I am sure some of you are familiar with the Pythagorean Theorem of Baseball, put together by Bill James in the ’80s. Here is a look at the NL Central to date. If you are unfamiliar, the formula for EX W-L is (RS/RA)/2. What is amazing to me is it almost always is within a win or two when you get to the end of the season.

Team EX W-L W-L +/-
St. Louis 43-27 45-25 +2
Chicagoo 36-33 36-33 0
Milwaukee 36-34 31-39 -5
Pittsburgh 33-36 32-37 -1
Houston 30-39 30-39 0
REDS 30-41 28-43 -2

As can see despite the claims that this is an inconsistent offense, the Reds expected Win /Loss Record is only two games better than their actual win total. If the claim about “Wasted Runs” were true, their Expected W-L would certainly be a lot higher. So despite what everyone’s “Common Sense” is telling them, The Reds are scoring just enough runs to win 28 games and lose 43.


35 Responses

  1. Mike

    No offense, but this formula does absolutely nothing to show the consistency vs. inconsistency of this offense. Is the argument that this offense is incosistent or that it’s causing them to lose games? While I think the offense is VERY inconsistent, I don’t think it makes a difference on a team where the ERA is a few points shy of a horrible team that plays their home games in the mile high air.

    This formula will always be a good indication of a team’s record, but it only shows the differece in RS vs. RA. The offense is not to blame for the dismal record, but they’re also not a good representation of their OPS, RS, etc.

    While the offense has been inconsistent the pitching staff has been anything but that. They consistently get rocked. If this team were losing games by a count of 2-1, 3-2, etc., then you could argue that the offense is failing to win games, and it would show up in this formula, but when they get beat 8-1, 6-1, etc. it really doesn’t matter.

  2. Brian Erts

    The Reds fooled this so well the past 2 years that it duped a good part of the fan base.

    My friend and I did a piece for BP on the Reds uncanny luck 2 years ago.


    This year Washington and Arizona are trying to buck the odds.

    Meanwhile the bounce has been put to bed in Cincinnati and the run differential is the 500 lb Gorilla in the room.

  3. Matt


    You are making less and less sense with every post. This formula shows very clearly that even 8-1 wins are balanced out by 1-8 losses. It proves that a team that scores 10 runs and gives up 10 runs will be a .500 team regardless of the number of games played. This formula proves that despite all the carping by people bitching about wasted runs, that over the long haul, that just isn’t true.

    Sorry that isn’t clear to you.

  4. Michael

    That is pretty cool that the pyth thm of baseball can be as accurate as it is but agree with Mike that it isn’t really addressing standard deviation/consistency……

    Also, on related topic, the Runs Created formula…..obviously, quite an achievement with all it’s gyrations and its accuracy but does anyone else see fundamental flaw in applying it at PLAYER LEVEL? At a TEAM level, that is one thing (all the individual player peculiarities offset one another) but to slice and dice total bases for a PLAYER and end up with a statement that so and so “created” x number of runs, does anyone else have fundamental issue with that?

    My understanding is in his latest versions James has added components for strikeouts, RISP hitting, solo homers etc…..in an effort to make it more accurate but the mere fact that he is acknowledging those components are needed I think points out flaws in using formula (particularly the basic versions) at a player level.

  5. Michael

    Matt, you’re confusing “Mike” and “Michael” that wasn’t my post…..

  6. Michael

    Of course, if you were just looking for another reason to insult me well have at it….I can take it………………

  7. Michael

    yes, at team level is where I have seen pyth thm used and I buy it. It makes perfect sense that you could predict team win/loss record by RS/RA.

    And I guess yes, if you buy into pth thm then it really makes the “consistency” issue kind of a mute point….

    When I brought up PLAYER level vs. TEAM level with RC I was talking about player appraisal (different issue). I wasn’t referring to pyth thm.

    As for your point about OPS correlating with RS. I buy that too at TEAM level. But that doesn’t mean that at PLAYER level whoever has highest OPS is the most valuable run producer (player) on team.

  8. Matt

    But that doesn’t mean that at PLAYER level whoever has highest OPS is the most valuable run producer (player) on team.

    Agreed. But given the same number of PA, etc. it does.

    a better stat for this is RC which I think is just OPS * PA.

    But BA with RISP and BA with Men on, or RBI are not nearly as accurate as good old OPS.

    ie. Dunn is as valuable to the Reds as Cabrera is to the Malrins from a pure hitting perspective right now.

    You don’t find that information from ba, or rbi, some situational stat, you can see it by looking at OPS.

    Dunn’s talents are being wasted when he bats 6th.

  9. Mike

    Matt, it is very clear to me what this formula represents. You were using this formula to show that the Reds offense was NOT inconsistent despite the claims, and you couldn’t be more wrong by trying to use this formula to prove your point. This formula takes into consideration that their pitching staff gets destroyed night in and night out, so of course the EX record will be similar to the actual.

    The Reds average just under 5 runs per game. If they scored 5 runs in every game this year they would still represent the same EX W-L record, so this does nothing to show how consistent/inconsistent this offense is. I’m not saying they’ve lost a lot of close games where the offense didn’t pull through. If that were the case then the EX W-L would show a greater difference than the actual W-L.

