Table of Contents

Sunday, April 13, 2008

Markov: Dusty Baker's lineups aren't half bad

Update: Due to several errors with how I was using John Beamer's Markov model, this study is frankly a load of hooey. I am leaving it here for archival purposes, but please disregard pretty much everything here. Sorry about that--I had done several checks to be sure I was "doing it right," but it turns out that the specific ways I was thinking about the input were absolutely incorrect. Embarassing to say the least, but that's what happens with research now and then...

I'll post an updated version of this study when I get a chance. The results are far less surprising, and much more in line with other work on lineups than these were.

There was a chorus of complaints from Reds' faithful over the Reds' opening-day lineup, and this has continued in reaction to subsequent lineups over the Reds' first two weeks of play. I asked folks to submit to me what they felt the opening day lineup should have been in a "Can you make a better lineup than Dusty Baker" contest of sorts.

I've now taken those lineups and, with the help of PECOTA '08 projections, I've plugged them all into John Beamer's Markov Chain spreadsheet that came with the Hardball Times 2008 Annual. The results surprised me, and I expect that they'll surprise a good number of you as well.

Background - Evaluating Lineups (you can skip if you want)

The past several years have seen increasingly sophisticated work done in the area of lineup construction. Among the most widely-publicized tools that stems from this effort is David Pinto's lineup tool, which I first discussed roughly two years ago. It is based on a set of studies that used linear regressions to relate player OBP and SLG at each lineup position to runs scored. Those regressions indicated that we should make some changes to how lineups have traditionally been designed. Around the same time, The Book was published; it used a different approach, but arrived at many of the same conclusions. Check out my old post for details.

The problem with approach upon which Pinto's tool, in particular, is built is that a lineup is an incredibly dynamic thing. Regressions just report typical relationships between OBP and SLG across different lineup spots based on how MLB managers have filled out their lineup cards in the past. That's a different thing from having a tool that you can use to try out radically different lineups, as Pinto's tool permits one to do. For example, if you hit the pitcher 1st, that will have large effect on the run-producing opportunities of the #2 and #3 hitters compared to hitting an on-base machine like Scott Hatteberg 1st. In other words, the player placed into each of the lineup slots will have direct effects on the opportunities of all other players in the lineup, and the consequences of a seemingly minor substitution might not be immediately apparent. Regression simply will not capture these interactions.

Enter Markov Chains. Markov chain models are models that organize complicated processes into steps. At each step, you input a certain probability that a variety of specific events will occur. The result is a series of branching event chains, which are then summarized according to their probabilities. John Beamer described them here in his introduction to his model.

It turns out that this is a great way to model a lineup's performance--if you can input the chances of different offensive events happening for each player (using, for example, PECOTA projections), you can have Markov step through a lineup throughout a game, keeping track of outs and innings, all the while keeping track of the entire range of possibilities in terms of offensive production. In other words, if you can design a Markov model that fits the game of baseball, and give it accurate data, it will provide you with more precise estimates of offensive production by a lineup than with the regression coefficients can ever hope to do because it actually attempts to simulate baseball.

In the 2008 THT Annual, John Beamer released an excel-based Markov chain model that is apparently capable of accurately modeling baseball just as I described above. It is probably the best publically-available tool for lineup analysis.

2008 Opening Day

First, let's look at the Opening Day lineup, isolating our choices to only those players that Dusty chose to play (i.e. no Joey Votto, no Jay Bruce, etc). That way, we can focus more on the effect of moving players around the batting order, and less on player substitutions.

Below is a table of the Reds' opening day players, along with their 2008 PECOTA projections broken down into my favorite set of diagnostic stats:

Patterson Corey 458 16% 5% 0.306 0.268 0.307 0.402 0.134 0.709 56.3 4.76 0.300
Keppinger Jeff 514 6% 8% 0.317 0.305 0.364 0.418 0.113 0.781 70.6 5.82 0.336
Griffey Ken 435 16% 11% 0.283 0.268 0.350 0.480 0.213 0.830 65.7 6.20 0.354
Phillips Brandon 629 16% 6% 0.302 0.274 0.325 0.444 0.170 0.769 86.4 5.43 0.324
Dunn Adam 579 25% 16% 0.298 0.261 0.388 0.549 0.288 0.937 103.0 7.73 0.392
Encarnacion Edwin 561 16% 8% 0.308 0.285 0.356 0.493 0.208 0.850 88.5 6.51 0.354
Hatteberg Scott 278 9% 11% 0.296 0.285 0.368 0.440 0.155 0.808 40.3 6.12 0.352
Valentin Javier 208 12% 9% 0.287 0.269 0.333 0.424 0.155 0.757 27.1 5.22 0.327
Pitcher Pitcher 363 35% 3% 0.202 0.123 0.156 0.153 0.030 0.309 ---
Note: Markov pays no attention to plate appearances, except to generate frequencies of each even happening. Therefore, it doesn't matter if a player has 200 or 500 PA's, what matters are the number of singles, doubles, strikeouts, walks, etc, per plate appearance. Also, Markov doesn't know about lefty/right splits--it just assumes an average pitcher, who is mostly (but not entirely) right-handed. :)

I received 14 different lineups from users both here and at RedsZone, and I threw in a few of mine own as well. There are actually 9! = 362,880 possible lineup combinations of these nine players (counting the pitcher slot) that we could theoretically try, but I think these represent a good part of the diversity of recommendations that most folks might like to try. Below, I list all of those lineups, as well as the Markov-based estimate of runs per game that those lineups could be expected to provide. The +/- Baker column lists the season-level differences in performance of each lineup compared to Dusty Baker's true opening day lineup (in italics).

