42 Responses to “Is it better to go 1-for-4 with a homer or 4-for-4 with 4 singles?”

1. Dcarson10 Says:
   April 4th, 2011 at 8:25 am

   I would say it's quite obviously four singles is more valuable than one homerun. While four singles doesn't gurantee any runs while one homer does, getting on base four times throughout a game gives you pretty good odds of scoring more than one run. That's my biggest problem with SLG and OPS. According to slugging, a double is worth two singles which just isn't true. I don't think a double increases your chances of scoring by 100 per cent. I mean I don't have numbers to back that thought up, but it just doesn't seem logical. And with OPS, it gives the same merit to OBP and SLG and I don't think the two are of equal value.

2. ctorg Says:
   April 4th, 2011 at 9:39 am

   This seems pretty obvious to me, too.

   The value of not making an out is always positive. It is the most important goal of a hitter in the vast majority of situations. 1-for-4 means three outs. Even if one of those times is a guaranteed full run, the other three take away value.

3. Jeff Says:
   April 4th, 2011 at 10:10 am

   The value of the 1-4 with a homer has a much wider range of values. In the study it goes from .6 to -.2, whereas the 4-4 goes from .2 to .05. So its safe and steady versus big potential.

4. BSK Says:
   April 4th, 2011 at 10:13 am

   I brought this up because it is something I used to wonder when I was younger. Then, I assumed the HR was better because it guaranteed a run (and possibly more). Sure, the BA would be low, but the power would offset that. Or so I thought. As I learned about better stats like OBP and SLUG, I started to think that my initial intution was wrong. I figured the 4-4 with no outs made and an OBP of 1.000 and a SLG equal to that of the 1-4 with a HR guy, it was obviously the singles. As even more advanced metrics (like WPA, among others) emerged, I was curious to see if that changed things back again.

   Thanks, Andy!

5. Andy Says:
   April 4th, 2011 at 10:15 am

   I live to serve, BSK. 🙂

6. Dvd Avins Says:
   April 4th, 2011 at 10:27 am

   A closer call is four walks vs. a HR and 3 outs. The HR still loses, though.

7. DavidRF Says:
   April 4th, 2011 at 10:29 am

   Isn't this a partial example of the "bases fallacy" that Neil was talking about a couple of weeks ago?

   If you go back to linear weights, it becomes clear that three outs and a homer are worth less than four singles.

8. Andy Says:
   April 4th, 2011 at 10:33 am

   #7 and others: Yes, I think it's quite clear that 4 singles is better. The point of this post was just to show a way of quantifying it. I was not trying to suggest that we've solved some incredibly huge mystery...

9. BSK Says:
   April 4th, 2011 at 10:41 am

   Here is what MIGHT be a huge mystery worth solving...

   What would Tim McCarver think the right answer to this question was? And, if he was wrong, what kind of ass backwards logic would he apply and would anything be able to change his mind?

   I still think back to the days where he refused to accept that a team scored 2 or more runs more often in an inning that started with a HR than with a BB. Mind boggling...

10. Andy Says:
    April 4th, 2011 at 10:46 am

    God, I had totally forgotten that McCarver said that. I wish you hadn't reminded me.

    At the time, I remembered thinking about whether there was any chance he could possible be right. I suspect in some VERY isolated cases there could be a "letdown" effect, i.e. batters who follow the leadoff homer don't try as hard because his team has already scored, or maybe the pitcher gets relieved by a more effective guy, or something like that. But it can't be the norm, of course, that a leadoff homer is ultimately worth less.

11. BSK Says:
    April 4th, 2011 at 11:19 am

    I remember when they posed the question, I thought, "This might be one of those situations where historical precedent is counter-intuitive." But as I thought about it, the answer became clear. Once the lead-off HR is hit, you are back in the same base-out situation, but a run has scored. The question is the same as asking whether you are more likely to score at least 1 run with no runners on and no outs or 2 runs with one runner on first and no outs. What was amazing is that he ran with it for several days, if not weeks. He simply couldn't accept the reality. Even if you account for probability, they were looking at historically what happened more often. He wanted to act as if history never happened.

12. Noodle Says:
    April 4th, 2011 at 11:24 am

    As far as OPS and it flaws, Aaron Gleeman once called another stat GPA (G for Gleeman?) which takes On Base and multiplies it by 1.8 then adds slugging; (We all "know" that not making an out has value; and OBP is worth more than eqaul value comapred to Slug)...then you divide the answer by 4 - you will usually get answers between .250 and .350, so it matches up with the Batting avg we are familar with. Try it and you will see that the great sluggers who make outs are worth less than lesser sluggers who don't. Pick some guys and try it!

