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2005-06-04 07:27
by Jon Weisman

The Reliever Reciprocity Rule, or Triple R, or RRR. It's very simple:

If you would use a reliever in a given moment in a game with a lead of X, you should use him with a deficit of X.


  • If you would use Yhency Brazoban in a given inning with a two-run lead, you should use him in the same inning with a two-run deficit.

  • If you would use Eric Gagne in a given inning with a one-run lead, you should use him in the same inning with a one-run deficit.

    Close games are winnable, whether you are in the lead or trailing. If the reliever is available to work with a lead, he is available to work without a lead. If he needs to rest that game, he needs to rest no matter what.

    This goes with the Just Get the Out Rule: Use your best reliever in a tight situation whenever it comes up. If you need an out - give yourself the best chance of getting the out. Worry about the rest later. Rest pitchers when they need to rest - not because you've rendered them irrelevant by using lesser pitchers.

    The RRR. The Just Get the Out. Learn it. Know it. Live it.

  • Comments (53)
    Show/Hide Comments 1-50
    2005-06-04 07:51:53
    1.   Jeromy
    Great point Jon. For the most part I completely agree. If the principle was used last night, Brazoban may have been chosen over Gio in the 8th.

    The only problem is that you do have some relievers in the pen who may get over/under used. Your principle only works if the variance of the games works out so that there is an equal distribution of close games and 3-4 run games and blowouts. What if you play a stretch where 10-12 games in a row are close and tight? You can't use Brazoban and Gagne every game. Some mid-relievers have to step up from time to time and get big outs. Carrara was on the spot last night and was one pitch away from getting it done. He hung a pitch and Hall got it. The RRR has potential as a general rule, though.

    2005-06-04 07:58:44
    2.   Jon Weisman
    Jeromy - when the Dodgers actualy play 10 close games in a row - or even five close games in a row - get back to me. You might be surprised how rare that is.

    Then, as I wrote above, you need to rest your top relievers.

    Then, Carrara has to be able to get the job done.

    Until then, it's not that Brazoban is a lock or Carrara is hopeless. It's just giving yourself the best possible chance.

    2005-06-04 08:12:01
    3.   walbers
    Jon, have you read the comment over on The Juice, about Gagne? it's the 2nd or 3rd comment under Will's post "blue corolla". very interesting....wasn't sure it had been commented on here, though i know some of your other readers have been talking about Gagne's apparent problems. thought you might want to bring that discussion over to this side. rgds, a different Will
    2005-06-04 08:35:15
    4.   Jon Weisman
    Will, there was an entire post and discussion on Gagne Thursday night/Friday - just scroll about three posts down.
    2005-06-04 09:28:17
    5.   Fearing Blue
    I agree with the general intent, but I don't think the formula works. Here's one reason:

    Currently and throughout last year, Gagne was pretty much used 9th inning or later in the range of a tie score through up by 3. Using this criteria, he pitched 81.1 innings, which we should probably assume is at or near his maximum. If we extend that range from down by 3 to up by 3, and keep the maximum of 81.1 innings, we would be guaranteed to have a number of those situations where he could not pitch. Thus, my belief is that any proposed relief strategy should keep the same sized ranges of innings and runs.

    2005-06-04 09:33:54
    6.   Jon Weisman
    Why should we assume 80 innings for Gagne is the magic maximum?

    In any case, the Dodgers already have guaranteed situations where he doesn't pitch. Unfortunately, those situations come in winnable games. Meanwhile, the Dodgers have also guaranteed he will work in games that are blowouts when he's over-rested, just to give him work.

    That's what needs to change.

    At least under the RRR, he would be used in a meaningful game every time. I don't see the flaw in that.

    2005-06-04 09:56:38
    7.   regfairfield
    Tracy loves to talk about how his pitchers need rest, yet he puts Gio into a clutch situation after pitching three innings the last two days.

    That pretty much invalidates any excuse he has for resting Gagne and Brazoban.