Name 1st 2nd 3rd 4th 5th 6th 7th 8th 9th R/G R/162G vBaker
Bluzer-OD Keppinger Hatteberg Phillips Dunn Griffey Encarnacion Patterson Valentin Pitcher 4.90 793.6 4.5
Chris-OD2 Keppinger Encarnacion Dunn Phillips Griffey Hatteberg Patterson Valentin Pitcher 4.89 792.9 3.8
Pickoff-OD Keppinger Encarnacion Dunn Griffey Phillips Hatteberg Patterson Valentin Pitcher 4.88 790.5 1.4
Patterson Keppinger Griffey Phillips Dunn Encarnacion Hatteberg Valentin Pitcher 4.87 789.1 0.0
AVG-rank Keppinger Encarnacion Hatteberg Phillips Patterson Griffey Valentin Dunn Pitcher 4.86 788.1 -1.0
brad-OD1 Keppinger Hatteberg Griffey Dunn Encarnacion Phillips Patterson Valentin Pitcher 4.86 787.6 -1.5
SLG-rank Dunn Encarnacion Griffey Phillips Hatteberg Patterson Valentin Keppinger Pitcher 4.86 786.8 -2.3
OPS-rank Dunn Encarnacion Griffey Hatteberg Keppinger Phillips Valentin Patterson Pitcher 4.84 783.4 -5.7
OBP-rank Dunn Keppinger Hatteberg Encarnacion Griffey Valentin Phillips Patterson Pitcher 4.83 782.7 -6.4
texasdave-OD Keppinger Hatteberg Dunn Encarnacion Griffey Phillips Valentin Patterson Pitcher 4.80 777.7 -11.4
Chris-OD Keppinger Hatteberg Encarnacion Dunn Griffey Valentin Phillips Patterson Pitcher 4.79 775.7 -13.4
jinaz-OD Encarnacion Dunn Keppinger Griffey Hatteberg Phillips Valentin Patterson Pitcher 4.77 772.2 -16.9
jinaz-OD-exploit Encarnacion Dunn Hatteberg Griffey Keppinger Phillips Valentin Patterson Pitcher 4.76 771.5 -17.6
Trace's Daddy-OD Hatteberg Dunn Griffey Phillips Encarnacion Keppinger Valentin Patterson Pitcher 4.76 770.7 -18.4
justincredible-OD Hatteberg Keppinger Griffey Dunn Phillips Encarnacion Patterson Valentin Pitcher 4.75 770.0 -19.1
OesterPoster-OD Hatteberg Keppinger Griffey Dunn Phillips Patterson Encarnacion Valentin Pitcher 4.74 768.0 -21.1
mlbfan30-OD Hatteberg Keppinger Dunn Encarnacion Griffey Phillips Patterson Valentin Pitcher 4.72 764.8 -24.3
Degenerate-OD Hatteberg Keppinger Dunn Encarnacion Griffey Phillips Patterson Valentin Pitcher 4.72 764.8 -24.3
fareast-OD Hatteberg Keppinger Phillips Griffey Dunn Encarnacion Valentin Patterson Pitcher 4.70 761.4 -27.7
brad-OD2 Hatteberg Dunn Encarnacion Griffey Phillips Keppinger Patterson Valentin Pitcher 4.69 760.6 -28.5
joel-OD1 Hatteberg Dunn Encarnacion Griffey Phillips Patterson Valentin Pitcher Keppinger 4.68 758.9 -30.2
redsmanrick-OD Hatteberg Dunn Encarnacion Griffey Keppinger Phillips Patterson Valentin Pitcher 4.66 755.5 -33.6

All I can say is "wow." Dusty's lineup didn't come out as #1, but it was darn hard to beat, and only an estimated 5 runs per season behind Bluzer's top-rated lineup.

Think about that. Baker's lineup violates one of the biggest "rules" for lineup construction that us stat people harp on--his leadoff hitter is projected to have a miserable 0.307 OBP this season. And yet, the interactions between players in his lineup are such that his lineup results in more wins per season than most other least, according to Markov. My own lineups, which I designed based largely on the lineup chapter in The Book, rated as a fairly middle-of-the-pack lineup, and came out a good 17 runs (~1.5 wins) behind Baker's model. And some of the user-submitted lineups, which look very reasonable to my eye, came out more than 30 runs per season behind Baker's. Again, "wow."

A few other observations and interpretations:
  • The range of performances of different lineups was about 38 runs per season, despite all lineups featuring the exact same players. That's almost 4 wins worth of variation! More than I expected to see.
  • Lineups with Keppinger leading off did better than lineups with Hatteberg leading off, despite them being rather similar hitters according to PECOTA--both are high OBP guys, though Hatteberg projects to have more power.
  • Most of the "best" lineups have Phillips batting in the 5th spot or higher in the lineup. Many of the "worst" lineups (like mine) have Phillips batting in the 5th spot or lower.
  • None of the lineups that bat Dunn in the #2 spot do very well, despite his crazy-high OBP.
  • My "idiot" lineups, in which I just ranked players by a rate stat like OPS, did pretty well for themselves (better than my "smart" ones). Ranks by AVG did particularly well, despite batting Dunn 8th!
Markov also can report how often each lineup slot will lead off an inning for any lineup configuration. Here is Baker's lineup, as well as the top-5 and bottom-5 lineups, broken down by how many innings each slot led off (on average):

Lineup Slot - # Innings led off
Lineup Name 1 2 3 4 5 6 7 8 9 StDev
Baker-OD 1.76 0.77 0.81 0.95 1.04 0.86 0.89 0.85 1.06 0.30
Top 5 Lineups