13. Whiz Says:
    April 4th, 2011 at 11:24 am

    WPA isn't necessarily the best way to measure this. Maybe better is to use changes in run expectancy, instead of changes in win expectancy. Of course that is basically what using linear weights would do (as DavidRF suggested), and it gives the same answer, at least in this case. And if you have enough data, the WPA would probably average out to roughly the linear weight result, too, so maybe it's not so bad after all 🙂

14. DavidRF Says:
    April 4th, 2011 at 11:29 am

    Part of McCarver's problem is the hubris in which he makes those statements. Even his book is called "baseball for brain surgeons".

    I actually tried reading that book. Early in the book he made some claim about how it wasn't good to have good hitters throughout the entire lineup because it made the offense "boring". I couldn't read the book after that.

    I hope my memory is fuzzy. Its been a while since I read that. I hope he was making some comment about how he didn't like the increased level of offense and/or the DH but at the time I didn't read it that way.

15. John Q Says:
    April 4th, 2011 at 12:54 pm

    I think #1 Dcarson10 made some good points in that slugging percentage gives the perception that a double is worth twice the value of a single, a triple 3x the value of a single and a HR 4x the value of a single which is wrong. A HR is usually about 3X the value of a single, a Triple is usually around 2.25X the value of a single, a Double is about 1.6X the value of a single.

    I have a copy of the Hardball times from 2006 and they had a listing of relative values of singles, doubles, etc. from 2002-2004 and the value was listed as this:

    Single: .465 of a run
    Double: .772 of a run
    Triple: .1.055 of a run
    HR: .1.394 of a run
    Non Intentional Walk: .315 of a run
    Intentional Walk: .176 of a run
    HBP: .342 of a run
    SH: -.127 of a run
    SF: -.052 of a run
    DP: -.839 of a run
    K: -.287 of a run
    Other outs: -.250 of run

    I would imagine these numbers change from year to year but I would think the ratios are still relatively the same. During these years a HR was 3x not 4x the value of a single. So according to these numbers with everything else being equal a 4-4 day with 4 singles was worth 1.86 runs on average and a 1-4 day with 1 HR was worth 1.394 runs on average.

    The ability to draw walks is still a tremendously underrated skill in baseball. A walk is usually worth about 2/3 the value of a single yet it's often looked upon by baseball fans/pundits as something like 1/10 the value of a single.

    A sacrifice hit is really a dumb play and should only be used when a pitcher is at bat. You could also maybe justify a SH when a very slow runner who can't hit with no power is up at bat so you can stay out of the Double Play.

    Grounding into a DP is an underreported negative event in BB. Billy Butler gets a lot of attention for his .318 batting average (6th in A.L.) but rarely are his league leading 32 GDP brought up.

    with all other things being equal:

    2-4 with two singles is more valuable than a 1-4 with a double. 3-4 with three singles is more valuable than a 1-4 with a triple. 4-4 with four singles is more valuable than a 1-4 with a HR.

16. Tommy Says:
    April 4th, 2011 at 12:55 pm

    On an OPS basis it's 2000 vs 1250; which I think pretty much sums up the excellent analysis. OPS (OPS+ for multi-season comparison) isn't 100% bulletproof (remember, it's an easy approximation for runs created) but as far as figuring out the offensive value of a player in one number, its combination of simplicity and accuracy is without peer.

17. John Autin Says:
    April 4th, 2011 at 1:57 pm

    I'm with Whiz @13 -- WPA isn't the most objective way to answer this question.

    Generally speaking, the measure of WPA increases as the game goes on, and is at its highest in the late innings. This creates a bias -- and I think a rather large one -- in favor of the 4-for-4 game, since at least one of those hits is almost sure to come in the late innings.

    Mind you, I think the 4 singles would still come out ahead by any reasonably good method of tackling this question. I just don't think WPA is the right tool for the job.

    Consider a season-regarding measure analogous to WPA, called Pennant Probability Added. Should we use that to determine the MVP Awards? By the same logic as used in WPA, the PPA leader could be some guy called up in the last week, who gets a big hit in the late innings of a do-or-die final game, which vaults his team into the playoffs.

    Sorry, but I'm not giving that guy the hardware.

