 runs (3%), and 15 runs (1%). I would then use this ?could have been? smeared probability distribution for the pitcher?s possible run support in evaluating his outing.

Now that I have answered some questions that you may have had, let me try to summarize the conceptual approach I take. I am introducing a method that evaluates a starting pitcher?s contribution to his team?s chance of winning the game if the score is RS to RA when he leaves the game at the conclusion of the Zth inning. I will first ?smear? the run support based upon RS and Z using a backwards Bayesian bootstrapping method. That will give me a probability distribution that the team could have scored X runs at the conclusion of the Zth inning, where X ranges from 0 to 25, say.

Next, using the smeared run support distribution, I will estimate the probability that the team would win a game when giving up RA runs at the conclusion of the Zth inning. Then, using the smeared run support distribution, I will estimate the probability that the team would win this game with league average pitching. I then will subtract these two probabilities to derive the pitcher?s win contribution for that game. For those readers interested in a mathematical representation, all the formulas are presented below.

===========

So, if I understand this correctly, Rob doesn't care what the score was when the pitcher is taken out (as almost all win probability measures do), but he does this reverse process in order to account for the "run in the first is worth as much as the run in the 9th" situation.

I think the bullpen issue might be valid (as would fielding), but I'm not sure.
15. Rob Wood Posted: April 15, 2003 at 12:57 AM (#610382)
Okay, now I am officially perplexed. When someone as baseball savvy as David doesn't grasp the concept, there is something definitely amiss. Maybe people just don't know the literature.

The concept of a win probability is not new. It dates back at least as far as the Mills Brothers in the 1960's. Doug Drinen used it in his relief pitcher stat, Michael Wolverton uses it in his support neutral win stat for starting pitchers, and all of the value-added approaches rely upon win probabilities in some way.

Here is my characterization of a win probability. For each game, of course, one team wins and one team loses. Roughly speaking, one "win probability" unit is allocated among the winning team's players, just as negative one unit is allocated among the losing team's players.

[This is not strictly correct because players on losing teams can do good things and players on winning teams can do bad things. But let's not worry about that right now.]

The basic idea is that a batter is allocated win probabilities based upon how he changes the game situation in each plate appearance relative to what a league average batter would likely have done. For example, if a batter hits a 2-out bottom of the ninth grand slam home run to win a game 4-3, he will get a large allocation of that one win probability unit since he took his team from a very likely losing situation to a win.

Suppose the next game the same guy hits a 2-out bottom of the ninth grand slam home run that only makes the score 15-4 (they were previously trailing 15-0). In this instance, the same event is worth far less due to the game score situation. The grand slam in this case barely changes the probability that his team will win from, say, .00001 to .00002, whereas the game-winning grand slam changed the probability of winning from, say, .20 to 1.00. Surely, everybody intuitively understands this.

What my new win value system does is apply this principle, with a few wrinkles, to starting pitchers. Consider two games. In the first game the team wins 3-2. The winning pitcher will likely get a lot of credit (allocation of that fixed one unit of win probability) in this situation. The next game the team wins 14-2. Here the winning pitcher will get far less of the credit, because, as David points out, the offense was really the reason the team won the game.

But that is exactly why the pitcher will get less of the fixed one unit. You cannot fix the pitcher's credit and allow the credit to the offense to vary, since by definition their sum must always be a constant (ignoring defense for the time being).

Neither win values nor win probabilities imply any causality. The pitcher has no control over the score (just as the batter who hit the grand slam had no control over the score of the game before his at bat, and is not presumed to have the ability to hit better when the game is on the line). But so what? The allocation of credit does depend upon the score, and thus the allocation of credit going to the pitcher will depend upon the score.

If this makes you uncomfortable, then you don't fully appreciate the concept of win probabilities. Go back and re-read the Mills Brothers' "Player Win Averages" or Drinen's "Win Probability Added" or Wolverton's "Support Neutral Wins" or Gary Skoog's "Runs Created: A Value-Added Approach".

And please stop saying that the win value system is bogus. Let's reserve that degree of criticism for stats or approaches that have no redeeming value whatsoever, such as the much-discussed HEQ stat.
16. tangotiger Posted: April 15, 2003 at 12:57 AM (#610384)
I think there are a few issues to tackle:

1 - Associating the Cy Young Award to a metric. Unlike the MVP, the Cy Young "should" go to the pitcher who performed the best, without consideration of his teammates' performanace. From that standpoint, the consideration should either be that you assume league-average run, bullpen and fielding support (or some other neutral baseline), or you also include a "pitching to the score" component. Pitching to the score occurs in real-time.

2 - The ingenious bootstrapping approach. While all other win probability measures are based in real-time (win probability before and after the occurrence of the event, with the change in win probability allocated in some way to the pitcher, hitter, fielders, and runners), Rob takes a different approach, as noted in my cut and paste. If I am understanding it correctly, it doesn't matter what the score was when the pitcher was removed, but rather what was the final score of the game. A pitcher taken out of a 3-2 game that ends at 3-2 or 10-2 will have a different win value. A pitcher taken out of a 3-0 or 8-0 game, with the final score being 9-0 will have the same win value. The process speaks to the readers who think a run is a run is a run, within the context of the same game.

