Low Scoring Teams: Better Than You Might Expect

The Seattle Mariners offense has been awful the last few years. Historically awful, in fact. Over the last decade, the two lowest scoring teams have been the 2010 Mariners (513 runs) and the 2011 Mariners (556 runs). At 619 runs, the 2012 Mariners moved all the way up to just 17th worst in the last 10 years. After three seasons of offensive ineptitude, it’s not a big surprise that the organization has dramatically shifted their focus, and has spent the winter collecting defensively challenged hitters with power, including Michael Morse, Kendrys Morales, Raul Ibanez, and taking a flier on the remains of Jason Bay.

None of these guys are great players, but they provide the team with something they haven’t had much of lately, and combined with adjusting the dimensions of Safeco Field, it’s a pretty good bet that the 2013 Mariners are going to score more runs than the line-ups that they’ve put on the field the last three seasons. But, the question remains, will those additional runs scored lead to more wins?

To understand the answer to that question, I decided to investigate the win estimators we have at our disposal, and see if perhaps there is perhaps an enhanced return to additional offensive levels for teams who have scored very low amounts of runs. Or, put more simply, does scoring 50 more runs help an offensively challenged team more than preventing 50 runs from scoring would?

For the answer, we turn to the pythag family of win estimators, of which Bill James pythagorean expectation is the most famous. You’ve probably heard about his tool, usually just referred to as “pythag” or “pythag record”, which takes a teams runs scored and runs allowed and converts it into an expected win-loss record by squaring and dividing the numbers. For most teams, in most situations, pythag holds up pretty well, but for mathematical reasons that you can read about here if you’re interested, it breaks down at the extremes. So, two noted sabermetricians — David Smyth, inventor of BaseRuns, and the man who goes by Patriot — independently found that pythag could be improved upon by using a variable exponent, rather than simply squaring runs scored and runs allowed for every team in every situation. That formula has come to be known as pythagenpat, and it is generally accepted as the most accurate win estimator in that family of tools.

Since it might help clarify why pythagenpat is preferable to pythag for these kinds of discussions, let’s look at how both tools project changes to the Mariners run differential in terms of wins and losses. We’ll just start with a baseline of 619 runs scored, using their 2012 season total, and then both add and subtract 100 runs from the total.

Team RS RA Diff Pythag Pythagenpat Pythag Wins Pat Wins
Seattle Mariners 619 651 -32 0.475 0.477 77 77
Add 100 Runs 719 651 68 0.550 0.546 89 88
Prevent 100 Runs 619 551 68 0.558 0.551 90 89

You can see the slight differences between the two systems start to show up here, as pythagenpat is more conservative by one win in both scenarios, whether you’re adding or subtracting 100 runs. However, it’s interesting to note that both systems actually prefer the run prevention approach, giving slightly higher expected winning percentages if the team prevented 100 runs from scoring rather than if the team added 100 runs of offense. It gets even more extreme if we make it 200 runs in either direction.

Team RS RA Diff Pythag Pythagenpat Pythag Wins Pat Wins
Seattle Mariners 619 651 -32 0.475 0.477 77 77
Add 200 Runs 819 651 168 0.613 0.606 99 98
Prevent 200 Runs 619 451 168 0.653 0.633 106 103

Here, you can start to really see the two diverge, as pythag begins to overestimate the amount of wins a team that allowed 450 runs to score would get. Again, pythagenpat is slightly more conservative, but again, both systems suggest that the team would win more games by preventing runs, rather than increasing their runs scored. The difference isn’t so large that the strategy should be on focusing solely on run prevention, but the results from both pythag and pythagenpat suggest that it doesn’t really matter too much which way the organization goes, whether it’s scoring more runs or preventing runs from being scored.

Now, that’s what the models tell us, but I understand that not everyone trusts statistical modeling, so let’s just take this a step further and look at pythg, pythagenpat, and actual winning percentage for every team over the last decade. That gives us a sample of 300 seasons and 24,294 games played. Over that span, how well did the models predict actual winning percentage from a team’s runs scored and runs allowed? And, are the models breaking down at the extremes, causing us to question whether a run prevented is really as valuable as a run scored to a low offense club?

The easiest way to evaluate those questions is to break the 300 teams down into smaller groups. I started off sorting by runs scored (by fewest number), then broke the 300 teams into deciles, or 10 groups of 30. Here is how those 10 groups performed.

Decile W L RS RA Diff Pythag Pythagenpat Actual
Group One 69 93 612 730 (118) 0.413 0.420 0.427
Group Two 75 87 661 718 (57) 0.459 0.462 0.465
Group Three 75 87 694 747 (53) 0.464 0.466 0.466
Group Four 79 83 716 744 (28) 0.481 0.482 0.485
Group Five 80 82 733 734 (1) 0.499 0.499 0.497
Group Six 80 82 752 772 (20) 0.487 0.487 0.494
Group Seven 85 77 775 738 37 0.524 0.523 0.526
Group Eight 89 73 799 716 83 0.555 0.552 0.551
Group Nine 85 77 830 782 47 0.529 0.528 0.526
Group Ten 92 70 888 778 110 0.566 0.564 0.565

Breaking news: Teams that score more runs win more games than teams that don’t, all else being relatively equal. Because we chose our groups by runs scored, the runs allowed number doesn’t fluctuate a great deal until you get to the last two groups, which contain a decent amount of teams that play in hitter friendly ballparks, leading both RS and RA to be higher than they are in the first eight groupings. Still, the pattern of run differential being the primary driver of wins and losses holds up pretty well, as both pythag and pythgenpat come pretty darn close to estimating overall group winning percentages for each decile. However, I think a visual aid will help you see that there is a pattern of the models missing slightly for certain types of teams.

Pythag

For the low run scoring groups, pythag and pythagenpat had a decent amount of divergence, as the floating variable suggested that the expected win totals were slightly higher despite their poor offenses than pythag would suggest. In reality, pythagenpat was right, but not right enough, as the low scoring teams outperformed their pythagenpat too. It ended up being a middle ground between pythag and actual, and only went half as far as it needed to in order to reflect actual wins and losses.