18. Andy Says:
    April 4th, 2011 at 2:00 pm

    JA, couldn't I I make the argument that WPA tends be lower earlier in games and at least 1 of the 4 singles is guaranteed to come early in the game?

19. John Autin Says:
    April 4th, 2011 at 2:39 pm

    Andy, yes, I see that. But I suspect that the leverage index increases at closer to an exponential than a linear rate as the game goes on, so the advantage gained from having a guaranteed hit late in the game would be greater than the disadvantage from having a guaranteed early hit.

20. John Autin Says:
    April 4th, 2011 at 2:44 pm

    Another question is whether 286 games (the 4-singles data set from 1996-2010) is enough to insure a normal distribution of leverage opportunities for the group.

    I would be more inclined to look at this question in simple terms of average Runs + RBI for each set ... and will try to post something on that as time allows.

21. kds Says:
    April 4th, 2011 at 2:57 pm

    JA, Two things greatly determine WPA; Closeness of the score and closeness to the end. A 3 run homer in the first inning of a tied game will have a greater WPA than that HR in the 9th of a 10-3 ballgame. (And you are much less likely to have a 7 run lead very early.)

22. John Autin Says:
    April 4th, 2011 at 3:29 pm

    OK, on second thought I realize that the individual (Runs + RBI) totals is a rotten tool for this comparison, because it ignores the team cost of the 3 outs made by the HR hitter. So instead of presenting that data, I'll show a couple of other measures. In each case, I used the exact same data samples Andy used

    (1) Team W%:
    Singles: .641 (184-103) -- projects to 104 wins for a regular season.
    HR: .603 (516-340) -- projects to 98 wins for a regular season.

    (2) Team R/G:
    Singles: 6.14 R/G
    HR: 5.00 R/G

    What's missing here, of course, is a sense of how much of the difference in W% or Team Scoring is attributable to the player in question. But regardless of that, it seems clear that, yes, 4 singles is more valuable than 1 HR.

    Other notes:
    -- I was surprised that the 4-4 players did not score a run in almost a third of their games. Their average runs scored was 1.05 R/G, virtually the same as the HR group. What this showed me is that I don't have an intuitive sense of the average rate of scoring a man on base.
    -- Perhaps a study such as this could help convince the remaining "RBI believers" of their folly? The HR group averaged twice as many RBI as the 4-single men (1.59 to 0.80) -- yet the singles-hitters' teams averaged 23% more runs per game.

23. John Autin Says:
    April 4th, 2011 at 4:04 pm

    Kds, I see your point. I am still trying to get my head around certain aspects of WPA. One in particular is, what are the relative weights of closeness and lateness?

    For example, on Opening Day, top of the 1st, scoreless game, Howie Kendrick hit a solo HR; WPA value about 0.10. In the bottom of the 9th, game tied again, Kila Ka'aihue hit a solo HR; WPA value about 0.36, or about 3-1/2 times the value of Kendrick's HR. That multiplier feels a little hefty to me.

    Also, in that same game, Jeff Francoeur drove in the tying run in the bottom of the 4th with a 1-out grounder to SS (infield presumably playing back). The WPA value of that event was roughly zero, because there were runners on 2nd and 3rd; Francoeur essentially didn't change the run expectancy calculation. What bothers me there is -- and correct me if I'm wrong, but this is based on the run expectancy / win expectancy info on B-R -- the calculations give no consideration to the batters coming up next. Well, Francoeur (bad as he is) was followed by Alcides Escobar, who is far worse. (Not to mention Brayan Pena and Chris Getz at the bottom of that lineup -- yikes!) Anyway, I think the run expectancy of that situation was a lot lower than presumed by the WPA formula, and so I think Francoeur producing a run, even with a weak groundout, was a positive event for his team.

24. Al Dimond Says:
    April 4th, 2011 at 4:27 pm

    LI doesn't go up late in games. It goes up late in close games. I don't know what it would mean for LI to go up "exponentially" as the game progressed, but I do know that the LI near the start of the game is close to 1, and LI is defined so its mean value is 1. It's obvious from this information that LI can't generally increase over the course of a game (I'm using the mathematician's "generally" here).

    But even if those things were true, they wouldn't give the singles hitters an advantage over the HR hitters. The singles hitters would hit a quarter of their singles in high-leverage situations, but the HR hitters would hit a quarter of their HR in high-leverage situations also. If you're taking the mean of WPA it evens out. This is *basic* math.