Bluzer-OD 1.80 0.78 0.79 1.08 0.95 0.85 1.15 0.88 0.72 0.33
Chris-OD2 1.81 0.77 0.79 1.03 1.02 0.88 1.13 0.83 0.73 0.33
Pickoff-OD 1.86 0.77 0.78 1.03 0.97 0.89 1.14 0.83 0.73 0.35
AVG-rank 1.78 0.77 0.68 1.01 1.05 0.89 1.13 0.92 0.78 0.33
brad-OD1 1.8 0.8 0.8 1.1 1 0.9 1.1 0.9 0.7 0.33
Bottom 5 Lineups

Degenerate-OD 1.80 0.77 0.79 1.38 0.93 0.86 0.90 0.83 0.73 0.36
fareast-OD 1.82 0.76 0.68 1.37 0.95 0.82 0.90 0.85 0.85 0.36
brad-OD2 1.84 0.77 0.79 1.38 0.93 0.80 0.86 0.90 0.72 0.37
joel-OD1 1.82 0.82 0.67 1.37 0.96 0.80 0.87 0.90 0.78 0.37
redsmanrick-OD 1.84 0.77 0.79 1.38 0.93 0.81 0.87 0.89 0.72 0.37

  • Baker's lineup is very different from the others:
    • It has the lowest frequency with which the leadoff hitter would lead off innings, though only by a small amount. Still, it might be enough to help diminish the problem of Patterson leading off.
    • It has the highest frequency with which the #3 hitter would lead off innings. The #3 hole is the spot in the lineup that most frequently bats with two outs and runners on in real baseball, but Baker's lineup might reduce this effect compared to the others.
    • Baker's lineup also has the pitcher leading off innings more often than any other lineup. That can't possibly be a good thing, can it?
  • Top-5 lineups vs. Bottom-5 lineups
    • The #4 slot leads off innings an awful lot for the bottom-5 set of lineups. This is typically a power hitter spot (either Griffey or Encarnacion in these cases), so you'd normally want runners on base when they're hitting. This problem is minimized in Baker's lineup.
    • One really neat finding: the standard deviation among lineup slots in the frequency with which they led off was consistently lower for "good" lineups then for "bad" ones. This might mean that the "bad" lineups have more bottlenecks that tend to kill innings, resulting in certain lineup spots being more likely to lead off the next inning. So, perhaps good lineups distribute the best hitters around the lineup more than poor ones?
...I'd like to do a bit more with these data, breaking down the different lineups based on their rate stats, but this has taken long enough to get written as it is. So, let's move on to the Best of the Organization lineups.

Best of the Organization Lineups

The other set of lineups I requested involved folks' choice of any players from within the Reds' organization. I received 26 of these lineups. Here they are, again along with Dusty Baker's opening day lineup, as well as a few of his others from the first week.

Name 1st 2nd 3rd 4th 5th 6th 7th 8th 9th R/G R/162G vBaker
mikegrayson-Best Bruce Keppinger Griffey Dunn Encarnacion Phillips Votto Ross Pitcher 5.01 811.3 22.2
brad-Best Keppinger Votto Bruce Dunn Griffey Encarnacion Phillips Valentin Pitcher 5.00 810.3 21.2
Chris-Best1 Keppinger Dunn Griffey Bruce Votto Encarnacion Phillips Valentin Pitcher 4.99 808.8 19.7
jinaz-Best-exploit Votto Dunn Bruce Encarnacion Griffey Keppinger Phillips Valentin Pitcher 4.95 802.0 12.9
ED44-Best2 Keppinger Votto Dunn Phillips Griffey Encarnacion Patterson Valentin Pitcher 4.95 801.9 12.8
Alex-Best Keppinger Votto Dunn Phillips Griffey Encarnacion Patterson Valentin Pitcher 4.95 801.9 12.8
Alex-best3 Freel Keppinger Dunn Phillips Griffey Encarnacion Votto Valentin Pitcher 4.94 799.7 10.6
Baker-Game4 Patterson Keppinger Griffey Phillips Dunn Encarnacion Votto Valentin Pitcher 4.93 798.0 8.9
ED44-Best Keppinger Bruce Dunn Phillips Griffey Votto Encarnacion Valentin Pitcher 4.92 797.7 8.6
Chris-Best2 Bruce Keppinger Encarnacion Dunn A_Phillips Griffey Phillips Hanigan Pitcher 4.90 794.0 4.9
justincredible-Best Votto Keppinger Griffey Dunn Phillips Bruce Encarnacion Ross Pitcher 4.88 789.8 0.7
mlbfan30-B Votto Keppinger Dunn Encarnacion Griffey Phillips Bruce Valentin Pitcher 4.88 789.8 0.7
Baker-OD Patterson Keppinger Griffey Phillips Dunn Encarnacion Hatteberg Valentin Pitcher 4.87 789.1 0.0
Alex-best2 Hopper Keppinger Dunn Phillips Griffey Encarnacion Votto Valentin Pitcher 4.85 785.7 -3.4
redsmanrick-best Votto Dunn Encarnacion Griffey Keppinger Bruce Phillips Ross Pitcher 4.85 785.6 -3.5
Enquirer-vsR Votto Dunn Encarnacion Bruce Griffey Phillips Valentin Keppinger Pitcher 4.84 783.9 -5.2
jinaz-Best Votto Encarnacion Dunn Phillips Griffey Bruce Keppinger Valentin Pitcher 4.83 782.0 -7.1
joel-Best1 Votto Dunn Encarnacion Griffey Bruce Phillips Valentin Pitcher Keppinger 4.81 779.8 -9.3
brad-Best Votto Dunn Encarnacion Griffey Bruce Phillips Keppinger Valentin Pitcher 4.80 778.4 -10.7
joel-Best2 Keppinger Dunn Phillips Bruce Encarnacion Griffey Ross Pitcher Gonzalez 4.80 778.2 -10.9
joel-Best3 Keppinger Dunn Phillips Encarnacion Griffey Patterson Ross Pitcher Hatteberg 4.79 776.5 -12.6
DannyB-B Keppinger Dunn Griffey Encarnacion Votto Phillips Hopper Valentin Pitcher 4.77 773.2 -15.9
texasdave-B Keppinger Votto Dunn Encarnacion Griffey Phillips Ross Hopper Pitcher 4.76 771.3 -17.8
fareast-Best Votto Phillips Griffey Dunn Bruce Encarnacion Gonzalez Ross Pitcher 4.76 770.5 -18.6
PastAndPending-B2 Freel Keppinger Bruce Griffey Phillips Dunn Votto Ross Pitcher 4.74 767.9 -21.2
Bluzer-B Hopper Keppinger Dunn Phillips Griffey Encarnacion Valentin Pitcher Freel 4.74 767.4 -21.7
Baker-Game2 Patterson Keppinger Griffey Phillips Dunn Encarnacion Votto Bako Pitcher 4.73 766.3 -22.8
PastAndPending-B Hopper Keppinger Griffey Phillips Dunn Votto Encarnacion Valentin Pitcher 4.72 764.9 -24.2
JamesB-B Hopper Keppinger Griffey Dunn Phillips Votto Encarnacion Valentin Pitcher 4.72 764.4 -24.7
redsmanrick-best2 Keppinger Phillips Dunn Encarnacion Griffey Ross Votto Pitcher Hopper 4.71 763.2 -25.9
DannyB-B2 Hopper Dunn Griffey Encarnacion Votto Phillips Gonzalez Ross Pitcher 4.69 759.3 -29.8
Enquirer-vsL Keppinger Dunn Phillips Bruce Encarnacion Griffey Ross Gonzalez Pitcher 4.68 758.7 -30.4
Baker-Game3 Freel Keppinger Griffey Phillips Dunn Encarnacion Hatteberg Bako Pitcher 4.63 750.1 -39.0

