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The very short version is that WPA is the combined contribution made to increasing or decreasing the chances of winning each game. Each 50 points of WPA is worth one win above or below .500. In other words, someone with 100 WPA has pushed the team from winning 81 games to winning 83 games, while someone with -100 WPA has dragged the team from 81 wins to 79 wins. Pretty simple, right?

Here are the Twins' WPA totals through 123 games:

Joe Nathan            414          Josh Rabe              -3
Justin Morneau        364          Willie Eyre            -8
Francisco Liriano     295          Brad Radke            -11
Johan Santana         291          Mike Smith            -25
Joe Mauer             240          Jason Kubel           -29
Juan Rincon           233          Lew Ford              -31
Michael Cuddyer       162          Matt Garza            -43
Dennys Reyes           97          Luis Castillo         -59
Jason Bartlett         75          Jesse Crain           -59
Pat Neshek             65          Boof Bonser           -73
Jason Tyner            58          Luis Rodriguez        -90
Nick Punto             48          Tony Batista          -95
Matt Guerrier          45          Scott Baker          -119
Ruben Sierra           27          Juan Castro          -121
Shannon Stewart        22          Kyle Lohse           -147
Mike Redmond           17          Torii Hunter         -155
Terry Tiffee            7          Carlos Silva         -158
                                   Rondell White        -186

Joe Nathan has been the team leader in WPA for each of the four updates, which shouldn't be overly surprising if you stop to consider the season he's had. Nathan pitches almost exclusively in what are called high-leverage situations, which means he only comes into the game in important spots. In fact, his Leverage Index of 1.56 is by far the highest on the team, with only Juan Rincon (1.26) above 1.10.

Not only has Nathan pitched in extremely tight spots all year, he's been nearly flawless while doing so. He's 6-0 with a 1.38 ERA in 48 appearances, has converted 25-of-26 save opportunities while holding opponents to a .172 batting average, and sports a 73-to-10 strikeout-to-walk ratio in 52 innings. He might be taken for granted, but because of Nathan the Twins almost never blow a lead and can take multiple shots at scoring to break ties while the other team is held in check.

After Nathan comes the four players everyone would identify if asked to name the team MVPs: Justin Morneau, Francisco Liriano, Johan Santana, and Joe Mauer. Mauer ranking fifth on the team in WPA might seem odd, but it's important to remember that WPA measures only offensive contributions and doesn't adjust them for position.

In other words, WPA shows Morneau as having had more of a raw impact offensively than Mauer, but that gap closes very quickly once you adjust for the fact that one plays first base and the other plays catcher. Not only is Mauer's defense significantly more valuable, his offense is considerably better than Morneau's when compared to the average performance of their respective positions.

All of which is what makes Jason Bartlett's 75 WPA particularly impressive. Bartlett has played in just 60 of the Twins' 123 games, yet ranks ninth in WPA even without the light-hitting nature of shortstop and his outstanding defensive contributions thrown into the mix. Also noteworthy is that Pat Neshek has racked up 65 WPA despite being in Rochester until July, because with a 0.84 ERA and 32-to-3 strikeout-to-walk ratio in 21.1 innings he's been even more unhittable than Nathan.

Much like Neshek, Jason Tyner has had a big impact in a short time, producing 58 WPA in 36 games. Tyner's overall hitting line of .323/.357/.353 isn't great, but he's come up with a lot of those singles in key spots. Toss in what has been very good defense in center field and left field, and Tyner certainly has a good case for being among the team's 10 most-valuable players. Seriously.

At the other end of spectrum are the usual suspects, with Rondell White (-186), Carlos Silva (-158), Kyle Lohse (-147), Juan Castro (-121), Scott Baker (-119), and Tony Batista (-95) making up six of the Twins' seven least-valuable players. It's interesting to note that five of those six guys are no longer on the active roster, with only Silva remaining.

Torii Hunter's inclusion as the seventh player in that least-valuable group would surely shock most Twins fans, but the relationship between his perceived value and actual value has been warped for some time. Hunter's overall line of .270/.343/.448 is solidly above average even without adjusting for position, but he's hit into rally-killing double plays, done poorly on the bases, and generally failed to come through in key situations.