This trend of pythagenpat giving slightly higher winning percentages than traditional pythag holds through the four lowest scoring groups, and actual winning percentage is higher than both estimators in three of the four groups, with it aligning with pythagenpat once. Actual winning percentage is higher in all four groups than traditional pythag suggests. The results are the opposite on the other side of the spectrum, with pythag overshooting actual wins and losses for each of the three highest run scoring groupings, while pythagenpat is very close to the actual at higher runs scored and runs allowed totals. Or, if you’d prefer to just see the differences by group between actual and the estimators, here’s a breakdown of the gaps by decile:

Decile Pythag Minus Actual Pat Minus Actual
Group One (0.014) (0.007)
Group Two (0.006) (0.003)
Group Three (0.002) (0.000)
Group Four (0.005) (0.004)
Group Five 0.002 0.002
Group Six (0.007) (0.006)
Group Seven (0.002) (0.003)
Group Eight 0.004 0.001
Group Nine 0.004 0.003
Group Ten 0.001 (0.001)

Here, you can clearly see pythgenpat’s superiority to pythag, even though we’re talking about thousandths of a point in terms of win percentage. But, for nearly every grouping, pythagenpat is closer to actual than pythag, and at the very lowest end of run scoring, the differences actually becoming meaningful. For that first decile, which contains the 30 lowest scoring teams of the last 10 years, the difference in wins over a season between pythag (.413, 67 wins), pythagenpat (.420, 68 wins), and the actual (.427, 69 wins) begin to show up in whole numbers.

Here’s where this wraps back into our original question about whether adding offense to a low run scoring club is preferable to adding run prevention, if we assume that an even number of runs saved or allowed can be achieved. The models suggested that preventing runs would be slightly preferable, but in testing the models, we actually found that they have slightly underestimated the number of wins that low scoring teams would have, and (very) slightly overrated the number of wins by higher run scoring teams. This suggests that if there has been a bias in the models over the last decade, it has been a pro-offense bias, suggesting that teams with low numbers of runs scored might be slightly better than even pythagenpat suggests, and are almost certainly better than traditional pythag would lead you to believe.

The differences we’re talking about here are small in magnitude, so please don’t take this as a critique of pythagenpat. If you’re questioning the model’s accuracy, these numbers sure reassure you that it’s fundamentally sound, and it does do a good job of modeling wins and losses from runs scored and runs allowed. And, because the apparent bias might swing in favor of higher offensive levels, we don’t need to question the original conclusions supported by pythagenpat about whether a run scored or run saved is more valuable to a team with a base of 619 runs. Traditional pythag, pythgenpat, and actual winning percentage all support the idea that teams with bad offenses should be just as interested in improving their pitching and defense as they are improving their offense.

There is no evidence of additional benefit from improving a bad offense rather than improving a strong run prevention squad. There is simply no way to look at this data and suggest that there are strong levels of diminishing returns for run prevention, or that the models overrate the likelihood of a team with a bad offense’s chances of winning. If anything, the data points to the models slightly underrating those types of teams, and confirming the idea that, when it comes to winning more baseball games, a run is a run is a run.

Now, it’s almost certainly easier to improve on a weak offense than it is to improve on a strong run prevention group, or even vice versa. Filling a hole with a moderately useful player is simply not as challenging as upgrading on that a productive member of your team, and it’s certainly engrained within our personal psyche to focus on fixing what’s broken rather than improving areas that are working just fine. I’m not using this data to say that a team with a bad offense should just be content to keep having bad offensive clubs and focus entirely on preventing runs.

I am saying, however, that if a team makes a conscious decision to trade 20 runs allowed for 15 runs scored, they’re making a bad decision, no matter how bad their offense was the previous year. What matters is maximizing your ratio of runs scored to runs allowed, not reaching some kind of ideal balance between the two. Making a larger downgrade in pitching and defense in order to fix a bad offense is a trade-off that is likely to result in fewer wins. The same is likely true for swapping out hitters for pitchers, if you had a bad pitching staff last year.

Building a baseball team isn’t about simply improving on weaknesses. Building a baseball team is about putting as many good players on the field as possible, and caring too much what kinds of good players those are often leads to poor decision making. Don’t focus so much on scoring more runs or preventing more runs. Just focus on outscoring your opponent. That’s what wins games.




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Dave is a co-founder of USSMariner.com and contributes to the Wall Street Journal.


79 Responses to “Low Scoring Teams: Better Than You Might Expect”

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  1. cerebralinfarction says:

    Very well done, of course, Dave. If I may however, I think a part of the data that you may be ignoring with this piece is that in your substantial data set, teams that score less than 650 runs in a season have virtually no shot of playing .500 or better baseball. I think that most would universally agree that once a team gets it’s offense up to a semi-respectable level that pitching/defense is more valuable than offense. But it appears that the Mariners have had a far from semi-respectably leveled offense in the most recently completed seasons.

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    • BX says:

      2012 LA Dodgers: WP: .531, 637 RS

      And the 2011 Braves, Dodgers, and Giants all finished above .500 with fewer than 650 runs scored.

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    • Dave Cameron says:

      Two of the four lowest scoring teams over the last 10 years had winning records – the 2011 Giants and 2003 Dodgers. So, no, that’s not really how it works.

      And, no, pitching and defense are not meaningfully more valuable than run scoring at any level of run distribution that we’ll ever see in the Major Leagues.

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      • cerebralinfarction says:

        Apologies. That wasn’t meant to be presented as a “conclusion”, which is why I included ‘I think’, ‘may be’ and ‘it appears’ in my initial response. I was simply seeking a little further insight into the methodology.

        Thank you for the further clarification of the data set.