    2005-06-04 10:15:28
    8.   Fearing Blue
    #6: We should assume 80 innings is the maximum because closers are dropping like flies due to injuries and Gagne has already spent time on the DL this season for two different injuries.

    Here is the breakdown of Gagne's usage last season:

    Standard Usage:

    Up 2 8th - 2 (2 innings x1)
    Up 3 8th - 2 (2 innings x2)
    Tied 9th - 9 (2 innings x3, 3 innings x1)
    Up 1 9th - 13
    Up 2 9th - 9
    Up 3 9th - 9
    Tied 10th - 3 (2 innings x1)
    Tied 11th - 2 (2 innings)
    Up 1 11th - 1

    Critical Situations:

    Up 1 in the 8th - 3 (1 on, 2 out, 1.1 innings)
    Up 2 in the 8th - 3 (1 on, 2 out, 1.1 innings)
    Up 3 in the 8th (1 on, 2 out, 1.1 innings)
    Up 4 in the 8th (2 on, 2 out, 1.1 innings)
    Up 3 in the 9th (1 on, 2 out, .1 innings)
    Up 4 in the 9th - 2 (2 on, 1 out, .2 innings)
    Up 5 in the 9th (3 on, 2 out, .1 innings)

    Getting Work:

    Down 3 9th - 1
    Down 6 8th - 1 (.1 innings)
    Up 4 9th - 1
    Up 5 9th - 2
    Up 7 9th - 1
    Up 9 9th - 1
    Up 10 9th - 1

    2005-06-04 10:25:29
    9.   Fearing Blue
    Here's a percentage summary of his innings pitched:

    Standard usage:

    Tied 9th or later = 26%
    Up 1 in the 9th or later = 17%
    Up 2 in the 9th = 11%
    Up 3 in the 9th = 11%
    8th inning up 2 or 3 (2 innings) = 9%

    Critical situations = 16%
    Getting work = 9%

    So, if you want to add something, than you need to take something out. And taking out the "getting work" section isn't reasonable. With any strategic assignment, you're going to hit lulls, and I can't imagine it being much less than 10%.

    2005-06-04 10:32:31
    10.   Fearing Blue
    Looking at the breakdown and the percentages, here is how I would suggest deploying Gagne.

    1) Gagne should come into tie games in the 9th. There's no reason he should be reserved for the 10th or 11th.

    2) Don't use Gagne when we are "Up 3 in the 9th". Instead save him for situations where we are "Down 1 in the 9th". Let Brazoban do the cherry picking for the easy save situations.

    3) Do a better job defining critical situations and allocate more innings to them by not having Gagne pitch to start the 8th with a 2 or 3 run lead. Let Brazoban handle the 8th unless he gets into trouble.

    2005-06-04 10:34:44
    11.   Formerly R
    What happens when you have to "just get the out" in the 4th, 6th, 7th, and 9th? In the 4th, not knowing you will need to "just get the out" a few more times throughout the game, who do you use? Do you immediately go to Gagne and Brazoban and hold your breath hoping you won't need them the rest of the game? Extreme example, I know, but sometimes you have to "just get the out" 2 or 3 times in the same game.

    What happens if you need to "just get the out" in the 9th and the out happens to be Derrek Lee and the only guy left in the bullpen is Elmer Dessens?

    I know that the above scenario would be rare, but I imagine that having to just get the out more the once isn't, particularly in crucial intra-divisional games in September.

    2005-06-04 10:42:10
    12.   Fearing Blue
    Correspondingly, I would deploy Brazoban as follows, along with my guesses at the percentages (my assumption is that a lead in the 8th has roughly the same probability as a lead in the 9th):

    Standard Usage:

    Up 3 in the 9th = 11%
    Down 1 in the 8th = 12%
    Tied 7th inning or later (only 9th or later if Gagne has already been used) = 20%
    Up 1 in the 8th = 16%
    Up 2 in the 8th = 12%