  • Player choice matters: here we see that Baker's opening day lineup can be beat regularly by employing Joey Votto and Jay Bruce in favor of Scott Hatteberg and Corey Patterson.
  • The difference between the best and worst lineups in this case was about 5 wins. That's lower than I expected given the 4-win range in the opening day dataset, but then again the personnel differences among these lineups aren't that dramatic.
  • I was gratified to see that my "exploitative" lineup, which takes advantage of the lack of information in the model about L/R splits and strings together Votto, Dunn, and Bruce in the top-3 slots, did quite well. So I'm not completely hopeless...
  • Mike Grayson's top-rated lineup has Jay Bruce and his projected 0.336 OBP in the leadoff slot, again indicating that the issue of OBP in the 1-hole is less of a big deal than it's often made out to be.
Let's look at the distribution of how often hitters lead off innings from this dataset and see if we see a similar trend to the prior dataset:

Lineup Slot - Innings led off
Lineup Name 1 2 3 4 5 6 7 8 9 StDev
Baker-OD 1.76 0.77 0.81 0.95 1.04 0.86 0.89 0.85 1.06 0.30
Top 5 lineups

mikegrayson-Best 1.77 0.77 0.78 0.94 0.98 0.88 0.91 0.90 1.06 0.30
brad-Best 1.80 0.78 0.77 1.07 0.89 0.88 1.17 0.88 0.77 0.33
Chris-Best1 1.79 0.77 0.77 1.03 0.89 0.88 1.17 0.87 0.83 0.32
jinaz-Best-exploit 1.78 0.77 0.77 1.38 0.87 0.89 0.87 0.88 0.79 0.35
ED44-Best2 1.80 0.78 0.79 1.08 1.02 0.83 1.14 0.84 0.72 0.33
Bottom 5 lineups

JamesB-B 1.77 0.78 0.79 1.03 0.97 0.79 0.91 0.92 1.05 0.31
redsmanrick-best2 1.79 0.80 0.73 0.95 1.06 0.91 1.12 0.84 0.80 0.32
DannyB-B2 1.75 0.76 0.78 1.03 1.02 0.88 0.77 0.93 1.07 0.30
Enquirer-vsL 1.83 0.76 0.67 1.36 0.95 0.81 0.89 0.91 0.82 0.37
Baker-Game3 1.76 0.77 0.78 0.95 1.05 0.86 0.91 0.87 1.07 0.30

Not the same trend. Mostly. The top lineups continue to have a fairly low standard deviation (at least compared to the bottom 5 from the opening day lineups), but we see low variation here among the bottom lineups as well. What's different?

Well, the bottom lineups tend to have inferior players to the better lineups this time around. Norris Hopper appears frequently instead of Corey Patterson in these lineups, which is a poor trade according to PECOTA. And Baker's game 3 lineup includes Freel and Bako instead of Patterson and Valentin.


Well, there's obviously a lot more to do on this front. I feel like we've really just started to scratch the surface on this issue. But I wanted to end with a summary of some of the tentative conclusions that I'm taking from this work.

1. There isn't one best way to make a successful lineup. Lineup interactions are such that there may be several very different styles of lineups that each result in similar overall performance.

2. In general, playing the best players is more important than lineup order. That's not to say that lineup order doesn't matter, but a poorly structured lineup with great players can beat a perfectly structured lineup with weak players.

3. Spreading one's best (and worst) hitters out to prevent bottlenecks may be an overlooked yet highly influential means of improving the performance of a lineup. The first dataset indicates to me that it might be more important than some of the other things we tend to worry about (like OBP in the leadoff slot). At the very least, it's worth further study.

4. Seemingly small differences between players can cause substantial differences in lineup performance when they are swapped between lineup spots. It may be that different sets of players may require substantially different lineup designs for optimal production.