        I still can’t help but notice that each of the successful sub-650 run teams presented above was a top-tier pitching club for the season presented. Seattle certainly would fit that criteria for 2012, but with the altered dimensions at Safeco (where the club posted a 2.97 ERA) coming into play in 2013 being a factor as well as the loss of a few key contributors to their run prevention efforts from last year’s staff I think that their projected success in 2013 may change slightly. And it would appear that what the Mariners have done is to trade off expendable pieces (Robinson, Jaso, Vargas) – only one of which truly played a factor in that run prevention, mind you – to upgrade their previously insufficient offensive options without hindering the club with cumbersome long-term commitments to a class of less-than-elite pitching free agents. I’ll add, too, that perhaps aside from Michael Bourn – who I don’t believe that they will realistically be in on – this winter’s collection of free agents and traded players also lacked defenders who had potential for positive influence in this regard.

        The position scarcity and obvious defensive shortcomings aside (which will clearly make final roster construction…interesting), I believe that in this case the club may have taken the correct route.

        Again, I appreciate the depth in the piece and the correlations presented in the pythag and pythagenpat comparison are meaningful and useful. I admit that I could be way off base here. After all, I’m actually a Blue Jays fan.

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  2. goat says:

    Of course any time you add a new variable to a model it is going to more closely match the data from the sample. I think the issue with the 2010 and 2011 Mariners is that they were so bad at scoring runs that there was nothing in the range to compare them to. If a model is known to not fit the data as well at the extremes, the best solution is not trying to overfit the data, but to instead to get more data at the extremes. A better way of getting at these extremes might be a simulation of thousands of 2010 Mariners teams against a league average team, but swapping out one relatively average player on the team for someone 2 runs better on the defensive side in one model and 2 runs better on the offensive side in the other model and them making a comparison.

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  3. glib says:

    I will take the 15 runs saved over the 20 runs scored anytime. There are pitcher arms (and fragile confidence) to be protected, and effects are strongly non-linear (very little damage below 100 pitches, increasing damage starting at 100). Most if not all teams already have a 7-man pen for the same reason. Pitcher parks that allow pitchers to pitch to contact, great fielders which do the same, great defensive catchers with arm and glove, all pull more weight than current stats suggest. Defensively oriented teams appear to play relatively better in the postseason, than slugging teams.

    All this even though low scoring games increase the chances of a loss for a good team, due to relatively higher statistical fluctuations in run production. What to make of the starters health, great success, extreme pitcher park, and generally strong defenses of the SF Giants 2009-2012?

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    • Troy says:

      “Defensively oriented teams appear to play relatively better in the postseason, than slugging teams.”

      Do you have any figures to back that up? Just look at RS/RA of just the 2012 playoff match-ups alone to see that this isn’t true.

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      • Antonio bananas says:

        Your rebuttal is also erroneous though. Small sample size. What if most years it actually is true and 2012 (and I’m guessing also 2011) are outliers?

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  4. jda says:

    A tiny potential benefit to low RS/RA teams: I think the bullpens ought to be more rested than their high RS/RA counterparts.

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  5. Marver says:

    Dave,

    Low scoring teams are better than you think for a simple mathematical reason:
    - teams will low run scoring totals are more likely to come from a low run scoring environment
    - low run scoring environments shorten games
    - shortened games level the playing field between good and bad teams

    For the low-scoring teams from low-scoring environments, their home records will be propped up by the shortened games. The statement holds for high scoring teams in high scoring environments (since it lengthens the game).

    This of course means that teams in low scoring environments will win more often at home than they should when they’re bad, and win less often at home than they should when they’re good; this is the reason a hitters park is preferable to a pitchers park.

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    • kwk9 says:

      I think I understand this argument, but I’m interested to see of history backs it up. Can you site any studies? Even if you do see these conclusions backed up – how could you be sure that you weren’t seeing the effect of focused roster/park optimization strategies implemented by teams in extreme pitcher parks?

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      • Marver says:

        I have done the research, and it does work out. I’d point you towards it, but it’s just pdf documents I’ve composed on my computer. Just a simple scatterplot of road wins versus home wins, binned by park factors, will show you this quite clearly.

        And, why would a team in a pitchers park want to have less wins when they’re good and more wins when they’re bad? It seems you’d want the opposite: either better playoff odds when you’re a potential playoff team, or a better draft pick when you’re not a potential playoff team.

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      • Ivan Grushenko says:

        One reason you might want more wins when bad might be if your payroll is very low then you might be bad more than you’re good. It’s a way for low payroll teams like the 2012 A’s to try to get lucky and outperform their peripherals by winning close games. If you’re chronically bad, it might be your best shot. Also once you think you’re going to be good, you can move the fences in.

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      • kwk9 says:

        Let me state this in another way, because things are getting confusing:

        You say “For the low-scoring teams from low-scoring environments, their home records will be propped up by the shortened games. The statement holds for high scoring teams in high scoring environments (since it lengthens the game).”

        I’m questioning your causation claim – what does the length of the game have to do with it?

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      • Marver says:

        I replicated what you’re insinuating by examining head-to-head records binned by scoring environments, and simultaneously binning the winning percentages based on differences in road wins (which is the proxy for best team). The better team won in low scoring environments much less frequently than in neutral environments, but won considerably more frequently in high scoring environments than neutral environments.

        In essence, the study is isolated against team construction since the better team (road wins) is independent (at least, statistically) from park factor.

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      • chuckb says:

        Marver, I’d like to see this research you’ve done posted in the community research section here at fangraphs. It’s difficult for us to understand your methodology and your conclusions based on the little information you’ve provided here. I’m intrigued by your research and would like to understand it better.

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      • kwk9 says:

        Spent a few minutes looking into this…

        Took all team seasons since ’98. Using FG park factors – created two bins: Year-Parks with factors 96 and under (n=70), and those with factors over 103 not including (extreme outlier) Colorado(n=75).

        Within both of these bins, I’m getting r^2s of (essentially) zero when I correlate team wRC+ (proxy for “high scoring” level) and homefield advantage (home winning% minus road winning%). This doesn’t support your claim that low (high) scoring teams records are going to be propped up by low (high) scoring environments.

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      • kwk9 says:

        Now, you’re also claiming that low run scoring environments even the playing field.

        In my pitchers-park bin, I’m getting a correlation between homefield advantage and overall pythag record (proxy for team goodness) of -.27 or so, which seems more promising for you.