Hunter has hit .242/.338/.355 in "close and late" situations, .252/.329/.394 with runners in scoring position, and .274/.345/.428 with runners on base. Hunter's -155 WPA ranks ahead of only White and Silva as the third-worst on the team, because the timing of his contributions have rarely actually led to the Twins having a significantly better chance to win games.

As usual, there is also a lot of interesting stuff to note away from the extremes. Backing up my claim yesterday that he's been a disappointment, Luis Castillo has produced a -59 WPA that ranks 11th on the team among hitters with at least 100 plate appearances. Luis Rodriguez has a -90 WPA in just 104 plate appearances thanks to coming up empty in many high-leverage spots as a pinch-hitter.

Aside from Liriano and Santana, no other starter has had a positive WPA contribution, although Brad Radke's -11 WPA puts him on the verge of getting into the black. What's amazing is that Radke was at -116 WPA through 86 games, which means he's been worth 105 WPA since mid-July. That's what happens when you begin the season with a 7.44 ERA through 10 starts and then go 8-3 with a 2.62 ERA over your next 16 outings.

Willie Eyre has an ugly 6.11 ERA in 45.2 innings, but because nearly all of his work has come in low-leverage situations his -8 WPA is relatively harmless. On the other hand, Jesse Crain has a 4.37 ERA in 59.2 innings, but has a -59 WPA thanks to being used in high-leverage spots and often coughing up runs.

However, with the emergence of Neshek and Dennys Reyes, and the return of Matt Guerrier from the disabled list, Crain's Leverage Index has plummeted as he's become more middle reliever than setup man. Here's how the bullpen's Leverage Index numbers have changed from the 86-game mark to now:

LEVERAGE INDEX         86G     123G
Joe Nathan            1.54     1.56
Juan Rincon           1.28     1.26
Jesse Crain           1.03     0.87
Dennys Reyes          0.53     0.74
Pat Neshek            ----     0.58
Matt Guerrier         0.56     0.54
Willie Eyre           0.31     0.27

The four constants in the bullpen have been Nathan in the ninth inning, Rincon in the eighth inning, Guerrier in middle relief, and Eyre mopping up. Those four relievers have barely seen any movement in their Leverage Index over the past 37 games. Meanwhile, Crain has been relegated to low-leverage spots, with Reyes' Leverage Index rising and Neshek emerging as Ron Gardenhire's preferred option in the sixth and seventh innings.

Much like with the lineup when it came to dispatching guys like Batista, Castro, and White in favor of Bartlett, Nick Punto, and Tyner, the bullpen has steadily evolved. Crain began the year coming in with runners on base and the game in doubt or pitching extra innings, but he'd now be hard-pressed to find any work in a playoff series.

As I've done to conclude each of the three previous WPA updates, here's what my WPA-based team MVP ballot looks like through 123 games after factoring in rough estimates for things like positional adjustments offensively, defensive value, and considerations for playing time:

1.  Joe Mauer
2.  Justin Morneau
3.  Joe Nathan
4.  Johan Santana
5.  Francisco Liriano
6.  Juan Rincon
7.  Michael Cuddyer
8.  Jason Bartlett
9.  Nick Punto
10. Brad Radke

In terms of who the actual team MVP is, I think reasonable cases could be made for any of the top five players and similarly reasonable arguments could be made for any of those five guys ranking fifth in the balloting. I prefer Mauer at this point because of defense and the rarity of great-hitting catchers, but I wouldn't quibble much with Morneau as the choice and the difference between the three pitchers is almost non-existent in my mind.

Rincon and Michael Cuddyer represent a clear second tier, providing the most value among Twins who aren't also AL MVP candidates. Bartlett and Punto are the third tier, with Bartlett moving up into the second tier if not for having wasted half the season in Rochester. The fourth tier is a fairly large group, which includes Radke, Reyes, Neshek, Tyner, Mike Redmond, Guerrier, and perhaps even Castillo.

Good arguments could be made for any of those fourth-tier players being more valuable than Radke, but the fact that he's thrown 155 innings in a year when the team has struggled to find reliable starting pitching at the back of the rotation has a lot of value. Plus, I view the "replacement level" for starting pitchers as much higher than for relievers, which is why Radke slides ahead of Reyes or Neshek.