    You might argue that hitters likely to go 4-4 with singles are likely to bat in different situations than hitters likely to go 1-4 with a HR -- but that would probably just mean the sluggers are in slightly higher-leverage situations overall.

    Some other interesting things: a lot of these games involve more than 4 plate appearances, while the players have only 4 AB because of walks (or other non-AB PAs like sacrifices). If we just want to measure 1B against HR we should eliminate those games, or alternately cut out the other stuff from the WPA scores. The comment on the rate of scoring by 4-4 players is interesting -- I wonder if there's some bias there in only counting games with 4 AB. A lot of good contact hitters hit at the top of the order. If a leadoff hitter goes 4-4, he'll bat 5 times unless the rest of his teammates get on base about 5 times or less (excepting double-plays and home teams that only bat 8 innings). Eliminating games with 5 or more AB might have some kind of selection effect.

    Anyway, the story is clear based on linear weights, WPA, and RE24... and the team W% and R/G numbers are interesting also!

25. Al Dimond Says:
    April 4th, 2011 at 4:32 pm

    @23: WPA indeed does not account for player strength -- it's pretty hard to do that, actually! Well, it's simple to think of how it might be done, but it requires some compute power to figure it out for every PA. There are actually a bunch of different ways you could look at WPA (and RE24, which is easier), for the purposes of looking at strategy or for measuring player performance, if you could easily adjust for strength of upcoming hitters, pitchers, etc.

26. BSK Says:
    April 4th, 2011 at 4:39 pm

    JA-

    I talked a while back about how amazing WPA would be if it actually factored in the situation. My understanding is that it is based on historical modeling. It doesn't matter whether the next batter up is Pujols or the pitcher... whether the guy on the mound is Mariano Rivera or Big Fat Bartolo Colon. WPA assumes all these things are equal. I would love it if it could say something along the lines of "A team down 1 with a runner on 2nd and 2 outs in the 9th wins X% of the time on average, but with Albert Pujols up, they have a Y% chance of winning." In all likelihood, even the best hitter would only make a minute difference between X and Y, but it would still be fascinating to see.

27. Jimbo Says:
    April 4th, 2011 at 5:04 pm

    Not making 3 outs is a big deal.

28. Al Dimond Says:
    April 4th, 2011 at 5:10 pm

    @26: One of the difficulties is in projecting a specific hitter-pitcher matchup. But... if you're willing to actually sit there, multiply each possible result of the plate appearance by what you feel are, say, the probabilities of Pujols doing each, then add them together... you can actually estimate the WPA with Pujols batting and a sea of averageness following. With basic programming skills and projections you believe in you could simulate whole lineups I guess... though at some point you have to start incorporating managerial moves into the predictions, and then it all gets crazy...

29. David in Toledo Says:
    April 4th, 2011 at 5:20 pm

    PI has established that 4-for-4 games are more rare than 1-for-4 home-run games. Games in which the winning team scores "a lot" of runs are also, by definition, rare. Might these two variables have significant overlap?

    That is, when a batter hits a homer but makes out on his other three trips, that might well be the only home run in the game -- one bad pitch, one lucky swing. The opposing pitcher(s) may be very effective.

    But if a batter goes 4-for-4, the opposing pitchers probably don't have very good "stuff," aren't fooling this batter (or most of the others), and are probably giving up lots of hits. Therefore, a greater correlation to win probability.

30. John Autin Says:
    April 4th, 2011 at 5:54 pm

    @24, Al Dimond -- I'm processing your points. As I said @23, I'm aware that I don't have a good grasp of the interaction between closeness and lateness as the game goes on. Perhaps I can find a table of score/inning/base/out situations that would help me.

    That said, I think your point on "even if those things were true..." is incorrect. What you said is true -- both the singles hitter and the HR hitter would have roughly 1/4 of their positive events late in the game. What you didn't say is that the HR hitter, in the other 3/4 of his late ABs that he doesn't hit a HR, makes an out (by the definition of our hypothetical), and thus amasses large negative WPA. The singles hitter (by the definition of our hypothetical) virtually never has a negative event; at least, he never makes a batting out. And so, if leverage index did tend to go up generally as the game wore on, then that would be an inherent advantage for the singles hitter.