        I guess I would say that without seeing your research, there’s just no way I can jump on the hitters-parks-are-preferable train

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      • Marver says:

        kwk9,

        Take the 80-100th percentile bin for road wins, and examine its home wins — helps if it is also normalized by road wins — binned by park factor. Likewise, take the 0-19th percentile bins, and examine its home wins, binned by park factor. If you just scatterplot the park factor bins with road wins on the x-axis and home wins on the y-axis, if you don’t notice distinct clusters for the different park factor bins, I would uninstall whatever plotting software you’re using ;)

        Tango has basically done this research before, though it was applied to other topics, and not explored directly. Here’s an example: http://www.tangotiger.net/winactuals.html

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  6. DrBGiantsfan says:

    Runs scored and runs prevented are likely asymtotic curves that are hard to move much at the extremes. In other words, because the Mariners are already good at preventing runs, it would be hard for them to get much better at that part of their game. The easiest way for them to improve dramatically is to score more runs because it is easier to find better offensive player than they already have than better defensive players or pitchers. The question becomes whether they sacrificed too much run prevention in order to achieve improved run production. Time will tell.

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    • kwk9 says:

      Dave mentions this in the third-to-last paragraph. It makes sense when you think about scarcity and strengths from a high view of the team; but in reality, it comes down to the cost of skills on the market and the players on your roster that can be upgraded. Just because the Mariners had a terrible offense necessarily mean that offensive upgrades at certain positions will be cheaper than defensive upgrades.

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    • Baltar says:

      I know much of my point in this comment has already been made by Dave and kwk9, but I wish to expand upon what they have said.
      Much of baseball discussion about trades and FA signings is focused on filling “needs,” i.e. whether a team “needs” a SS or a LH reliever or whatever.
      In fact it does not matter whether a team strengthens a strength or weakness, as long as it improves itself. Replacing a 3 WAR 1B with a 5 WAR 1B is a 2-win improvement, just as replacing a 1 WAR SS with a 3 WAR SS is. Yes, there are other factors involved, such as what is done with the replaced player, and finding a 3 WAR SS may be easier than finding a 5 WAR 1B.
      When considering the team as a whole, it does not matter if Power, speed, pitching, defense, or whatever is improved. Yet teams, as well as writers and fans (even on this site) make statements such as, “Our main need is a speedy centerfielder, so we are going to get one,” instead of such as, “We are going to get any player who will improve our team.”
      I wish every GM, fan and writer would realize this point, so I don’t have to hear and read that nonsense. Reading this article would be a good start.
      Having said that, Seattle’s accumulation of high-offense, low-defense LF-1B-DH’s is suicide, as they don’t really improve the team on net plus they don’t have enough playing time for all these same types.

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      • Bhaakon says:

        “When considering the team as a whole, it does not matter if Power, speed, pitching, defense, or whatever is improved.”

        But, when you get down to the extreme examples, doesn’t it matter?

        If you have a good offense, then improving the power from the #7 spot will have less impact than a poor offense making the same improvement in the #3 spot, because of the difference in PA between those lineup spots.

        If you have great pitching, then getting a great defender will have less of an impact (because great pitching almost always means fewer balls in play). Similarly, if your staff is strongly GB-inducing, then a great CF will have less value.

        If you have a great hitting lineup, then adding speed has less value (because the high scoring environment demands a higher SB success rate to break even).

        I agree that trading strength for weakness is usually a bad idea, or at best lateral move, but there are roster effects that make some otherwise equivalent upgrades more or less valuable to a given team than to others.

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  7. Hank says:

    I’m confused (maybe I’m reading the tables wrong). Doesn’t your Pythagpat table suggest you can get extra wins preventing additional runs over scoring additional runs? You dismiss this as “about the same” yet it looks like an extra win preventing 100 runs as opposed to scoring 100 runs and when you up that to 200, the gap grows further.

    So given the choice between adding 200runs (98wins) and preventing 200runs (103wins)… why again is it no difference between adding runs as opposed to preventing those runs? If I could add 21 wins adding 200 runs or add 26 winds preventing 200 runs… well that doesn’t seem like a 6 of one, half dozen of the other decision in my view.

    Also given that pythagpat seems to underestimate the actual wins at the low scoring end (assuming the data is sufficient), it would suggest that this is another reason to go the low scoring route as it is undestimating the actual win % more.

    I’m not sure I understand the conclusion of the article (if there is one) and how it relates to the Mariners – as you didn’t look at all at the run prevention vs run addition of the changes they made… are you assuming it is an even tradeoff?

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    • Bip says:

      The conclusion of the article is that being a good run-prevention/bad run-scoring team does not imply that you will be benefited disproportionately by scoring additional runs vs preventing more.

      Our common sense idea is a good pitching/bad hitting team should go after hitting. The conclusion is that that approach is not necessarily correct. An opportunity to improve run prevention further should still be taken.

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  8. Bip says:

    I can’t help but think this article is also informed by the Royals-Rays trade.

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  9. kwk9 says:

    What I wonder about this is how (if) teams/parks of the lower deciles skew the results. I imagine those groupings are filled with Padres and Mariners seasons, so I’d think you could potentially have team-specific factors (roster, park optimization strategies, etc) muddying the picture.

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  10. schlomsd says:

    I’m assuming most teams know this, so why are so many teams moving their fences in instead of out?

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    • Bip says:

      Because baseball fans like seeing home runs.

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      • baycommuter says:

        I took a roadtrip to Seattle to see the A’s play in 2011. Neither team had any offense and they were pretty sleepy games. It’s impossible to fit excitement into these models, but I can see how a GM of a team that can’t score and is unlikely to be a contender would be told by the owner to get some power whether that maximizes wins or not. At least it’s better than being in Boston and having the guy in charge of TV contract tell the GM he needs players who are sexier.

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    • chuckb says:

      None of the Padres, Mets, or Mariners have won anything in quite some time. The Giants, on the other hand, are leaving the fences where they are. That’s no coincidence.