    Critical situations = 20%
    Getting work = 9%

    2005-06-04 10:44:20
    13.   Fearing Blue
    #11: I would use Brazoban to get critical outs in the 6th and 7th and Gagne to get critical outs in the 8th and 9th, and then leave them in for the subsequent inning. Blowing one of them too early in the game (for instance, the 4th) means you're going to be seeing a lot of Erickson and Houlton the rest of the game.
    2005-06-04 10:52:12
    14.   Fearing Blue
    #6: Additionally, when a team is down by 2 or 3 in the 9th it's not a very meaningful game. The chance of winning is very low for either situation. The historicals website estimates at 5%/7% and 2%/3% for top/bottom halves of the 9th, with a ton of data points for each.
    2005-06-04 10:52:32
    15.   Jon Weisman
    #11 -

    Of course, no system is perfect. Yes, you will have situations where you have to get the out more than once. All I'm saying is - all I'm saying is - if Gagne is available, use him. If he needs rest, then rest him and hope for the best. But don't hold him back because you might need him later, and risk not using him when you could have.

    If you have more than one "get the out" situation, then does it really matter what order you use the pitchers in? Really. Does it matter?

    2005-06-04 11:00:50
    16.   Jon Weisman
    #8 - and as far relating Gagne's innings go to injury, I don't by this assumption. His injury this year was not a wear-and-tear injury, it was a knee injury from playing pepper after months of rest - the arm injury that followed came from compensating from the knee injury.

    #14 - It's all about reciprocity. If you don't want to use Gagne down by three in the ninth, then don't use him up by three in the ninth. If the game is that remote from winning in the ninth when you're down, it must be that remorte from losing in the ninth when you're up. Are you reading what I wrote in the original post carefully?

    2005-06-04 11:12:44
    17.   Sam DC
    This is fascinating -- would be interesting to run the same principles to ground re pinch hitters.

    Bob -- Here's hoping today's RDGC is 1968.

    2005-06-04 11:28:34
    18.   Bob Timmermann
    From looking at older Dodger games, I'm trying to see when Lasorda adopted the present day usage of relievers. The Dodgers were something of late adaptors in the relief pitching world.

    Aside from the freak year of 1974 when Mike Marshall would pitch in just about ANY tough situation, Alston was not one to use the pen a lot. His other relief stars, primarily Perranoski and Brewer didn't put in that many innings, but they often had 2 inning appearances.

    As most of us remember, Lasorda in the 1980s would use a reliever until the guy's arm fell off (e.g. Tom Niedenfuer in 1985). Even when Jay Howell came by in 1988, he wasn't used in Eckersley-like style.

    It seems that the acquisition of Todd Worrell, who was accustomed to being used in just save situations in St. Louis, made Lasorda change his style.

    There really hasn't been any manager in baseball who has deviated from the usage patterns of relievers like Tracy has since Jack McKeon managed in Cincinnati and would bring in Williamson or Graves for a couple of innings as the situation dictated.

    That was in 1999 and both Graves and Williams topped 110 IP.
    But McKeon also had some rather mediocre starters in 1999 aside from Pete Harnisch.

    While I like the RRR in principle, in practice, the problem is one of unilateral diarmament as it were. Baseball managers, are rather conservative now when it comes to changes. There is too much criticism if someone does something different.

    I can't imagine a manager who thought he could change things around a lot, like a Paul Richards, being hired.

    Bobby Valentine, who was one of the last managers to pass for an inconoclast out here, didn't use his bullpen much differently from anyone else.

    Strangely, Japanese baseball for years operated using the "smokejumper" phenomenon. But when Kaz Sasaki started to have success for Yokohama, his manager would just use him in save situations. He had an insane season there in 1997. He had 38 saves and pitched in 49 games and had an ERA of 0.90. The next year. The next year he had 45 saves in 51 games and an ERA of 0.64.

    Yokohama's manager was considered something of a rebel for using his ace reliever in just save situations.

    Valentine is in Japan now and his time, Chiba, is having a good year. His closer, Kobayashi, has 16 saves. He's pitched in 18 games and has thrown 16 1/3 innings.

    2005-06-04 11:31:12
    19.   Bob Timmermann
    Sorry it won't be 1968 today.

