What WPA Can Tell Us About Playersby Dave Studeman
July 24, 2006
Last week, we took a little time to review this new-fangled stat called Win Probability Added, and we compared WPA to the number of runs scored and allowed by teams. Today, I'm going to do the same thing, but I'm going to do my best to extrapolate runs to individual players and analyze some of the key differences between WPA and runs created/avoided for individual batters/pitchers. In the end, we'll have an interesting take on which players have "stepped up" with the game on the line.
But first, a couple of sidebars:
Starters and Relievers
Here are the total innings pitched and pitching WPA allocated to each type of pitcher (starter or reliever, based on my sorting pitchers into each bucket). I've also included the average Leverage Index of each type of pitcher:
POS IP WPA LI SP 15,643 3.93 0.96 RP 7,897 20.95 1.04 Total 23,539 24.87 0.99As you can see, relievers received about 17 WPA points (or 34 wins) more than starters, despite pitching in only half as many innings. Also, relievers have pitched in more crucial situations, on average, with a Leverage Index of 1.04. So few numbers, so much information.
Relievers have a number of advantages over starters in WPA world:
- It's easier to relieve than start. As The Book has documented, relievers probably have as much as a 0.80 ERA advantage over starters.
- Managers choose when to bring in specific relievers. Bad relievers tend to appear in blowouts (when they can't have much effect on a game) and good relievers appear in close games, when they can have a big impact. There is no such contrast among starters—the best and worst starters enter games at the very same time, the first inning, regardless of the score.
- WPA only looks at games above and below .500, not total wins and losses.
Thanks to my good buddy and THT colleague David Gassko, we were able to mathematically estimate the total number of wins and losses that would be allocated to pitchers by WPA. I've put the specific calculation in the footnote; I'll just post the totals here:
POS W L W% WPAB SP 429 422 .505 174 RP 254 212 .545 114 Diff 175 210 --- 60Now you can see one of the problems with looking at just wins above average. Starters actually have 175 more wins than relievers; the problem is that they also have 210 more losses and a lower winning percentage. If you take a slightly different approach and calculate Win Probability Above Baseline (I used a .300 winning percentage as a baseline), you find that starters contribute over 50% more WPAB than relievers (174 vs. 114).
By the way, this is the same issue that plagues Win Shares. Ideally, you really need to know Loss Shares, or use an alternative baseline, to get a clear idea of how much a player contributed to his team's won/loss record. That's why we like to use Win Shares Above Bench in our Win Shares articles.
This new table still doesn't resolve the first two WPA issues noted above; it's relatively easier to relieve and managers "mix and match" relievers with the situation. We'll save those adjustments for another day.
The above stats might make you wonder how all positions rank by WPA. Here are the WPA totals by position (based on which position each player has played most often). Starting pitchers have a much lower WPA total in this table because their batting performances are included.
POS WPA C -13.60 1B 14.42 2B -9.34 SS -5.66 3B 9.23 OF 21.07 DH 2.48 SP -36.21 RP 18.76The key thing to remember is that Fangraph's WPA doesn't reflect fielding contributions, just the offensive contributions of the everyday positions. In general, this table reflects the relative fielding value of each position (the higher the WPA, the more emphasis on batting for that position), but look at how poorly designated hitters are doing. Make that an exclamation point!
Here is the WPA leaderboard for all pitchers. I've included the 23 pitchers with at least 2 WPA. Note that the list is pretty evenly divided between starters and relievers, though relievers are at the top of the board.
Pitcher Team IP ERA WPA LI Jonathan Papelbon BOS 46 0.59 3.68 1.76 B.J. Ryan TOR 43 0.84 3.36 1.62 Brandon Webb ARI 139 2.65 3.29 0.99 Bobby Jenks CHA 41 2.83 3.22 2.04 Trevor Hoffman SD 35 1.03 3.01 1.91 Joe Nathan MIN 36 1.75 2.90 1.54 Jason Schmidt SF 126 2.78 2.85 1.13 Jeremy Bonderman DET 120 3.46 2.83 1.02 Joel Zumaya DET 43 2.08 2.59 1.74 J.J. Putz SEA 43 2.11 2.57 1.38 Francisco Liriano MIN 88 1.83 2.55 0.82 Roy Halladay TOR 129 2.92 2.37 0.97 Chris Young SD 110 3.12 2.32 0.96 Chris Ray BAL 37 3.19 2.30 1.82 Roy Oswalt HOU 120 3.15 2.30 1.04 Chris Carpenter STL 111 2.92 2.28 1.05 Johan Santana MIN 131 2.95 2.15 0.95 Brad Penny LAN 108 2.91 2.07 0.98 Mariano Rivera NYA 46 1.76 2.06 1.80 Chris Capuano MIL 129 3.21 2.03 0.97 Francisco Rodriguez LAA 37 2.89 2.02 1.93 Duaner Sanchez NYN 48 2.45 2.01 1.53 Scott Kazmir TB 116 3.27 2.00 1.10These are rankings as of the All-Star break. I'd say that Brandon Webb is more likely to retain his ERA (2.65) than Jonathan Papelbon (0.59) or B.J. Ryan (0.84) are, so you may see a starter at the top of the list by the end of the year.