31. jojo Says:
    April 4th, 2011 at 6:55 pm

    This is a silly discussion. Of course 4 for 4 is better than 1 for 4 with a homer......Just imagine that a team where everyone went 1 for 4 with a
    homer played a team where everyone went 4 for 4....what would be the final score...infinity to 9 or thereabouts.
    A better question would be, "Is 3 for 4 (all singles) better than one for 4 with a homer....It certainly appears to me it is....if everyone on the team goes 3 for 4, you have one run in, and men on first and second (or third) with one out in the first inning....with two .750 hitters coming up....the other team gets one run per inning on average....what's the choice?
    2 for 4 might be as good as the homer team, since singles are going to bunch up at times, and be worth a lot....it would be interesting to run a computer program of a team where everyone went 2 for 4 all the time....run a random hit chart for the season and see what the average number of runs per game for that team would be.....I'll bet it's close to the nine or ten the homer team gets.

32. Al Dimond Says:
    April 4th, 2011 at 7:37 pm

    @30: The negative WPA amassed by the sluggers' outs is (roughly) proportional to the LI. The sluggers' outs move around the leverage spectrum just as their HR do. I just can't see where the bias comes from.

    @31: That's an interesting way to look at things, but it probably answers a different question than what's been asked. You're using, essentially, a per-out method of measuring offense. That makes sense when measuring team offense, because outs are baseball's "clock". A team that bats .750 must make 27 outs and thus must rack up around 81 hits (not always exact due to double plays, etc), and will usually score over 50 runs per game (usually more than 80 baserunners, and they can only strand 27 per game, only hit into 9 double plays, etc). An individual player going 4-4, or 3-4, doesn't affect what his teammates do very much. He gives his teammates (and maybe himself) a few more chances to bat, but not the 100+ chances per game that a team batting .750 gets. So it typically makes more sense to measure individual hitting on a per-PA basis.

33. Artie Z Says:
    April 4th, 2011 at 8:36 pm

    @22 JA - How did you handle the double counting problem when calculating those winning percentages? Looking at the data, it's not really a problem with the 4-4 games as there is only 1 game (7/7/96, Angels vs. A's) where 2 players on the same team went 4-4 with 4 singles (Garret Anderson and Chili Davis in case people are curious - and yes, the Angels won).

    There are 70 games where 2 players on the same team went 1-4 with a HR and 7 games where 3 players on the same team went 1-4 with a HR. Teams were 50-20 in the games in which exactly 2 players went 1-4 with a HR and were 6-1 in the games in which 3 players went 1-4 with a HR.

    I don't know the best way to handle that problem, but if you only count each game once, it drops to a .573 winning percentage "games in which exactly 1 player went 1-4 with a HR". The 4-4 winning percentage drops to .639. This probably provides a lower bound on expected winning percentage.

34. John Autin Says:
    April 4th, 2011 at 10:42 pm

    @33, Artie Z -- Maybe I'm dumb -- the double-counting problem, as you put it, didn't occur to me. Can you explain why it matters? Given that I made no other attempt to control for the performance of their teammates, it seems OK to me to double-count those games. The question being pursued was not, "What is a team's record when exactly one player goes 1 for 4 with a HR," but rather, "When any player goes 1 for 4 with a HR, what is his team's record, regardless of what his teammates do?"

    And if I shouldn't double-count the games with "paired" events, what should I do about games where a player went 1 for 4 with a HR, while a teammate went 4-4, all singles? Is it OK to count that game for each group? And then what about players doing one or the other event for opposing teams in the same game? Is there a basic principle of statistical analysis that I'm ignoring? Seriously, I'm trying to understand.

35. Al Dimond Says:
    April 4th, 2011 at 10:57 pm

    By the way, this is a leverage index table. I don't know what years this data was taken from. At the start of the game the LI is 0.9; you'll note that in the 9th inning the LI has much higher peaks than in the 1st inning, but also lower valleys.

36. John Autin Says:
    April 4th, 2011 at 10:59 pm

    @30 -- Maybe what I was calling "bias" is no more than WPA "doing its job," so to speak. If there's an "inherent advantage" in WPA for the 4-4/singles group, I guess that just means that collection of events has more WPA value, on average, then the 1-4/HR events.

    As I think more about WPA in general and this question in particular, I'm better able to grasp, as you noted earlier, that leverage index does not necessarily increase as the game goes on; it increases in close games, but decreases in games with a large score differential.

    But could you comment on the game I described @23? One player hit a go-ahead HR in the 1st; another hit a walk-off HR in the 9th. WPA values the latter about 3-1/2 times as much as the former. But in prosaic terms, do you think the walk-off HR was that much more important to the game's outcome?