    I just looked at the game for 1968 when it comes up.


    2005-06-04 11:40:04
    20.   Fearing Blue
    #16: I've read it a few times now.

    I would argue that the reciprocity is based around how much an additional run changes your probability of winning, not your current probability of winning. By bringing in your best reliever, you're trying to maximize the chance the other team does not score, so conversely you should evaluate the value by the cost of the additional run.

    Thus, if you would use a reliever up by 3 (an additional run puts you up by 2), you should also use him down by 1 (an additional run puts you down by 2).

    2005-06-04 11:42:33
    21.   Fearing Blue
    Doh.. messed that up. It should be that you should use him down by 2, since an additional run puts you down by 3. The delta from up by 3 to up by 2 is the same as the delta from down by 2 to down by 3.
    2005-06-04 12:18:21
    22.   Steve
    It is extraordinarily frustrating to me that one would need any kind of formula other than one's inborn common sense to tell you to bring in Brazoban instead of Carrara. But it appears Tracy has none, and therefore we must create some sort of "artificial" rule of thumb -- a replacement-level common sense. FB, the beauty of its rule is its simplicity. If Tracy doesn't have the inborn common sense that tells him to bring in Brazoban instead of Carrara (or to put his pants on over his legs instead of his head), how is he going to grasp all of the permutations and nuances you're talking about?
    2005-06-04 12:19:09
    23.   Steve
    And when I say "you," I mean the royal "you" meaning "one" and not "you" personally.
    2005-06-04 12:26:38
    24.   Fearing Blue
    Had to go take a shower to think about this for a while. Jon, you are absolutely correct, reciprocity is an easy and important way to argue for improving closer usage. But, as stated in #20, the center of reciprocity is between Up-1 and Tied. I'll try to demonstrate that fact mathemetically (skip the rest if you don't care). If we are the visitor (V) and the home (H) team is up in the bottom of the 8th, we'll look at two situations. Let H and V be the respective situations.

    We assume at the end of an inning V(x) = H(x), which is roughly accurate, though there is always a slight edge to the home team (about 3%).

    We look at the following two situations to begin the 8th; V - H = 1 (Up-1) & V - H = 0 (Tied).

    Our reliever can let in any number of runs (0, 1, 2, etc..) in the inning, but we'll just compare 0 runs and 1 run for simplicity.

    IF, V - H was 1 and is still 1, H's and V's winning %s are equal to H(-1)% and V(1)% respectively. V(1)% = 1 - H(-1)% since the probabilities have to add up to 1.
    IF, V - H was 1 and is now 0, H's and V's winning %s, H(0)% and V(0)% are both now equal to 50%.
    Thus, the change in V's winning % is equal to V(1)% - 50% = 1 - H(-1)% - 50% = 50% - H(-1)%.

    IF, V - H was 0 and is still 0, H's and V's winning %s, H(0)% and V(0)% are both equal to 50%.
    IF, V - H was 0 and is now -1, H's winning % is now H(1)% and V's winning % is now V(-1)%.
    Thus, the change in V's winning % is equal to 50% - V(-1)% = 50% - H(-1)%.

    Thus, the additional run is equally critical in those two game situations. You can show the same analysis for V - H = 2 being equivalent to V - H = -1 and so forth.

    Thank you for the post. I think this is really cool stuff.

    2005-06-04 12:29:38
    25.   Fearing Blue
    #23: Agreed. Brazoban was the right, and fairly obvious, call in that situation. There are two parts two Jon's relief strategy, reciprocity and getting important outs. I'm just working on analyzing reciprocity. Getting the important out should be obvious (to anyone but Tracy), but it's a lot harder to prove.
    2005-06-04 12:29:59
    26.   Bob Timmermann
    Wow, I actually understood that math.

    Now I need to take a shower!

    2005-06-04 12:30:47
    27.   Fearing Blue
    #24: Should say "... end of an inning V(x)% = H(x)%, which is...".
    2005-06-04 12:32:17
    28.   Bob Timmermann

    I still don't think Tracy's relief pitcher usage patterns is much different than any other manager.