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    • Paul says:

      Not that it’s necessarily the right decision, but I think it has a lot to do with roster construction and the situation. For example, the Royals have two guys who would hit for significantly more power in other parks. Alex Gordon clearly has embraced being a high avg gap hitter, and gets beat a lot on the inside part of the plate, because he fears the dimensions at the K. Billy Butler uses the big part of the park and balls smoked to the warning track are very common. It was almost comical watching him in Camden Yards last year, all the HRs that he hit would have been very routine outs at the K, it was like watching the big kid in little league who just completely overmatches smaller kids until they start growing.

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    • Bhaakon says:

      Because making an extreme pitchers park puts your team at a disadvantage in attracting or extending hitters, and hitters are still a safer investment than pitchers.

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  11. Bip says:

    Here’s an idea for why low run-scoring teams might outperform their estimates.

    We all know that not all runs are equally valuable. We all know a home run is less valuable when you’re winning 10 to 0 than when you’re down 3 to 2. We also know Pythagorean estimates do not take this into account, making an implicit assumption that teams are not more or less likely to score runs in high-leverage situations, and that if they appear to, it is due to random variation. The high accuracy with which Pythagorean estimates predict team record over large samples bears this out.

    But, what if this assumption breaks down at the extremes? I’m thinking particularly of low scoring teams. This group probably has a higher incidence of good pitching staffs, partially because of playing in pitcher’s parks and partially because it might represent an organizational strategy to prioritize pitching. A good pitching staff may be such because of a good rotation, but they also are often characterized by a lock-down bullpen. What a few elite relievers are able to do is maximize the value of a prevented run. While there are flaws with how teams use their closers today, it is still undeniable that pitching a scoreless inning up 1-0 in the ninth is more valuable than a scoreless first inning. Having a reliever like Kimbrel, who prevents runs with efficiency approaching perfection, allows a team to choose when a prevented run is most valuable and then basically guarantee that run is prevented. The equivalent offensively would be a pinch hitter that can only get 1 at bat every 2 games, but will hit a homer in about half his at bats. The value of this would be incredible.

    So in conclusion, I don’t think any number of runs will inherently break the estimation system. However, teams at the extremes may be constructed in a way that violates an assumption of the Pythagorean estimates.

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    • kwk9 says:

      “it is still undeniable that pitching a scoreless inning up 1-0 in the ninth is more valuable than a scoreless first inning”

      The run prevention in each of innings 1-8 in that game is equally valuable to the run prevention in the 9th. WPA value.

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      • kwk9 says:

        WPA does not equal value, I mean.

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      • Bip says:

        You are incorrect. WPA DOES equal value. We’re talking about predicting a team’s final W/L record. In order to do that, we need to know how each action actually affects the result of a game. Right now, these measures assume that value is context-independent because we assume that teams cannot take advantage of context to maximize value. I’m saying that in this case, they can, and in context-dependent cases, you have to use WPA.

        You are right when you say the WPA value is constant across the game. The issue, however, is that the WPA value is not constant across different games, because the whole score matters. A starter can give two pitching performances that are identical in terms of the results, but both will have different WPA values because the score of the game will be different in both cases. If he gets 10 runs of support, his performance will have a lower WPA than if he gets 5.

        So, knowing this, it would be extremely helpful if you could pick your starter based on how many runs your team is planning to score that day. If you foresee a burst of hitting resulting in 8 runs, you put in your 5th starter. If you see a meager 2 runs, then put in your ace. The problem of course is you can’t know how many runs you will score before the game has started. On the other hand, after 8 innings, you do more or less know how many runs you will score. At that point, you know the WPA value of a scoreless inning. So, when that WPA value is highest, you put in your guy who gives you the best chance to get that scoreless inning.

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      • Jonathan says:

        Think about it in the following scenario: Your number 5 starter comes out to start the game and pitches a scoreless first inning. Your team comes up to bat, scores one run and then the inning ends.

        Context in this case will dictate the manager not bringing out his best pitcher to relieve his number 5 starter in the top of the second inning. Due to limited resources composing a 25-man roster, it would be foolish to play as if getting a scoreless second inning was just as crucial as getting a scoreless ninth inning. If the manager’s resources were unlimited, you would be correct in saying run prevention is equal in value for each inning because there would be no motivation to conserve your best weapons.

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    • ralph says:

      I have sort of speculated about a similar but kind of opposite effect that would need to be tested.

      Specifically, the better the offense, the more runs the offense will score against bad pitching… and such runs are more likely to be meaningless. So there might actually be a tiny bit of systemic error in converting runs to wins for high scoring teams.

      But I’m not really sure how I’d test the theory that bad pitching disproportionately improves good offenses compared to bad offenses.

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      • Bip says:

        I’m not sure I understand. Do you mean to say that bad pitching disproportionately improves *bad* offenses? As in a team with a bad offense will experience a greater improve from facing bad pitching than will a team with a good offense?

        Your second paragraph makes sense. The improvement in record from a 5 R/G to a 10 R/G offense would be enormous and from 10 to 20 relatively insignificant. You can never really prevent too many runs because every offense has its 2 or 1 (or 0) run games, but one can sort of score too many. At least, it may be possible to see the Wins/Run Scored graph start to flatten out a but at the upper extreme.

        Either way, that’s another theory that suggests the same conclusion.

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  12. coreyjro says:

    I’d be very interested to see the same chart and technique used for runs allowed.

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  13. jcxy says:

    To piggyback on others…

    While we should all agree with Dave’s conclusion about whether it’s better to add or subtract runs, predicting whether you’ve added 100 runs is (or should be) easier than predicting whether you’ve subtracted 100. Go back to Dave’s “would you rather add 100 or subtract 100″. This is an incomplete mental exercise…Let’s say I set out to add 100 runs. I’d guess, just from fantasy projections year over year performance, that we could be 70% or so sure that we’d added ~80-120 runs. Tight.

    Now let’s consider subtracting 100 runs through pitching and defense. Again, from fantasy projection models, we’re (much) less able to project pitching/defense performance year over year. The variance is much greater and/or the outcome distribution pattern is much closer to uniform and, thus, our confidence in our ability to subtract 100 runs erodes.

    Basically, I’m saying it’s tougher to accomplish subtracting 100 runs than it is to add 100 and so to treat them similarly is a little unfair.