Here are the individual batting WPA leaders. To no one's surprise, King Albert is at the top of the list. But you may be surprised to see that Jermaine Dye is third and even more surprised to see that Barry Bonds is fifth. I've also included each batter's Base Runs Above Average (see my explanation of BRAA in the footnote).
Batter WPA BRAA Albert Pujols 5.52 32 David Ortiz 3.40 19 Jermaine Dye 3.26 24 Derek Jeter 3.18 14 Barry Bonds 2.86 14 David Wright 2.62 23 Bobby Abreu 2.57 17 Travis Hafner 2.52 33 Manny Ramirez 2.51 23 Jim Thome 2.43 29 Jason Giambi 2.41 23 Nomar Garciaparra 2.36 23 Chase Utley 2.32 17 Ryan Zimmerman 2.31 5 Todd Helton 2.26 12 Lance Berkman 2.24 24 Frank Catalanotto 2.21 8 Curtis Granderson 2.21 9 Melvin Mora 2.21 1 Justin Morneau 2.20 16
In the last article, we used WPA to identify whether batting or pitching was driving each team's pythagorean variance. I'd like to apply the same thinking to individual batters. The end result will be a list of which batters have contributed more WPA than their general offensive stats would predict.
To predict WPA, I regressed each batter's Base Runs Above Average against WPA (R-Squared of .6 for you math types) and calculated the difference between the actual WPA and predicted WPA for each batter. The difference is the result of a batter's relative performance in high vs. low leverage situations. You might call high-leverage situations "clutch," so I'm calling the difference "Clutch WPA" or ClWPA in the table. That's not a suggested label, by the way. Just one to use for this article.
Surprise! The best clutch batter, by this definition, is Milwaukee's Geoff Jenkins.
Batter Team WPA BRAA ClWPA LI Geoff Jenkins MIL 2.05 -3 2.43 1.07 Albert Pujols STL 5.52 32 2.28 1.06 Melvin Mora BAL 2.21 1 2.10 0.96 Mark Loretta BOS 1.24 -6 1.86 1.00 Ryan Zimmerman WAS 2.31 5 1.79 1.12 Derek Jeter NYA 3.18 14 1.76 1.07 Ken Griffey Jr. CIN 2.01 4 1.68 1.07 Barry Bonds SF 2.86 14 1.45 0.98 David Ortiz BOS 3.40 19 1.44 0.97 Frank Catalanotto TOR 2.21 8 1.43 1.03 Michael Young TEX 1.45 1 1.36 0.92 Jeff Francoeur ATL 0.82 -5 1.33 1.12 Ty Wigginton TB 0.83 -4 1.31 0.93 Ramon Hernandez BAL 1.78 5 1.31 1.03 Curtis Granderson DET 2.21 9 1.30 0.89 Orlando Cabrera LAA 1.67 4 1.29 0.99 Gabe Gross MIL 1.43 2 1.27 1.10 Jason Varitek BOS 0.13 -10 1.21 1.07 Jay Payton OAK 0.61 -5 1.20 1.09 Alex Cintron CHA 0.77 -3 1.12 1.05 Hank Blalock TEX 1.16 1 1.11 1.00 Todd Helton COL 2.26 12 1.08 0.90 Jacque Jones CHN 1.83 8 1.08 0.98 Nick Swisher OAK 2.17 11 1.07 1.08 Paul Lo Duca NYN 0.93 -1 1.04 0.97 Marcus Giles ATL 0.81 -2 1.03 1.02Jenkins has had some key hits in high-leverage situations. For instance, he hit a two-run single in the bottom of the ninth off Bob Wickman to beat the Indians, 3-2 on June 17. That game alone was worth .43 WPA, almost an entire win. According to STATS Inc., Jenkins has batted .377/.426/.604 in "close and late" situations. His WPA reflects that.