    As for “wasted runs” (not sure there is such a thing when you have the Reds pitching staff), Any wasted runs that they’ve had on offense have easily been topped by additional runs given up where they lose by large amounts, so of course it washes out.

  10. Michael

    RE: OPS
    Even given number of PAs, highest OPS at PLAYER level still doesn’t mean best run producing player.

    At team level, fine….throw all the bases in a bucket and TEAM with highest OPS is likely the best run producing team.

    But at PLAYER level, there will be players whose run producing value exceeds what their OPS would suggest. And there will be players with a relatively soft OPS.

    For easy example, compare the similar OPS of Pujols and Dunn.

    Another example would be a guy like Freel where he swaps 20 extra bases which leads to more run scoring and does the optimal thing for his slot in batting order (get on base and run) – his OPS is likely understated regarding how strong a run producer he is.

  11. Matt

    I would love to compare Dunn to Pujlols, but there is nothing similar about their OPS. I have no idea what you are talking about. they have a similar OBA, but Pujols has a much higher SLG. Pujols is a better hitter than Dunn…GASP

    Great point on Freel. But besides his SB, you also have to look at his CS. The last study was that CS *2 – SB was the most accurate value of the SB. So that nets Freel with 8 SB. Which is not reflected in OPS…which is why it isn’t a perfect stat.

  12. Michael

    Matt then at least we’re not destined for full disagreement because I’ve had similar dialog with folks who will contend Pujols and Dunn are close to equal.

    Pujols OPS has hovered ~.1000 and Dunn’s has been up that high but more in the .950s-.960’s. Dunn was up over .1000 for a while though. I’d give you specific stats on that but work web filters prohibit those stat sites.

    Point remains, Dunn’s OPS is pumped up by a BB-driven OBP. Pujols is hitting .333. Pujols has 91 HITS ! ! to Dunn’s 55 but their OPS at times this year has been ~equal and right now only ~50-60 points difference. Dunn’s OPS is WAY overstated.

  13. Michael

    (in regards to his run production/value added)

  14. Matt


    Your judgement is clouded the fact that you think 91 hits is better than 55 hits, with no other input. OPS does not treat a walk and a hit equally. It gives more weight to a single, which it should. Anybody that argues that Dunn and Pujols are equal are ignoring facts. 1.000 OPS is going to be better than .950 about 100% of the time. What is missing in OPS is SB, and park effects. But batting average or RBI doesn’t give you that either.

  15. Michael

    I’m clouded by nothing of the sort.

    Given 2 ~equal OBPs give me the one that is less BB-driven EVERY SINGLE DAY OF THE WEEK. And if you don’t see that then you my friend Matt, are the one buried in the clouds.

  16. Michael

    especially when we’re talking about an “rbi guy” who doesn’t steal bases and doesn’t even run them that well….

  17. Michael

    all those “singles” Brian that Pujols gets (dragging down TB/AB) DRIVE IN RUNS. Dunn is getting BBs in those cases so Rich Aurilia can give a “professional” groundout to end a scoreless inning.

    Also, if going to credit Dunn for all those BBs in other stats should probably use PAs when comparing with TB or runs scored to be fair.

  18. Brian Erts

    Pujols 128 ab’s with runners on 49 RBI’s
    1 RBI every 2.6 ab

    Pujols 145 ab’s with no one on 9 RBI’s
    1 RBI every 16 ab

    Dunn 85 AB’s with runners on 28 RBI

    1 RBI every 3.1 ab

    Dunn 85 AB’s with runners on 28 RBI

    1 RBI every 3.1

    Dunn 145 AB’s with no one on 10 RBI

    1 RBI every 14 ab

  19. Joel

    Isn’t batting average counted twice in OPS? (H/AB is a portion of TB/AB and hits are part of getting on base)

    It seems to me that Pujols gets plenty of credit for his batting average in OPS.

  20. Michael

    oh man…I didn’t know it was a day game today ! ! darnit…
    ha ha 2 HRs and a K.. 😀
    yeah….timely time for dunn discussion

  21. Matt

    batting average is counted twice in OPS which is why it gives a boost to a single over BB. Michael, I am done arguing with you, as long as you think swinging at balls and making outs is better than a Walk, you will not understand why Dunn is as good as he is. Fans like you are a reason why we get announcers like Marty and grande, and beat writers that are stuck on BA and RBI. They are just preaching to the audience.

    You can have a team of Caseys and Randas and Freels, and you will lose more often than a team of Dunns.

  22. Michael

    oh man, dunn is in 7th hole today….maybe that he’s mad and taking it out on the ball :mrgreen:

    well Matt, it’s pretty sad when people “like you” label people “trolls” or insult them just because they don’t agree with you, draw different conclusions from stats and/or don’t think Adam Dunn is the next superstar – pretty sad indeed.

  23. Matt

    I thought it had to a troll, I didn’t think anybody could believe such nonsense.

    Sorry for calling you a troll. And BTW, what you do is not “interpreting stats”. YOu are just ignoring what has been proven by many many people.

