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There is plenty of evidence that the bullpen has been the biggest weakness for the Diamondbacks this year.  The bullpen has only earned 13 saves in 2010, and has been charged with 12 blown save opportunities.  Of course, not all of the blown saves led to a Diamondback loss, and often the team blew two save chances in the same game.  So how many games has the bullpen really cost the team?  There are several ways to estimate this - let's look at the bullpen performance in a "macro" way first, and then check out the game-by-game results. The Pythagorean theorem for baseball is a win-loss predictor based on runs scored and runs allowed.  The formula* is Win% = RS^2 / (RS^2 + RA^2), where RS is Runs Scored and RA is Runs Allowed.  The team has scored 307 Runs and allowed 370 runs, so their predicted winning percentage is .408, which over 64 games would lead to a Win-Loss record of 26-38, which actually is the team's actual record.  The Diamondbacks' bullpen has allowed an amazing 138 Earned Runs in 169.1 IP, for an ERA of 7.33. This ERA is more than one and a half run higher than any other NL team. The average NL bullpen has an ERA of 4.17; if we exclude the Diamondbacks from the totals, the NL Bullpen ERA drops all the way to 3.98.  So if the Diamondbacks had an "average" NL bullpen, it would have allowed around 75 runs in their 169 IP, instead of their actual total of 138. This would have led to a Runs Allowed total of 306, and led to a predicted record of .500, or a 32-32 record. Let's look at a game-by-game breakdown of the bullpen's performance, and try to estimate how many games the bullpen has cost the team. Below is the game-by-game summary of how the bullpen has performed in each game. Color Code: Green = Save; Red = Bad Blown Save and Loss; Blue = Bullpen Loss; Pink = Close Deficit turned into Large One