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  14. Jaker says:

    Interesting article but I don’t see how you can make the following conclusion:

    “Making a larger downgrade in pitching and defense in order to fix a bad offense is a trade-off that is likely to result in fewer wins.”

    You can’t really support that statement with the data you’ve shown. Only at the very extremes does this become even remotely true. 100 runs prevented vs. 100 runs added resulted in only 1 win differential. Such a scenario is near impossible in real life.

    “I am saying, however, that if a team makes a conscious decision to trade 20 runs allowed for 15 runs scored, they’re making a bad decision, no matter how bad their offense was the previous year.”

    By pythagpat there is no difference in wins for the above scenario.

    Besides, how can you say with any certainty that a team has traded 20 runs allowed for 15 runs scored?

    Finally, are you sure your numbers of pythagpat are correct? I got 79 wins for Mariners baseline using an online calculator for pythagpat.

    Vote -1 Vote +1

    • Jonathan says:

      I voted thumbs up, but only by accident. I meant to leave a comment.

      The pythag formula family is based on the strength of run differential, so yes, giving back 20 runs on one side of the ball to get 15 on the other side lowers your run differential by 5 runs. As a single move may go, you’re right, this would not amount to much of a difference in win-loss % at the end of the year. What Dave means to point out is that as an organizational trend, this would be a bad approach, almost like robbing Peter to pay Paul. The goal is not to improve weaknesses for the sake of improving them, but to maximize your run differential over your opponents. Even this is stating somewhat simply and probably the best way to say is to maximize the probability in which you outscore your opponent in any given game.

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      • Jaker says:

        Okay but that’s kind of obvious. My point is that whether you choose to upgrade your offense or add to your run suppression, the differential — so long as you’re adding the same runs (or close to the same) as you would be suppressing — is negligible. Even on a multi-move/organizational level.

        In reality, no team will strive to add 100 runs by forgoing the opportunity to suppress 100 runs. And I use 100 because that’s the level where such a discussion becomes meaningful.

        If offense is a weakness, then adding to it won’t be any less successful than adding to pitching strength. Sure if you continue down that path many times over it will eventually be to one’s detriment but no organization would do that.

        Taking Seattle as an example, the choice between adding a bat versus building on pitching is negligible. Either way works towards maximizing run differential. There are also intangible notions like “hitting is infectious”. I have no idea if that’s true by the numbers but there is a belief in team culture and creating a more offensive environment might be spark the team as a whole.

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      • Jaker says:

        To build on this further:

        More offense also appears to generate greater attendance as another poster pointed out. I’d also assume that it leads to greater merchandising revenue and greater media coverage.

        Keeping that in mind, if we further consider that the difference in win expectancy is negligible, that strong offense is probably more infectious to other hitters than strong pitching is to other pitchers — yes that’s another assumption — then it’s easy to defend adding offense over pitching, particularly for an offensively starved team.

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      • Jonathan says:

        You’re not understanding what they mean by run suppression. The quote you put up from Dave touches upon the idea stemming from the Mariners’ recent trade where a team deals from its active production on one end to patch up production in another. Giving away 20 runs to get 15 runs back is a reduction in your differential from opponents by 5 runs. That’s negligible as one move over a full year. It’s not negligible as many moves over a full year because a team gains nothing that way.

        I think what you’re trying to say is that improved run prevention on the field OR improved run scoring at the plate is equally valuable given that nothing else has happened, and that’s correct to most extent. At a certain maximum, the value of improving run scoring or run preventing decreases because there is only so much talent and so many spots in which to place talent.

        That’s where this idea begins to break down when it comes to the Mariners’ dealing Jaso. Jaso is a valuable player in a vacuum. But in the context of this roster in this coming year, he was far less valuable to Seattle than Michael Morse was because the M’s simply have no where to hit Jaso without taking at bats from players in which they’re more invested. (i.e. Montero, Morales, etc) In this case they dealt a productive player to get one back, and you can call it a lateral move when in reality, Morse has a spot where his offense will play, whereas Jaso did not. Had the M’s done nothing, well, then what?

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      • Jonathan says:

        Also, the poster showing trends in attendance also indicated that the best predictor of attendance increase was winning, with the highest R value and lowest p-value. Also, the second best in each was run differential. You can say run scoring was third, and more significant than run prevention, but its correlative value was nowhere close to 1 and the p-value in the run prevention analysis indicates its correlative value of -0.21 probably isn’t very accurate. Those two might be closer an indicator than you think.

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      • Jaker says:

        “I think what you’re trying to say is that improved run prevention on the field OR improved run scoring at the plate is equally valuable given that nothing else has happened.”

        Yes that’s the point I was making. Re-reading Dave’s article I now understand what he was getting at. Thanks! And I agree with his assessment but ultimately, as you say, it’s more of a lateral move given the issues with playing time.

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  15. Daven says:

    For the Mariners (at least an argument I’ve heard Wedge and GMZ allude to), there might be a psychological benefit though. When you have so many young players on a complete crap of an offense, there’s potential for them to mess up their swing trying to hard, which can have long term detrimental effects as their confidence is shattered.

    So even though the Mariners might be making themselves worse overall, by creating a decent enough offense by sacrificing defense, this takes a lot of pressure off the young players offensively, who are already having to deal with an amazing amount of pressure.

    There’s also some incentive to prove to players that you can hit at the “new” Safeco. Even with a boatload of money and prospects available, Jack Z can’t seem to convince any good hitter to come play for the Mariners, and that can’t just be because the team has been bad for a while. Lots of bad teams are able to sign good hitters, so long as they have the money to throw at them, which the Mariners do. That hasn’t seemed to work for the Mariners, even getting shut down via trade for such a bat.

    So there also might be some benefit to making the offense look as good as possible this year, the first with the drawn in fences, perhaps sacrificing some wins overall because of the crap defense, so that next off season, as the M’s get closer to being able to compete, their younger players are a bit more comfortable and confident, and they can sign free agent players who are better overall to replace all the “1 year left” crap defensive players, who can hit dingers.