    Also, I don't think anyone has commented on my hypothetical Pennant Probability Added measurement (I should have called it Postseason Probability Added), applying the WPA model to an entire season instead of a single game. Would that be a meaningful measure to you? And if not, why not?

37. cheese Says:
    April 4th, 2011 at 11:13 pm

    McCutchen went 1-4 with a homerun today, and they won 🙂

38. Yippeeyappee Says:
    April 5th, 2011 at 11:02 am

    I'll take the 1-4 with the home run if the other 3 AB's are E9's!

39. Al Dimond Says:
    April 5th, 2011 at 3:49 pm

    @36: Consider a team that rallies from a 10-run 9th inning deficit with 2 outs by hitting, like, 13 straight singles. The first of those singles will have a WPA of almost nothing and the last few probably somewhere around .2? In the end, every one of those singles was necessary. Had any one of the hitters made an out the game would have been over, and we know, from our post-game perspective, that the batting team won -- that if the ump had called the first hitter out in a close play at first rather than safe, he not only would have turned a hit into an out, but a win into a loss. What we didn't know when WPA was calculated for that event was that it was a *win* that the ump turned into a loss. We thought it was a game we were almost sure to lose, maybe .000001 of a win that was turned into a loss.

    WPA for every different event is calculated from the perspective of the time it occurred. From the yet different post-game perspective we might think of things differently. When a player hits a late home run when trailing by a lot, that's seen just as a garbage-time hit, too-little too-late, if his team eventually loses. If his team eventually wins, however, it's the start of a heroic comeback. WPA. If a pitcher gives up runs with the lead and still wins, some say he "pitched to the score" and that the runs he gave up were meaningless. If his bullpen later blows it, the pitcher "let them stay in the game", and is called a bum. WPA just says, "When the pitcher started the inning we had a 70% chance of winning. Now it's 65%".

    Something like RE24 is based on yet another perspective: an inning-out-of-game perspective. It says that the runs scored in any inning are bound to average out to about the same win-value. A run is a run is a run. If a team scores 10 additional runs over the course of a year they will win about one more game on average. You can also have a plate-appearance-out-of-inning perspective: over time a player will hit some 3-run homers and some solo shots, and ultimately they'll average out, so you can assign a single value to a home run completely out of context -- that's what Linear Weights do.

    But you can think about importance however you want to. In-game, post-game, out-of-game, out-of-inning, whatever. How you think about it probably depends on how you're watching the game... as a fan of a player, as a fan of a team, as a fan of the game, as a coach, as a player, as a scout. It's all up to you. If you believe in pluralism you can even consider multiple perspectives at once!

40. Johnny Twisto Says:
    April 5th, 2011 at 4:00 pm

    But could you comment on the game I described @23? One player hit a go-ahead HR in the 1st; another hit a walk-off HR in the 9th. WPA values the latter about 3-1/2 times as much as the former. But in prosaic terms, do you think the walk-off HR was that much more important to the game's outcome?

    Once the game was over, of course not. But at the time it was hit, yes, it changed the probability of winning the game much more than a first-inning HR. Would you pitch Mariano Rivera in the first inning?

    Also, I don't think anyone has commented on my hypothetical Pennant Probability Added measurement (I should have called it Postseason Probability Added), applying the WPA model to an entire season instead of a single game. Would that be a meaningful measure to you? And if not, why not?

    Not entirely hypothetical. I think the Hardball Times calculated this a few years ago (I don't know if they (or anyone) does it on a regular basis.) Yes, it would be a meaningful measure to me. In an MVP vote, I do think context matters, and give a boost to players on contending teams and who perform best in the "biggest" games. It's not all I would consider, of course.

41. Al Dimond Says:
    April 5th, 2011 at 7:54 pm

    One interesting thing about the Hardball Times metric is that, because many games affect the postseason chances of teams that aren't playing, and because the teams are playing simultaneously, the total added probabilities don't add up to 0. To make them all add up to 0 would be a tremendous feat by hand -- you'd have to put every event from every game in correct order, recalculate postseason odds after every event, and assign WPA for various different teams to the involved player (CC Sabathia's late-season dominance in 2008 was the impetus for the study... say on one day he pitched a shutout; he simultaneously helped the Brewers, hurt his daily opponent, hurt the Brewers' divisional and wild-card rivals, and in some cases helped his daily opponents' divisional rivals). It would be possible with a pretty simple computer program and all the data.

42. Sean Says:
    April 6th, 2011 at 7:59 am

    Doesn't this depend on the situation?