5. We fans may not know as much about lineup construction as we think we do. In my case, at least, I'm feeling pretty clueless after working through this project. This post by J.C. Bradbury seems pretty apt. So, I'm inclined to give Dusty Baker the benefit of the doubt with his lineup order at this point...though I reserve the right to complain about personnel choices!

That's about as far as I'm willing and able to go for now. If you have suggestions, specific tests (or specific lineups) you'd like to see done, etc, let me know. I'm happy to continue working on this stuff as my (limited) time permits.

A few caveats and notes:
  • All of the above results are obviously dependent on the quality and reliability of the Markov model upon which they're based. It seems really solid, but we should always keep this in mind. Again, I'll refer to the Bradbury post.
  • As implied above, a different set of players--say, #1-#9 lineup splits for NL teams...not to mention AL teams--might result in very different findings. Such is the nature of this sort of thing.
  • For pitchers and their pinch hitters, I just used 2007 Reds' pitcher totals. Maybe I should have used #9 hitter totals instead, as they would recognize the contributions of pinch hitters. But I didn't think about that until about a minute before hitting "publish post."
  • With some assistance from John Beamer (thanks John!), I modified the spreadsheet to automatically input the actual % times each hitter led off an inning, based on the output of the model. You'll need to do this as well if you want to replicate my results. Drop me a line and I can help ya out on that.
  • I used the standard baserunning tables in the spreadsheet, and I did click the Update SBA button after constructing each lineup. I have no idea how much modifying those baserunning tables might affect the results.
  • I also just wanted to again thank John Beamer for publishing his Markov model with the Hardball Times Annual. If nothing else, it's provided a lot of food for thought!
Photo by Getty Images/Jonathan Daniel

Additional discussion about this project can be found at:


  1. Wow, I guess I should gloat a little bit, but when you think about it, .03 R/G is not much to gloat about, is it?

  2. I was in the bottom 5? Well, obviously your methodology is wrong. :)

  3. I wasn't sure if I should attach folks' names or not to the lineups. But I figured that most people would want to be able to easily find "their" lineup in the list, so kept 'em. But it does mean that I'm identifying folks as being among the bottom 5, which kind of sucks.. -j

  4. I honestly don't mind. I think the potential findings that you listed are interesting. It kind of makes sense that you don't want to bottleneck your lineup. Given the looping nature of a lineup, you probably help yourself more by having a mix of hitters that can extend innings and such.

  5. Justin -- great work. And great to see someone putting the Markov to use.

    It just goes to show how complex the interactions between different hitters can be.

    It also goes to show that at the margins line-up doesn't make *that* much difference

  6. Justin,

    I assume that the Markov model does not include baserunning?

    Also, does the model include GDP's and the differences, for example, between a strike out and batted ball out (moving runners over, etc.)?

    Does it move runners over differently on a batted ball out, depending on the handedness of the batter?

    Finally, if it uses GDP, does it use a GDP projection for each player or does it assume the same GIDP rate for all players? If the latter, it it based on BIP for that player, and does it distinguish between RH and LH batters (the former hit into DP's more than twice the rate as the latter)?

    Obviously these are all important variables for lineup construction, especially the base running and GIDP rates.

    I have a sim that incorporates everything. I can run it on several lineups if you want and report back.

    Also, one of the more important things about lineup construction, I think, is making sure you use an optimal lineup versus RH and LH starting pitchers. They can be very different. If you want to evaluate a manager's lineup, you have to look at his two versions. For example, let's say that he has a great overall (against all starters) lineup, but that he uses the same one against RHP as LHP. Well, it might be a bad lineups against each, even though it is great overall (unlikely, but possible).

    Plus, splitting up lefties, even if it costs a few runs a year, is important I think, and should be taken into consideration.


  7. Are you using the Team Batting tab? I'm using the THT Markov spreadsheet, but the "number of innings led off" row doesn't change on mine. I'm curious how you're getting the different leadoff numbers for different lineups.

  8. @Anthony, that's a modification that I had to do with Beamer's help. Here's how I'm doing it:

    First, in row 31, I created some lineup lookup numbers. So, C31 is 1, D31 is 2, E31 is 3, etc.

    Then, in row 32, columns C-K, I pull the actual innings led off from the model. The code in C32 is "='Line-up start'!L61" (without double quotes). D32 is L62, E32 is L63, and so on.

    Finally, I then use an Hlookup function to pull the correct innings led off from row 32. The code for C30 is: "=HLOOKUP(C29,$C$31:$K$32,2,FALSE)". D30 is the same, except that the lookup cell is D29 instead of C29.

    I uploaded a screenshot of how it looks here. Let me know if this is unclear. -j

  9. @MGL,

    John Beamer's the better person to ask about the inner workings of the model. I'm just plugging in numbers. But here's what I know:

    I assume that the Markov model does not include baserunning?

    The model does include situation-based baserunning. But aside from stolen bases I don't think it varies the probabilities of taking extra bases, pickoffs, etc, based on the given batter's skills. I *think* the best we can do in this model is make adjustments across all batters and see how that changes the results. I haven't messed with this at all.

    Also, does the model include GDP's and the differences, for example, between a strike out and batted ball out (moving runners over, etc.)?

    The model does request inputs of GDP's and strikeouts, so I'm pretty sure that it includes those in its calculations. And that it handles advancement on strikeouts differently than regular outs. Not positive about that, however.

    Does it move runners over differently on a batted ball out, depending on the handedness of the batter?

    There is a matrix that allows one to manipulate the frequency with which one takes a base on an out, and it does so for all base/out situations. However, the model knows absolutely nothing about the handedness of the batter.