    Reading between the lines of a lot of Jack Z and Eric Wedge interviews this offseason, I’d say those things are on their mind, correct or not.

    Vote -1 Vote +1

  16. Klatz says:

    While the equality of offense and defense/pitching is true in terms of wins, I think it’d be more relevant to think of which factors affect attendance the most.

    In an ideal sense management should build for wins but perhaps one method, offense versus defense, would offer more benefit in terms of attendance gains/losses.

    I just took a very simple, and probably simplistic view of the relationship between attendance in 2012 versus various factors, wins, runs scored, and runs against in 2011.

    Just doing a simple linear regression you get the following R-squared values (1 or -1 being the best)

    Attendance 2012 vs wins 2011 = 0.59, p =.0006
    Atttendance 2012 vs RS-RA 2011 = .5022, p=.0047
    Attendance 2012 vs RS 2011 = .3988, p = .029
    Attendance 2012 vs RA 2011 = -0.21, p = .225

    The upshot being that wins or run differential were the best predictors of attendance the following year. Not unexpected. But offense was a better predictor of future than run prevention. So I think in business terms, offensive gains would be better and making more people come out to games.

    Wins (or the related variable run differential) trumps all but if you can’t wins perhaps it’s better to get offense than defense.

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  17. what if... says:

    a team that scores more runs will, in general, force more pitches out of the opposition. more pitches leads to more pitchers faced. more pitchers faced leads to the shallow end of the bullpen, where runs will be found easier than they possibly have already been accounted for.

    its a waterfall effect. adding 100 runs on paper might lead to 120 in games

    Vote -1 Vote +1

    • Bip says:

      Usually a bullpen will be quite good at preventing runs as well, given how they can be used more optimally than starters, and with higher exertion. Doing this might have a long term effect on opponents but I wouldn’t necessarily expect it to have a noticeable effect within one game. Maybe if you really wear them out in the first two games of a series, by the third you’re facing a noticeably weaker pitching staff.

      Vote -1 Vote +1

    • Baltar says:

      Relievers give up fewer runs than starters (about 1/2 run difference in ERA). This is just a fact.
      If the game is close, your hypothetical good offensive team will score fewer runs once they knock out the starter.
      They will only face the dregs of the bullpen if they already have a huge lead, so the extra runs are meaningless.

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  18. Jeff Gilham says:

    I hate to mess with the ongoing narrative but the Mariner’s did not have a bad offense last year. While it is true that they scored very few runs they play half of their games at Safeco which was red-hot death to offense last year (for them as well as for their opponents).

    If you look at the Mariner’s road run production in 2012 you would find that they scored 362 runs on the road which was good for 5th best in the AL! The only teams that scored more runs on the road were the Angels, Yankees, A’s and the Rays.

    How many people would have guessed that the Mariners outscored Texas on the road.

    Similarly, Seattle’s run prevention is overrated. If you look at their run-prevention on the road they were 4th worst. They allowed 391 runs on the road which was worse than every AL team except the Indians, Twins and Blue Jays.

    Yet somehow “improving” the offense was the priority?

    +5 Vote -1 Vote +1

    • jcxy says:

      This is a really good comment.

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    • Drew7 says:

      To what extent can we contribute the M’s road-scoring compared to other teams to the fact that all other teams are playing in the “red-hot death” on the road? I mean, all teams except the M’s having the disadvantage of cavernous Safeco bringing down their offensive totals during their road games surely boosts that ranking a bit, right?

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      • Jeff Gilham says:

        You are correct that other AL teams have their road production suppressed while playing in Safeco and that the Mariner’s have their road production enhanced by playing in a weighted average of parks that does not include “red hot death” to offense. This effect is real and is most pronounced for teams with the at the extremes of park factor – so excellent point. I do remember looking at this (don’t have the numbers in front of me) and I was surprised that the average park played in on the road is fairly neutral for all teams (but i think it can account for 1% or 2%. For the Mariner’s if we took 2% off their offensive numbers on the road (and I think this is generous) they still had a decent offense in 2012.

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      • Hank says:

        Rangers road wRC+ 101
        Mariners road wRC+91

        In short, folks should not be looking at runs scored in a vacuum. Texas’ offense was significantly better on the road despite scoring fewer runs.

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      • Jeff Gilham says:

        Hank makes a really interesting point and it has got me thinking. How does a team with a WRC+ of 91 score the 4th most runs on the road? That is an enormous disparity and is more in line with the “eye test”.

        I watched a lot of M’s last year and their offense didn’t look good to me anywhere.

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  19. McExpos says:

    This makes sense, unless the Mariners have determined through either scouting or statistical analysis that Jaso is not a viable option at catcher. I am willing to agree with you on a lot of different ways, but the fact is, we just don’t have the information to say anything definitive about catcher defense. The Mariners could very well agree with you, and view this as a push move on offense while improving catcher defense.

    Analytical analysis is good, scouting is good, and both is best. But the only arguments that I’ve heard for Jaso being a viable catcher are vague assertions made on alarmingly small sample sizes.

    I only ask this – if we are able to take a deeper look at catcher ability in a few years, and we are able to see that Jaso as a catcher was basically cancelling out his value, please do not write any articles trotting out the typical “Well, good results from bad process is still poor management,” because it’s possible that the Mariners had different-yet-better data than us at the time of this transaction.

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  20. I says:

    That’s interesting and all, but from the Mariners perspective, how many teams have allowed fewer than 550 runs in a season? Only 2 teams have accomplished that in the last 20 years. That would be awfully difficult. 450? Yikes!

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  21. CMB says:

    That’s interesting and all, but from the Mariners perspective, how many teams have allowed fewer than 550 runs in a season? Only 2 teams have accomplished that in the last 20 years. That would be awfully difficult. 450? Yikes!

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  22. gnomez says:

    Great work, Dave! Best article of the year so far. This is why I read Fangraphs.

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  23. Jason H says:

    Looking back in time, it is certainly the case that run differential is a major factor in winning and losing ballgames. However, this, in no way, justifies Dave’s conclusion that a GM should be equally interested in run prevention and run scoring. GMs should undoubtedly favor run scoring for field players.