Gm Opp Score Bullpen Comment
1 SD W 6-3 Howry gives up 2 in the 9th
2 SD L 3-6 Bullpen allows 3 of 6 runs
3 SD W 5-3 Bullpen throws 4 scoreless innings
4 PIT W 9-1 3 more scoreless innings for the pen
5 PIT L 3-6 Haren allows all of the runs
6 PIT W 15-6 Howry again allows 2 runs in the 9th
7 LAD L 5-9 Vasquez allows 3 runs to put game out reach
8 LAD W 9-7 Boyer/Qualls each blow a Save , but team wins
9 LAD L 5-6 Heilman/Qualls each blow Save, Boyer takes L
10 SD L 3-6 Guti. blows Save and gaves up 4 runs in the 9th
11 SD L 0-5 Norberto allows 3 in 7th to put game out of reach
12 SD L 3-5 Heilman/Guti. allows 5 runs to blow 2-run lead
13 STL L 2-4 Boyer and Qualls each allow run in 8th and 9th
14 STL W 9-7 3 Scoreless innings from the bullpen
15 STL L 4-9 Qualls and Howry allow 5 runs in the 9th
16 PHI W 7-4 Bullpen holds on to a 4 run lead
17 PHI L 2-3 Gutierrez gives up a run in the 9th to lose
18 PHI W 8-6 3 Scoreless innings from the bullpen
19 COL W 5-3 Qualls puts the tying runs on, but gets the Save
20 COL L 1-12 Bullpen only allows 2 runs in 5 IP
21 COL W 12-11 Rosales gives up 7 ER, but rest of pen is very good
22 CHC W 13-5 Bullpen only needs to throw 1 IP behind Kenendy
23 CHC L 5-11 5 runs in 2 IP lets this game get out of hand
24 CHC L 5-7 Howry/Gutierrez each give up 2 to blow win
25 CHC L 5-10 Bullpen only allows 2 ER in 4 IP
26 HOU W 9-1 4 Scoreless IP for the pen
27 HOU W 1-0 Gutierrez and Qualls preserve Kennedy's 1-0 win
28 HOU L 2-4 Gutierrez gives up another walk-off HR
29 HOU W 6-3 Haren with the Complete Game
30 MIL L 2-3 2 Scoreless IP for the bulpen
31 MIL L 3-17 Bullpen gives up 10 runs
32 MIL L 1-6 Vasquez gives up 4 ER, turning 2-1 deficit into 6-1
33 LAD L 3-7 Howry gives up 3 in the 9th, from 4-2 to 7-2
34 LAD L 3-13 Bullpen gives up 9 runs, turning game into a rout
35 LAD L 3-6 2.1 scoreless IP for the bullpen
36 ATL L 5-6 Gutierrez and Qualls each get a blown save
37 ATL W 11-1 Only 1 IP for the 'pen
38 ATL L 1-13 6 more ER for the bullpen, but game already over
39 FLA W 5-1 Again, only 1 IP for the 'pen
40 FLA L 0-8 Rivera gives up 5 ER, turning 2-0 into 7-0 deficit
41 SFG W 13-1 Again, only 1 IP for the 'pen
42 SFG W 8-7 Only 1 ER in 4 IP; Wfor Heilman and S for Qualls
43 TOR W 8-6 Gutierrez gives up 2 in the 9th, but Qualls gets Sv
44 TOR W 8-5 Qualls gets his 3rd straight save
45 TOR L 4-12 Bullpen gives up 4 runs in 5 IP
46 COL L 2-3 3 Scoreless innings from the bullpen
47 COL L 3-7 Gutierrez gives up 3 ER to put game out of reach
48 COL L 2-8 Bullpen only used for 1.2 IP
49 SFG L 0-5 Qualls gives up 2 ER in pen's only inning
50 SFG L 1-12 Rivera and Vasquez give up 5 ER in the last 2 inn.
51 SFG L 5-6 Qualls blows the Save, Rosa takes the walk-off L
52 LAD L 4-5 Vasquez balks in the winning run
53 LAD L 0-1 Gutierrez gives up walkoff HR to Kemp
54 LAD L 0-1 Bullpen has 4 good IP, but Valdez takes L in 10th
55 COL W 7-6 3 Scoreless IP, and Qualls get the win
56 COL W 4-3 Bullpen gives up 3 ER in 3 IP, but Qualls gets Save
57 COL L 2-3 2 Scoreless IP from Valdez
58 ATL W 7-4 Good outing for the 'pen; Save for Qualls
59 ATL L 5-7 Vasquez and Gutierrez each allow 1 ER for the loss
60 ATL W 2-1 Qualls picks up his 12th Save
61 ATL L 7-11 Qualls gives up 4 ER in the 9th for the loss
62 STL L 2-5 2 Scoreless IP for the bulpen
63 STL W 7-2 1 Scoreless IP from Heilman
64 STL W 7-5 Qualls and Vasquez blow the Save, but team wins
Obviously, a bullpen cannot be expected to hold onto every lead. But some blown saves are particularly bad. The team has a total of 12 Blown Saves for the season, but the 6 games marked in red are ones that the Diamondbacks had a very high probability of winning, but didn't. In the first red game (Game 9), both Aaron Heilman and Chad Qualls blew  separate 2-run leads, before Blaine Boyer took the loss in the 10th. The next day, Game 10, Juan Gutierrez first allowed the tying run in the 9th, and then later gave up a walk-off HR to Chase Headley. In Game 12, the bullpen again blew a late 2-run lead to the Padres. In Game 24, the bullpen blew a 2-run lead, and then gave up 2 more for the loss. In Game 36, Qualls again blew the save, and followed that up by also taking the Loss. Finally, in Game 54, the Diamondbacks bullpen allowed 1 run in the 8th and 2 in the 9th to blow the Save, and then Carlos Rosa took the loss in the 10th. In addition to these 6 games that the Diamondbacks probably should have won, there are 8 more games in which the team was in a tie situation, but the bullpen blew the game and took the loss.  These games are marked in Blue. Some of these were particularly bad, such as Game 15, where the bullpen turned a 4-4 tie in the 9th into a sure loss by allowing 5 runs. Also marked in Blue are a pair of walk-off losses to the Dodgers, including the balk-off loss by Esmerling Vasquez followed by the walk-off HR allowed by Juan Gutierrez to Matt Kemp (Games 52 and 53). Finally, marked in the pink/purple color are 11 more games where the bullpen turned a small deficit into an almost sure loss.  Putting all of this together, there are 6 bad blown saves, 8 blown ties, and 11 games that got of hand.  Clearly, not all of these should be Diamondback wins, but given the team's offense, I think a safe estimate is that the Diamondbacks could have won 8-10 more games with a league-average bullpen. Conclusion With an ERA of 7.33 and 12 blown saves, the Diamondbacks' bullpen has been a nightmare all season. A league-average bullpen would have allowed around 64 fewer runs, which would add 6 more games to the win column. This would have turned the 26-38 record to a respectable 32-32. Looking at the game-by-game breakdown, the bullpen performance appears even worse. There were 6 particularly bad blown saves, and 8 more games where the bullpen turned a tie game into a loss. 11 more times a close game was turned into a blowout. Combining all of this, I estimate the bullpen has already cost the team around 9 wins, so the Diamondbacks could have been 35-29 with an average bullpen. This would have put them right in the middle of the NL West race.

* Analysis has shown that an exponent of 1.83 is more accurate than 2, but for simplicity, we will use two here.