    Finally, if it uses GDP, does it use a GDP projection for each player or does it assume the same GIDP rate for all players? If the latter, it it based on BIP for that player, and does it distinguish between RH and LH batters (the former hit into DP's more than twice the rate as the latter)?

    It does ask for input on GDP's, and the baserunning matrices have a specific category for what happens to baserunners during a double play.

    However, because I'm using PECOTA projections, which do not include GDP projections, I estimated GDP's for all players based on 2007 averages. I did it based on BIP rates (i.e. GDP / [AB-K-HR]), not GDP/PA. I imagine that including information about speed would also be helpful, but I didn't do this.

    I have a sim that incorporates everything. I can run it on several lineups if you want and report back.

    If you'd like to run your sim on the Baker opening day lineup and the top 3 (or whatever) and bottom 3 opening day lineups according to this model, I think that'd be pretty interesting to compare to the results!

    I also agree about the left vs. right lineups, and breaking up lefties to prevent late-inning left-handed relievers from neutralizing your lineup. However, this model doesn't have the capability of dealing with that yet (right John?). Still, the philosophy behind left & right lineups should be similar, no? It's just that you use different input data, i.e. data that recognizes left/right splits of players.

    In other words, while this model might not allow us to identify The Best Real Life Lineup, it should help us understand what approach(es) to lineup construction are most successful given a set of input data.

    Thanks for dropping by!

  10. Brilliant! Thanks, Justin.

  11. Using my sim, I ran each lineup 100,000 times at home (neutral stats adjusted for home field advantage) in a neutral park against a neutral, league-average (neither RH nor LH) pitcher, using my projections for each player. My sim includes baserunning, GIDP, etc., so it is pretty much all encompassing. The standard deviation of runs per game for one team in 100,000 games is .009. So these numbers are plus or minus .018 runs at 2 sigma (with a 95% confidence interval).

    Baker: 4.560
    Baker with Votto rather than Hatteberg: 4.646 rpg +13.9
    Your #1: 4.604 +7.1
    Your #2: 4.618 +9.4
    Your #3: 4.615 +8.9
    Your worst: 4.626 +10.7
    Your 3rd worst: 4.620 +9.7
    Your 4th worst: 4.549 +1.8
    Jinaz-OD: 4.588 +4.5
    Jinaz-OD-exploit: 4.579 +3.1

    I re-ran each lineup at home at GABP, rather than a neutral park:

    Baker: 4.640
    Baker with Votto rather than Hatteberg: 4.763 +19.9
    Your #1: 4.706 +10.7
    Your #2: 4.736 +15.6
    Your #3: 4.758 +19.1
    Your worst: 4.729 +14.4
    Your 3rd worst: 4.731 +14.7
    Your 4th worst: 4.672 +5.18
    Jonaz-OD: 4.679 +6.3
    Jinaz-OD-exploit: 4.690 +8.1

    Let me say a couple of things: One, Dusty’s lineup is one of the worst you can put out there, as you can see from the above, based on my projections and my sim. You really have to make an effort to do as badly as Dusty.

    I have much more confidence in a comprehensive sim than a “dry Markov chain.” In fact, I think that using a Markov chain that does not include handedness, baserunning, etc., is a waste of time for evaluating lineups.

    Two, the Reds have a roughly average first-string lineup, despite what you often hear about them having a very good one or even a great one. And of course, the defense is awful, as long as Griff, Dunn, and Phillips are out there.

    Three, can we stop saying that Griffey is a “great hitter.” He is not anymore. Not even close. He is a below-average hitting corner outfielder. With his terrible defense and baserunning, he is near replacement level. One of the worst overall players in baseball. Possibly the worst full-time player. Has been for a few years.

    Four, Baker’s (or whoever makes those decisions) biggest mistake is playing Hatteberg over Votto. I don’t know about their defense, but Votto is almost a win and a half better with the bat than Hatty. If Hatty is a better defender, it probably is not more than a win, unless Votto is a DH-like entity, awful with the glove. And of course Hatty cannot run the bases a lick. I don’t know about Votto.

    Five, the Reds lineup is quite balanced, as compared to many or even most, so that it does not make that much difference who you put where, as you can see from the above. As long as Keppy, Griffey, Dunn and Encarnacion are near the top or middle of the lineup, you are fine. And no one is that bad that they can’t pretty much bat anywhere, although Valentine being the worst and the slowest should probably bat last in any lineup.

    Six, just eyeballing the above Zips projections, my projections are quite a bit different. I have, in a neutral setting, something like, in wOBA, Dunn, .386, Encarnacion, .368, Keppinger, .353, Griffey, .348, Hatty, .338, Phillips, .338, Patterson, .338, Valentine, .323.

  12. Try from opening day players:

  13. Hi MGL,

    Thanks for the quick work!

    It is a bit unnerving to see how different your results are. You absolutely could be right about the importance of the handedness and baserunning details that your simulator takes into account. I do wonder how much your final point about the differences between your projections and the PECOTAs I used might also be coming into play though. Looks like the big differences were on Keppinger, Hatteberg, and especially Patterson. As you say, the Reds' lineup is fairly balanced, so differences like that could result in big differences in the rank order of lineups. Of course, the Patterson difference should just help Dusty's case, and he clearly got creamed in your sim.

    As for your other points, I generally agree (though I still think that UZR must be missing low with Phillips given how he does with the Fans, PMR, and RZR...but we've had that conversation already!). A point I've made a few times is that if the Reds are going to contend, they're going to need surprises from both their offense and defense. And the only way they'll get surprises from their offense is if they play high-upside players like Jay Bruce and Joey Votto over known quantities like Patterson and Hatteberg.

    FWIW, Votto does have pretty good speed for a first-baseman (perhaps average overall?), though reviews of his glove have been a bit mixed. I'm just assuming that he's an average defender for now. Hatteberg's been all over the place from year to year defensively, but I think he's at least not terrible.