    Why? Because GMs aren’t looking backwards in time, they are looking forward. Predicting whether a player generate at least X number of actual real-world runs with his bat is pretty easy (and easier the more the hitter relies on slugging). Predicting whether a player will save X number of runs is not possible. Hell, measuring whether a player has saved X number of runs after the fact isn’t even possible.

    So, in the real world, smart GMs ought to prefer the safer bet of offense over defense.

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    • Jason H says:

      A GM that values defense the same as offense for field players is like someone playing at a bizarre roulette wheel that has equal payout for all bets, and still betting “seven” over “even”… ….yeah, sure seven might win, and odd might lose, but its still a stupid bet.

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    • Bip says:

      We’re not talking about offense vs. defense, it’s offense vs. defense AND pitching. That’s a big “and and thing followed by and.”

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      • Jason H says:

        Bip,

        I agree about pitching. That is why I was careful to exclude pitchers from my statement. However, Dave is clearly talking about defense in addition to pitching:

        “Making a larger downgrade in pitching and defense in order to fix a bad offense is a trade-off that is likely to result in fewer wins.”

        Here, he makes no distinction that there is a real difference between pitching and defense. To Dave, they are all run prevention and should both be considered equal to run scoring.

        Dave then goes on to conclude the following:

        “…caring too much what kinds of good players those are often leads to poor decision making. ”

        Dave is almost exactly wrong with this conclusion. In fact, making decisions about players without caring what kind of good they are often leads to poor decisions. Considering poorly measured and unpredictable skills equal to well-quantified and predictable skills does not lead to good decisions. ….it leads to the Mariners.

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  24. Joe says:

    2003 Dodgers come to mind.

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  25. JoeElPaso says:

    This is an interesting and valuable article. Thanks. Mathematically, it makes sense. The possible range of runs is truncated at zero going down, but is infinite in the other direction. This means there are a few more instances when teams waste offensive runs (vs. needed to win) than waste defensive “runs.” Think of it this way. Suppose a team’s modal run total is 4 scored and 4 allowed. Improving the probabilities on the defensive side means increasing the chances of only 4 outcomes, 0,1,2 and 3. Each of those is fairly common and slightly ups the chances of winning a one run game (zero wasted runs to win): 4-3, 3-2, etc. Improving the probabilities on the offensive side of course is good also, and ups the chances of winning one run games like 5-4, 6-5, etc., but also includes a longer “tail” in the distribution of games like 9-4, 10-5, etc. There are not just four possible improved outcomes (like the bottom side) but many more than four (5, 6, 7, 8, 9, 10, 11, etc.) Rare outcomes at the top end, yes, but enough to account for the slightly greater effectiveness of defensive runs saved than offensive runs added.

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  26. Colin says:

    Is not the ultimate question here about team construction still centered around variance? In the Mariners case, for instance, they are probably in the bottom half of AL teams in terms of talent and likelihood of competing for a playoff spot. It seems like they would benefit by having a higher powered offense at the expense of pitching and defense simply because that raises their variance.

    Run differential might not change and their pythag might not change, but a team that scores more and gives up more runs will have a higher variance of WL record than a team that gives up fewer runs and scores less. In that case they are increasing their odds of being competitive during that particular season by accumulating more risk, thus shifting odds away from the middles and towards the extremes. So it seems like offense is preferable for lower ranking teams.

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    • JoeElPaso says:

      That’s a very good point, Colin. My point which goes in the opposite direction of yours, is that the aggregated variance of each game as discrete events favors low scoring teams. It explains the Pythagenpat findings in the main article. It indicates a very small but real advantage for the middle outcome for investing in defensive “runs.” But what you say about the team as a whole having a chance to surprise favoring high scoring teams makes sense (it goes the other way also–a higher chance of being awful). Is there empirical support for this? Last year’s A’s and O’s (ha) were among the most surprising teams in a while. Do they fit this hypothesis?

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  27. Brian says:

    Here’s where this wraps back into our original question about whether adding offense to a low run scoring club is preferable to adding run prevention, if we assume that an even number of runs saved or allowed can be achieved.

    Not to rain on the parade, but this is already common knowledge. Aside from being obvious (winning 2-1 is preferable to winning 9-8), this question has been asked and answered conclusively ages ago. I can’t find the exact links but here are some from google:

    http://www.beyondtheboxscore.com/2011/2/22/1994723/is-it-better-to-be-an-elite-run-producing-or-run-preventing-team

    http://fonzieforever.blogspot.com/2010/01/why-allowing-less-runs-is-better-than.html

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    • JoeElPaso says:

      I can believe this was established long ago, but the linked items have limitations. Additional references would be good if people can append them here. The first item is promising, but it involves generalizing from empirical evidence, the records of successful teams–a good thing to do–but to go from that empirical record to the general statement that defensive runs saved are (slightly, at the margins) more valuable than offensive runs added, would take an analysis that attempted to control for many variables, which the article does not do. It would take some sort of multiple regression modeling, I think, and even then the complexity is daunting. For example, do high offense stadiums result in physically exhausting teams over the course of the season more than low offense ones? That may shape the empirical record, even as it does not affect Dave Cameron’s initial question. As for the second item, it does start with a key issue, the distribution of runs in games as outcomes, in turn affect game events (win/not). But it then proposes a naive and unhelpful reply, which is that a run on the offensive side is a lower percentage increase than a defensive run save (1 run added is 20% of 5 but 1 run saved is 25% of 5). But percentage increase/decrease does not affect score distributions or game outcomes.

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      • Brian says:

        I agree with you that there is a lot more work to do. The best line from the second article comes here when he calculates the pythag records:

        [The team adding a run to their offense], in a season, would score 972 runs but allow 810. Their pythagorean win total would be 94, and would win 58% of their games. [The team preventing an additional run], in a season, would score 810 and allow only 648. Their pythagorean win total would be 97, and would win 59.8% of their games.

        A 162 run improvement on the offense side yields 94 wins, while a 162 run improvement on the prevention side yields 97 wins. At least by pythag, for what it’s worth. I wish I could find better articles.

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