    Not that it's right. But I don't think he's an outlier in this area. He just expects the relievers to do better and they're not. And I don't know if he can adjust much with the personnel he has.

    2005-06-04 12:37:27
    29.   Fearing Blue
    #28: I agree. Some teams like the Padres, can get away with incorrect bullpen management, because the difference in relievers top to bottom isn't that large. Thus, when the Padres bring Chris Hammond into the most critical game situation it isn't that bad.

    But, when the difference is consistently using Carrara in the most critical game situation instead of Gagne, you're likely going on DePodesta's list.

    2005-06-04 12:57:44
    30.   Bob Timmermann
    So far, the Padres have been able to avoid having a big gaping hole in their bullpen. Reyes isn't all that good, but even Rudy Seanez, on comeback version 5.2, is OK. And Hammond throw about as hard as I do.

    It could be worse for Tracy. He could have the Giants relievers to work with.

    The Giants started a pitcher with an ERA over 5 (Lowry) and the three relievers after (Levine, Brower, and Walker) are also all over 5.

    The DBacks are trying to "improve" their pen, but that so far has consisted of acquiring Matt Herges and Claudio Vargas.

    2005-06-04 13:00:17
    31.   Bob Timmermann
    I wonder if I heard a scream from Utah when Adam Kennedy stole third down 3 runs with nobody out.

    However he was safe and Anderson hit a 3-run homer to give the Halos a 6-5 lead in the 7th.

    2005-06-04 13:43:02
    32.   Xeifrank
    Jon and Fearing Blue both make great points, backed up by data analysis. I think part of the problem is that we really only have 2 guys in the bullpen who we can rely on for getting outs. Actually both Brazoban and Gagne have had their flaws too, which just makes it even worse. If we had two more stoppers in the bullpen, not great pitchers but better than we have now, this wouldn't be such a glaring hole.
    vr, Xei
    2005-06-04 13:43:19
    33.   Xeifrank
    Over/Under for Houlton tonight is 4 2/3 IPs.
    vr, Xei
    2005-06-04 13:53:22
    34.   Fearing Blue
    I'll go over on my boy Houlton.
    2005-06-04 13:54:42
    35.   coachjpark
    I was at the game watching in the left field pavilion into the bullpen, and I believe Tracy is at fault for two reasons:

    1) He could have just let Duaner Sanchez pitch the entire inning. He got the first two outs. Why not let him get that 3rd out?

    2) If you plan on using the "micro" managing strategy, I agree that you bring in Yhency Brazoban to get the final out of the inning.

    2005-06-04 14:02:12
    36.   Sam DC
    BTW, for everyone not named Bob (or Eric or Jon, or actually, like half the folks reading this probably already know what I'm bout to write), the reason I asked about 1968 was that I saw in the paper that, on this day in 1968, the Dodgers beat the Pirates 5-0, with Don Drysdale pitching his sixth consecutive shutout on route to 58.2 scoreless innings.

    Now that'll simplify your bullpen management.

    2005-06-04 14:15:01
    37.   Formerly R
    Jon, re: #15. Does it really matter? I think so, yes. Again, perhaps this is an extreme comparison. Suppose you have a "just get the out" situation in the top of the 5th and your reliever fails. Your team now trails. Well, your offense has many opportunities to get that lead back.

    Compare that to the very same "just get the out" situation in the top of the 8th. If your reliever fails then your offense has far fewer outs to work with to get the lead back.

    So, in response to the question, is there really a difference between the two, I'd say yes. I mean, fundamentally, yes there is.

    Am I being overly simplistic?