  14. @Anonymous,

    I get 4.87 R/g, 788.5 runs/season, -0.6 runs above Baker per season.


  15. MGL

    The model includes baserunning and GDPs. It also includes the the difference between a strike out and a batted ball out.

    The GDP variable is calculated for each player individually based (principally) on the number of singles they have.

    There is an implict, debatable assumptions here: that the ratio of GB/1B is roughly constant (no idea if this is true).

    One thing I don't adjust for is left handed vs right handed batters. As you point out I probably should.

    I tested the line-up part of the Markov extensively against real world data (especialy the PA per batting position) so I think it works fairly well (within the constraints of the Markov approach). Of course a fully fledged sim allows you take into account more variables but doesn't model the essence of the game, which is what the Markov does (not that that matters).

    Justin -- if there is additional work you want me to do drop me a line. Also I am more than happy to make the Markov "source code" available to anyone who has bought the THT annual -- the only reason I didn't is because it is pretty complicated.


    ps to do the lineup analysis correctly you have to iterate the PA per position. For similar line-ups this shouldn't make a difference but can be a source in instability ... you do this by copying and pasting the computed PA per position into the relevant part of the line-up spreadsheet.

  16. ps to do the lineup analysis correctly you have to iterate the PA per position. For similar line-ups this shouldn't make a difference but can be a source in instability ... you do this by copying and pasting the computed PA per position into the relevant part of the line-up spreadsheet.

    This sounds like it could potentially make a difference, so I'd like to try it.

    I'm having a hard time figuring out how to do this, though. I snooped around the common calculations page, but I'm not seeing it. Do I need the source code version to find the calculated PA? I'm also unclear about where I'd paste them.


  17. Justin -- no you do it manually. Let me have a look when I have 5 mins today and drop you a line with detailed instructions.

    By the way to compare this with MGL's sim we should absolutely use identical forecasts ...

  18. I don’t know how much difference it makes, but the sim uses all kinds of other variables, such as each player’s projected sb/cs rate, foul out rate, infield singles rate, roe rate, bunt rate (attempts and results), sacrifice rate (attempts and results), IBB rates, etc. Shouldn’t really make much difference in terms of batting order, I wouldn’t think.

    Here are the projections it is using for each player, more or less. Singles are regular, infield, and bunt (sac and regular bunts) attempts combined. All are per 510 PA, where a PA is not including an IBB. These are park neutral and scaled to average NL offensive rates for 05-07, where the average wOBA for a non-pitcher is .340.

    S 51 d 22 t .9 hr 29 bb+hp 83 so 127 sb 4 cs 1 wOBA .382

    S 79 d 29 t 1.7 hr 17 bb+hp 50 so 75 sb 7 cs 2 wOBA .360

    S 107 d 24 t 3.0 hr 6 bb+hp 38 so 33 sb 4 cs 2 wOBA .342

    S 68 d 22 t .7 hr 20 bb+hp 52 so 87 sb 4 cs 1 wOBA .335

    S 81 d 24 t .9 hr 8 bb+hp 61 so 46 sb 1 cs 1 wOBA .329

    S 82 d 22 t 3.2 hr 15 bb+hp 35 so 76 sb 14 cs 5 wOBA .324

    S 79 d 26 t .8 hr 12 bb+hp 37 so 68 sb 1 cs 1 wOBA .311

    S 84 d 25 t 4.1 hr 15 bb+hp 26 so 98 sb 25 cs 8 wOBA .311

    As you can see, my projections are not very flattering - only 3 players are above average hitters and the entire lineup averages .337 in wOBA, 3 points below the NL average, which amounts to 15 runs worse than average per year. And that is with their best lineups (not including Votto and Bruce, I guess).

    I don't have much optimism for the Reds, BTW. Pre-season I had them at 77 wins. As of yesterday, I had them at 78 wins. After today, it is 77.5, with a 1% chance of winning the pennant and 0% (rounded off to the nearest percent) chance of winning the WS. I do have them with a 7% chance of making the post-season. I have them as the 6th worst team in the NL (could be worse I guess) in front of only PIT, WAS, HOU, FLO, and SF. My season projections include some significant playing time for good players like Bailey, Votto, and Bruce. I actually like their pitching (3 wins over average). I have their staff as the 5th best in the NL, behind only ARI, LA, Mets, and SD, with MIL right behind them.


  19. Oh, and I was mixing up Phillips with someone else in my mind. He was +5 in 07 UZR and I have him with an average defensive projection overall.

    The Reds still have one of the worst projected team defenses (-33 per 150), though, owing mostly to Griffey and Dunn, who are a combined 35 runs or so below average per 150 in projected UZR (-15 for Dunn and -20 for Griff).

    I have Hatty with an average defensive (UZR) projection and below average (-2) in "scooping bad throws."


  20. MGL, thanks for those projections. I'll try to give them a run tonight in the Markov and see what happens. I may try Beamer's additional step of iterating the PA based on lineup spot as well if I can figure that out.