  24. Mike

    Let’s just not allow ourselves to get so frustrated over opinions on different stats. Let’s instead direct our frustration towards the Reds, which is really where this all stems from 🙂

    I think people need to keep in mind that when you compare OPS there is a major difference between someone like Dunn .965 as opposed to someone like Pujols 1.013. A 0.48 difference is quite significant. That doesn’t always pop out for people that don’t use the stat as much.

    I think this simple RC formula (OBP*TB) gives the “common fan” a better comparison for a players value, however, the common fan is not going to have a clue how to calculate RC, but it’s great at comparing a players value separate from his team and it’s very easy to do.

    TPA 286 OPS .965 RC 51.6 RS 49 RBI 38

    TPA 316 OPS 1.013 RC 68.1 RS 57 RBI 58

    Obviously their RS and RBI numbers are lower than RC due to the fact that these two guys are the most productive players on their team, but I like this stat when comparing a players value
    (assuming they have had a similar number of TPA) You can adjust TPA to get a more accurate result. This would knock Pujols down to 61.3 with a TPA of 286.

  25. Mike

    I think you may be confused, Matt. This is Mike and my comment was that there is a major difference between 0.48 OPS. That wasn’t directed at you, simply saying what you already understand, that 0.48 difference is major. I don’t know that anyone is saying that you have tried to compare Dunn to Pujols.

    I was showing an example of what this difference looks like for RC in comparison to the OPS difference. For the “common fan” perhaps they could see the greater difference in RC vs. OPS when comparing players.

  26. Matt

    AH…well mike you need to change your name…there are too many of you to keep up with. Like I said before I agree OPS isn’t the perfect stat, it clearly misses lots of important information, but its easy to look up, and its more accurate than others. Sorry for confusing you two again.

  27. Mike

    And I totally agree with you. It’s the best stat that is easy to use, and for guys like you and me who use it a lot, we know what we’re looking at when comparing two players.

  28. Michael

    I fully understand OPS. And as noted, actually Dunn’s OPS was over .1000 too for much of the season. Either way, 40 points of OPS is really only 20 each of OBP and Slugging (for example) which though a difference is still very comparable…….

    But when you look at the actual effective production (raw numbers) of those two, Pujols numbers are far better than the 4-5% difference which this metric would suggest.

  29. Matt


    apparently you don’t understand OPS.

    RBI and RS are a team stat that require your TEAMMATES to do things for you. RC and OPS are individual stats that tell how well YOU as individual performed. Given the same number of TPA before today Pujols is worth about 10 runs more this year than Dunn. That is what OPS tells us.

  30. Michael

    i’m not interested in “arguing” Matt. I’ll agree to disagree with you.

    I’ll leave you this thought though. Maybe they’re old school (guys like Miley/Narron) but don’t you think they’ve picked up a few things spending their lifetime in a baseball dugout??

    They may not be interested in the math behind baseball to the extent that some are but unless you have just no belief in “humans” in general to LEARN, don’t you think they probably have some real world smarts on this that you might lack?

    He was down to 6 with Miley, may be headed for 7 hole with Narron??…

    No doubt Dunn does some good things but a legitimate 3/4 hole hitter he is NOT.

  31. Matt

    yeah, these baseball people have done a FANTASTIC job with all of their smarts. Just to go along with them, because there fat ass was lucky enough to be a mediocre hitter long enough to stay in the ML long enough to become a “baseball person” is moronic. Facts are Facts, you can believe in Santa Claus and the Easter Bunny too if it feels good, but the facts don’t back them up either. Dunn and his .950 OPS is the most legitimate 3-hole hitter this team has. These baseball genius you talk of that have learned so much in the dugout cost this team runs everyday when they bat Casey in the 3-hole over him.

  32. Brian Erts

    He was down to 6 with Miley, may be headed for 7 hole with Narron??…

    Narron mentioned that he was going to perhaps put him in at #2, also #7 vs. Muldar (a LH) and yet… 2 hr’s (he led off 3 innings… can’t drive em in in those situations) Dunn leads the team in batting with the bases empty…. and yet in those situations he leads the team in RBI’s.

  33. Mike

    I thought this was an interesting comparison; Mench vs. Dunn (before Wed results). While ranking LF OPS I just noticed that they equaled each other (.948), but here is a good representation of someone who has a more heavy BB OPS against someone with only 21 BB on the season and a BA 63 points higher. The difference ends up being around 4 runs from this point in the season (with same TPA).

    TPA 280
    OPS .948
    OBA .395
    SLG .553
    AVG .241
    BB:52, 1B:22, 2B:13, 3B:2, HR:18
    Simple RC 49.77 (OBA*TB)
    RC/TPA = .1777

    Mench (played in 9 less games)
    TPA 238
    OPS .948
    OBA .372
    SLG .576
    AVG .304
    BB:21, 1B:33, 2B:19, 3B:2, HR:12
    Simple RC 45.75 (53.82 w/same TPA as Dunn)
    RC/TPA .192

    What is interesting is that they both have the same amount of RBI’s, but Dunn has scored 12 more runs on the season, this would equal out a bit more with more PA from Mench. It does show a good comparison of basic RC and OPS.