    2005-06-04 14:18:18
    38.   Jon Weisman
    Well, except, if you get the out in the fifth inning, you now have a greater chance of having a lead by the time you get to the eighth.
    2005-06-04 14:23:09
    39.   Fearing Blue
    #38: Except that you're now forcing yourself to use secondary relievers later in the game, so you may not have a better chance of having the lead in the eighth. Figuring out when to apply "get the out" is mathematically complex because it needs to take into account the expectations of the alternative. In my mind, it's very similar to the decision as to whether to bat for Weaver in the 4th last night.
    2005-06-04 14:27:17
    40.   Fearing Blue
    #35: Yeah.. I absolutely agree. In my mind the quality of the Dodgers bullpen is ordered as followed (considering that Houlton is currently in the rotation):

    1) Gagne
    2) Brazoban
    3) Sanchez
    4) Wunsch
    5) Carrara
    6) Alvarez
    7) Erickson

    Sanchez had gotten two outs and had only let one man on due to a curveball to the foot. I can somewhat see bringing Wunsch in to "get the out", because he may be better against lefties. But, if you're already playing "get the out" with Wunsch, what the heck are you doing bringing in Carrara?

    2005-06-04 14:29:11
    41.   Fearing Blue
    #39/40: Scary. I used "In my mind" twice. Perhaps I need to get out more, instead of having all these conversations with my imaginary friends.
    2005-06-04 14:32:56
    42.   Fearing Blue
    #41: I agree.
    2005-06-04 14:33:03
    43.   Fearing Blue
    #41: Me too!
    2005-06-04 15:03:51
    44.   Steve
    Over! He's not Weaver, Alvarez, Carrara, or Erickson. Therefore, I allow myself to be blinded by hope.
    2005-06-04 15:13:46
    45.   Jim Hitchcock
    Hey! Steve! Buddy!


    2005-06-04 15:34:36
    46.   Bob Timmermann
    The DBacks supposed ace, Javy Vazquez, is getting clobbered in the first game of a doubleheader in Philly. It's 8-1 after 4.

    Archfiend Russ Ortiz is pitching in the nightcap, which means Bob Melvin is going to have to be judicious in his use of the bullpen.

    Watching a rain delay in an NCAA softball game is not an interesting sight.

    2005-06-04 15:37:08
    47.   Bob Timmermann
    When I get to the 1968 game, the starting pitcher is going to be Claude Osteen.

    He won't got the distance. The Dodgers relievers in 1968 weren't all that bad. But boy did those hitters stink.

    2005-06-04 16:05:29
    48.   Formerly R
    Re: 15, 38, and 39.

    You may get out of the fifth with the lead, but for the remaining innings you're playing Russian Roulette with your bullpen. One of 'em's got the bullet. And if one of them blows up in the 8th or 9th, then where are you?

    But, in any event, back to the original question (#15), I still say, yes, it does matter. It may not matter as much as MLB managers try to make us believe it does, but it does matter. I know that this is painfully rudimentary, but outs are the clock of baseball and I don't think you can disregard that.

    I'm all for using more effective relievers earlier in the game, but I think you still need to save a stud for the end. You can't blow all your ammo in the middle innings and hope the guys that are left will get it done.

    Maybe this is what the fancy formulas are saying but I'll say it anyway. No matter how you slice it, the more quality arms you have in the pen, the better off you are.

    2005-06-04 16:11:42
    49.   molokai
    Taking the under. By the time this game is over everyone will be wondering why a team who is supposed to be contending for the West is carrying an old rule 5 pitcher who doesn't have much of an upside. Hoping for a slugfest.
    Depo should use some of the salary he's holding back to sign Mike Maddox. What he's done with that pitching staff is amazing.
    2005-06-04 16:14:31
    50.   Marty
    I won't be around until maybe the end of the game. I'll take the over on DJ. I like him (for no logical reason) for 6 tonight. I'd like to see Werth break out with some power one of these days.

    Have fun guys/gals

    Show/Hide Comments 51-100
    2005-06-04 16:31:45
    51.   Steve
    For no other reason other than Tim Brown amuses me:

    Mike Lowell's OPS: .582

    2005-06-04 16:48:12
    52.   LAT
    I am taking the under. Can't drink the kool-aid tonight and forget DJ is a retread.
    2005-06-04 17:30:41
    53.   LAT
    Maybe tonight will be a good night after all: fat tub of goo Daryl Ward just grounded into DP with bases loaded

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