What WPA Can Tell Us About Players

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   0.99

As 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.

We can mathematically adjust WPA for all three of these issues; today, let’s tackle the last one.

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     ---       60

Now 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.

All Players

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         18.76

The 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!

Individual Pitchers

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    1.10

These 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.

Individual Batters

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

“Clutch” Batters

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  1.02

Jenkins 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.

Individual Pitchers

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   0.75

Mariano 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 & 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.