The question to ask is the merits of figuring win values based on a game-by-game basis, as opposed to play-by-play. This method is the only one that allows to you satisfy the condition "a run in the 1st is as valuable as a run in the 9th". From that standpoint, this method deserves to be looked at with greater detail.

3 - Bullpen and fielder support. These are valid points that I've not really looked at. Fielder support is very legitimate for pitchers on teams with good/bad fielders. The impact of this can be considered by looking at the 2002 Angels, who may have contributed over 0.5 runs / game (or .05 wins) over league average. For a 234 inning pitcher, that's 1.3 wins, which is HUGE. However, Win Values is not alone in treating a team's fielders as league average. For bullpen support, you probably have similar issues.

Perhaps we can center the discussion on the mechanics of the measure, rather than making conclusions that it's no good (or is the best thing in the world).
17. tangotiger Posted: April 15, 2003 at 12:57 AM (#610387)
I don't think this measure addresses the "pitched to the score", since that should happen in real-time, and not after the fact.

The term "value" can really mean anything, and therefore, it's best that it is defined before discussing it.

This measure attempts to quantify the win impact a pitcher has on a game, after the outcome of the game has been decided. It does this by using the final run support of the game, and "reversing it" through a Bayesian process to establish probability and frequency rates, back to when the pitcher was removed from the game. You then move forward, using league average rates to establish a win probability for when the pitcher left the game, with this new run support. The difference between the win/loss of the game, and this new win probability is his "value".

Did I get that right Rob?

It's a fascinating process, though I'm still not sure of what it's really telling us.
18. Rob Wood Posted: April 15, 2003 at 12:57 AM (#610391)
Just a quick note for now. The only reason that I frequently tie the win value results to Cy Young voting is that it is a simple way to frame the discussion. Even I would not base a Cy Young ballot exclusively on win values, but neither would I only look at ERA+, WAA, or SNW, etc. Each of these stats is worth considering.

Win values are an estimate of how much the pitcher's performances contributed to his team's winning over the course of the season, taking his game-by-game run support as a given. This is the best approach to estimate a pitcher's value-added wins in the sense described by the Mills Brothers, et al.
19. steve Posted: April 21, 2003 at 12:58 AM (#610446)
i guess i don't buy the basic assumption of this metric: that a pitcher's value is affected by the performance of his team's hitters. some shutouts help a team more than others, it's true, but what evidence do you have that 1-0 shutouts result from more gritty, "valuable" pitching than 10-0 shutouts?

win values aren't really that similar to win shares, either, because a premise of win shares is the size of the pie. i'm guessing that win values penalizes good pitchers on dominant teams, since their victories would generally be more lopsided.
20. Rob Wood Posted: April 21, 2003 at 12:58 AM (#610455)
Suppose the 1927 Yankees and the 1965 Dodgers were bidding for Sandy Koufax. I think it is clear that the Dodgers would rightly bid more for him since he is more valuable to a low-offense team than to a high-offense team.

Let's say Koufax would pitch as well for the 1927 Yankees. Why is this worth less? Because the 1927 Yankees would have won with merely good pitching; it didn't require pitchers of Koufax's ability. A game won 8-2 is as valuable in the standings as a game won 8-5.

Or, to say it another way. Everybody would agree that a pitcher who hits a home run and pitches a shutout to lead his team to a 1-0 victory deserves a great deal of the credit for the win. But once you agree to that premise, the relative value argument kicks in. A pitcher who pitches a shutout in a 10-0 win must, perforce, have less relative value since the hitters deserve at least some of the credit. The second statement follows directly from the first.
21. steve Posted: April 22, 2003 at 12:59 AM (#610471)
hi, rob, thanks for the quick response. i'm confused by your example, though, since the '65 dodgers had koufax, and i'm not sure what it means to think of them having to bid on him. do you mean: suppose the '27 yankees and the '65 dodgers could bid on, say, randy johnson? in that case, i don't see why the addition of johnson wouldn't make either team that much more dominant.

or to respond in another way to your example: what if both teams could bid on gehrig? the '65 dodgers would become a high-offense team, and thus dominant; the '27 yankees were a better team anyway, but would not have been nearly so dominant without gehrig.

as for the pitcher who homers and pitches a 1-0 shutout, he deserves credit for his home run because he hit it, not because the game was so close.

the only way it makes sense to me to value the 1-0 shutout pitcher above the 10-0 shutout pitcher is to say that the 1-0 shutout pitcher PITCHES BETTER. that doesn't make sense to me, since both pitchers allowed zero runs.

maybe it's true that sometimes a pitcher can boost his game when the pressure's on, and the ability to do so is a value unaccounted for by traditional metrics. but i don't think you've shown that your metric can establish or evaluate this ability.
22. Rob Wood Posted: April 23, 2003 at 12:59 AM (#610485)
The underlying win probabilities are fairly constant from season to season, so I am planning to do what Lennox suggested. Namely track win values during the season, periodically reporting the league leaders throughout the season.

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