This is certainly a very interesting list of batters. Remember that this list reflects the difference between predicted WPA and actual WPA, which means that these leaders have performed relatively better in high-leverage situations. It doesn't mean these are the best batters you want at bat in key situations. Personally, I'd still pick Pujols in clutch situations over Jenkins.
For a final list, let's calculate the same "clutch" performance for pitchers. In this analysis, we'll used Runs Saved Above Average instead of Base Runs. RSAA presents some issues when comparing relievers and starters, but it seems like the best alternative in a pinch. We'll also include Leverage Index in the initial regression because there are significant differences between pitchers in leverage opportunities. For you mathematicians, the R-Squared for the regression is .73.
Here's the list of all pitchers with at least 0.75 "ClWPA." As you can see, the top of the list consists entirely of the game's best relievers.
Pitcher Team WPA LI ClWPA Bobby Jenks CHA 3.22 2.04 2.02 Joe Nathan MIN 2.90 1.54 1.55 Trevor Hoffman SD 3.01 1.91 1.49 Chris Ray BAL 2.30 1.82 1.48 Jonathan Papelbon BOS 3.68 1.76 1.45 B.J. Ryan TOR 3.36 1.62 1.41 J.J. Putz SEA 2.57 1.38 1.20 Joel Zumaya DET 2.59 1.74 1.19 Francisco Rodriguez LAA 2.02 1.93 1.14 Jorge de la Rosa MIL -0.02 0.83 1.13 Jason Marquis STL 0.08 0.86 1.10 Jim Brower TOT -0.46 0.39 1.08 J.C. Romero LAA 0.20 0.70 1.05 Tom Martin COL 1.06 0.68 1.01 Jeremy Bonderman DET 2.83 1.02 0.99 Juan Rincon MIN 1.93 1.28 0.98 Billy Wagner NYN 1.88 1.99 0.95 Duaner Sanchez NYN 2.01 1.53 0.95 Horacio Ramirez ATL 0.76 1.26 0.86 Chad Harville TB 0.86 0.99 0.84 Fernando Rodney DET 1.02 1.66 0.81 Oliver Perez PIT -1.17 0.96 0.79 Dave Borkowski HOU 0.87 0.41 0.78 Roberto Novoa CHN 0.14 0.42 0.76 Carlos Silva MIN -1.62 0.86 0.75Mariano Rivera? He's 74th on the list, with a ClWPA of 0.43.
There is so much we can do with Win Probability. This article, though it contains a lot of information, only scratches the surface. But you'll be happy to know that David Appelman is working on a number of upgrades to the Fangraphs site that will permit you to view WPA in even more detail. And this year's Hardball Times Annual (which is now available for preorder) will contain a veritable plethora of WPA stats and analysis. Yes, there is more WPA to come!
References and Resources
Many thanks to Fangraphs for calculating WPA each day, and to Tangotiger for the underlying math.
To calculate pitcher wins and losses, David and I used LI*IP/9*.51 to calculate "expected wins." Actual WPA wins were calculated as Expected Wins plus WPA and losses were calculated as Expected Win minus WPA. We used .51 instead of .5 (remember, one win equals .5 WPA) because the tables behind Fangraphs' WPA are based on a slightly higher run environment than the one we've experienced so far this year. That's also why total pitching WPA doesn't equal zero. If we wanted to show totals in which pitching and hitting contributed equally to a team's wins, we would have used .255.
Tangotiger reminded me about a site that ranks all pitchers in WPA from 1972-2002. As you can see, top starters lead top relievers on the list over entire careers, which is illustrative of how an entire career's stats may be necessary to properly use WPA. This list makes you wonder why Goose Gossage isn't in the Hall of Fame yet. Some folks might also be interested in Bert Blyleven's ranking.
I calculated Base Runs, created many moons ago by David Smyth, for batters. Base Runs is similar to Runs Created in many ways, but it has a number of advantages for certain analyses. For instance, in this case I set the "run scoring multiplier" on a team-specific basis, and then calculated the team's runs with and without each specific batter. In that way, my Base Runs totals equal the team's total runs scored. That makes this analysis more consistent with last week's article. By the way, it took ten Base Runs to "predict" one WPA, which is very consistent with other run/win ratios.
Dave was called a "national treasure" by Rob Neyer. Seriously. Comments about this article can be sent to him through the miracle of e-mail.