    I really would think that these two approaches would result in fairly similar results, at least in a gross sense. If nothing else, they both should be vastly superior to the regression-based analyses we've seen. -j

  21. Justin, this is a nice excercise. Great job. I have a question, and I must admit that I haven't yet read the whole study (I will, I will). The Pinto tool for projecting runs per season, did you make any adjustments for "splits", ie - LHB vs LHP, LHB vs RHP? Does the Pinto model take into account speed/baserunning? If not, do you think it's important that you take into consideration more factors than OBP and SLG? Perhaps you'd see at the very minimum some adjustments to the run totals. Thanks!
    vr, Xeifrank

  22. Ok, my questions were answered in reading the comments. I was thinking along the same lines as MGL, that a simulator would do a better job than a Markov Chain. I have a simulator too, but he beat me to it. :) Good work everyone.
    vr, Xeifrank

  23. Xeifrank, the above results are not based on David Pinto's lineup tool. they use Markov chains, which is definitely a better tool for this purpose. The sim might be better, but I honestly wouldn't expect them to be *that* different given how much info the Markov uses. -j

  24. Justin, that's great that John put this tool together. Like he said you and MGL need to use the same input data. Keep up the great blog, your site is an every day must read. vr, Xei

  25. Justin

    The iteration step is straightforward. The PA per line up spot should "converge" all you need to do is copy the computed PA into the PA per position 2-3 times, update the SBA (push the button) and the rpg shouldn't change.

    If you do get different results perhaps you can send me the exact input data you use and I will look into the Markov logic and try to piece if anything is falling down. I'm pretty sure everything is working as it should but as with all these things you never know. Then I can also adjust for other stuff like handedness etc. All those variables you can adjust for manually in the code but it is harder to automate in a mathematical model as you have to make assumptions that don't hold up to reality


  26. Important Note!!

    John Beamer discovered an error in my use of his model tonight. I'll re-do all of the lineups using this modification, but I ran out of time to do it tonight. Initially, it looks like the major findings remain the same, and that Baker continues to do well...better, in fact.

    MGL, I haven't given your projections a try yet, but will tomorrow night (hopefully).

    @Anthony, my instructions to you weren't quite right. Forget the Hlookup. What you should do is just copy the entire row in your new row 32 up to row 30. Row 30 does not know anything about the lineup order that you manipulate in row 29. In other words, whatever is in C30 is always associated with the leadoff hitter.

    John recommends doing this a few times, pushing the SBA button in between, until the values converge. I'm finding that just creating a direct link to row 32 works fine--no apparent problem with infinite loops, etc.

  27. Ok, I've run MGL's splits through the model. And I'm sure I'm now using the model correctly.

    Those projections are much worse than the PECOTAs! But the rank order from this model has Baker actually coming out on top. Here are the results, listed in the same order you listed them:

    Baker OD: 4.41 r/g, 715 r/sea

    Old Top 3:
    Bluzer OD: 4.32 r/g, 700 r/sea, -16 above Baker
    Chris-OD2: 4.34 r/g, 703 r/sea, -12 above baker
    Pickoff-OD: 4.36 r/g, 706 r/sea, -9 above Baker

    Old Bottom 3 (bottom first):
    redmanrick-OD: 4.26 r/g, 691 r/sea, -24 above Baker
    Brad-OD2: 4.30 r/g, 697 r/sea, -18 above baker
    fareast-OD: 4.33 r/g, 701 r/sea, -14 above baker

    jinaz-OD: 4.39 r/g, 711 r/sea, -4 above Baker
    jinaz-OD-exploit: 4.33 r/g, 701 r/sea, -14 above baker

    I'm using 2007 #9-slot hitting totals now, which come to a 0.170/0.216/0.250 hitting line. Before I was using pitchers only, but this helps account for the late-inning pinch hitters.

    So...Still disagreements between the two systems. These come out much lower than yours (using the same projections, mostly), and with a different rank order. And the range is a bit higher as well, with ~24 runs between the worst and best in the Markov and ~11 runs between the best and worst in your sim.

    The rank order differences are just bizarre though. Baker's lineup comes out on top in this Markov, but is doing terribly in your sim. In fact, the worst lineup according to this Markov is the best in your's almost like they're inverted!


  28. Fun stuff, Justin. I thought you were accounting for platoon splits, for some reason - hence my two lineups for everything.

    The "bottleneck" theory is a very interesting one. Baker is sailing into the wind here, but some of the typical nonsense moves we might expect (Juan Castro batting second; Phillips' crappy OBP in the cleanup spot) may actually be beneficial.

  29. Justin,
    That's amazing that the two systems are inverted on the top and bottom lineups. Perhaps, i should try running the two on my simulator and see which one my simulator trends towards. If you'd like me to try that, I could but I format my hitters input data a little differently. I would need to know OBP, AB, 1B, 2B, 3B, HR, BB, K for the hitters.
    vr, Xeifrank

  30. Xeifrank, the more the merrier! Tango is also going to run MGL's projections on these lineups and see what his simple markov comes up with.

    As for the data, you should be able to calculate all of that from MGL's posted projections. But I can also look them up for you when I get a sec. -j

  31. Hmmm... looks like the post was lost.

    Using the PECOTA forecasts noted in the main blog entry, and ignoring batting handedness, speed, and GIDP (all things I would not normally ignore), with wOBA in parens:

    1. Hatty (.358)
    2. Dunn (.401)
    3. Junior (.360)
    4. Encarnacion (.367)
    5. Keppinger (.348)
    6. Phillips (.334)
    7. Valentin (.333)
    8. Pitcher (.160)
    9. Patterson (.311)

    I don’t see how it’s possible to have such a big disagreement here. Other than Dunn and Patterson, the PECOTA forecasts are very tight for the rest of the players.

    Here’s a reasonable lineup (5 best players remain in the top 5, don’t touch the pitcher), but in the worst possible combination:
    1. Encarnacion (.367)
    2. Junior (.360)
    3. Dunn (.401)
    4. Keppinger (.348)
    5. Hatty (.358)

    6. Patterson (.311)
    7. Phillips (.334)
    8. Pitcher (.160)
    9. Valentin (.333)

    And that’s just 3 runs worse than the optimal one that my Linear Weights model would suggest.

    Basically, it’s pretty difficult to create a bad lineup (notwithstanding the exceptions I noted at the start of this post).