The best way (in my opinion) to determine which lineup is the best is to actually trot out every single lineup and see which one wins the most games. Of course you would have to hold the opponent constant, using the same starters, lineup and starting pitcher. How hard could that be to do? Let's see, with nine batters in a lineup you would only have 362,880 lineups to go through. How long could that take to play over 350,000 baseball games. You could probably filter those permutations down to 25,000 or so by limiting left handed batters from hitting back to back, limiting the pitcher (NL) to batting either 8th or 9th, plus a few other obvious things. Even if you could narrow things down to just two lineups, you would still need to play more than one game to determine which one was better. So how many samples/games would you need? 10? 20? or maybe an entire season (162) of games? No. You would need a lot more than that. Try tens of thousands just to separate the bad lineups from the good and then try a million or two to compare the best lineups.
Well, I think it is pretty impossible to play thousands of games one time or a couple of games a million times. Hypothetically, if one were able to play games with thousands of different lineups, thousands or millions of times against the exact same opponent then you would get a very good idea as to which lineups were the best. This is where simulation comes in handy. A simulator that could play actual baseball games, by actual baseball rules, taking into consideration the important facets of a real baseball game like speed, defense, pitchers getting tired the more pitches they throw, splits, hitter vs pitcher matchups and outcomes and throw in some good player projections like the ones available for free at Fangraphs and then maybe through the power of the computer you could plow through tens of thousands of likely lineups to determine the best ones.
Now, you would be able to test the synergy of batting certain groups of players next to each other. You would be able to experiment with various types of hitters hitting in different spots. In fact, you could just let the computer run through each lineup and let you know what the top ones were, even tabulating how many times each player showed up at each spot in the top lineups. Now you would have a good list of top lineups and be able to measure how many wins a manager might be leaving on the table by using the lineup(s) that he used. Wouldn't it be very worthwhile for a team to know what its best lineups might be? Of course it would, especially considering that on the free agent market one win (or WAR) is typically worth around $7M. For managers that might not want to hit certain batters in certain lineup spots for whatever reason, he could use the filtering option to only measure lineups that fit his parameters.
Well, now on to what my game simulator using Steamer hitting projections lists as the top fifty lineups for the 2015 Oakland Athletics. I only looked at lineups against a right handed starting pitcher and took the nine most likely starters from the list at the Roster Resource website and I have of course used their most common lineup as one of the many (10,000+) lineups that I am looking at. Along with the top fifty lineups, there is a table showing how many times each player shows up in each lineup spot and what the most common back to back slottings are as well as back to back to back slottings (think synergy here).
Summary:
The batting order frequency table tells a lot here. If you were to piece together a lineup from only the frequency table you would likely come up with what is the second ranked optimal lineup. The lineup listed from the Roster Resource website came in listed 34th. I've ran a few of these now for various teams and the Athletics seem to have a very balanced lineup with no one player way better than the others not causing much of a spread between the top lineups. I also purposely added a bad lineup to the bottom of the top 50 list just to see what the maximum spread for the team looks like. According to the simulator, there are not a lot of wins for the Athletics manager to leave on the table vs RHP compared to some of the other teams.
Top 50 Lineups (vs RHP)
| Rank | Lineup | Wins/162 Games Behind |
|---|---|---|
| 1 | Zobrist-Reddick-Lawrie-Davis-Crisp-Semien-Vogt-Butler-Fuld | 0 |
| 2 | Crisp-Reddick-Lawrie-Davis-Zobrist-Vogt-Semien-Butler-Fuld | 0.001 |
| 3 | Reddick-Crisp-Lawrie-Davis-Zobrist-Vogt-Semien-Fuld-Butler | 0.016 |
| 4 | Crisp-Vogt-Lawrie-Davis-Zobrist-Reddick-Semien-Butler-Fuld | 0.042 |
| 5 | Zobrist-Fuld-Lawrie-Reddick-Crisp-Vogt-Semien-Butler-Davis | 0.067 |
| 6 | Crisp-Vogt-Lawrie-Davis-Zobrist-Semien-Fuld-Butler-Reddick | 0.093 |
| 7 | Fuld-Crisp-Butler-Davis-Zobrist-Reddick-Lawrie-Vogt-Semien | 0.094 |
| 8 | Davis-Zobrist-Lawrie-Reddick-Crisp-Vogt-Semien-Fuld-Butler | 0.103 |
| 9 | Reddick-Semien-Lawrie-Davis-Crisp-Fuld-Zobrist-Vogt-Butler | 0.107 |
| 10 | Zobrist-Reddick-Lawrie-Davis-Semien-Crisp-Vogt-Butler-Fuld | 0.108 |
| 11 | Lawrie-Crisp-Davis-Zobrist-Reddick-Semien-Vogt-Butler-Fuld | 0.108 |
| 12 | Semien-Davis-Lawrie-Reddick-Crisp-Fuld-Zobrist-Vogt-Butler | 0.109 |
| 13 | Zobrist-Reddick-Lawrie-Davis-Crisp-Fuld-Butler-Vogt-Semien | 0.117 |
| 14 | Crisp-Reddick-Lawrie-Davis-Semien-Zobrist-Fuld-Butler-Vogt | 0.123 |
| 15 | Zobrist-Crisp-Reddick-Lawrie-Davis-Semien-Fuld-Butler-Vogt | 0.14 |
| 16 | Semien-Davis-Lawrie-Reddick-Zobrist-Crisp-Vogt-Butler-Fuld | 0.141 |
| 17 | Semien-Fuld-Butler-Davis-Zobrist-Reddick-Lawrie-Crisp-Vogt | 0.146 |
| 18 | Zobrist-Reddick-Lawrie-Davis-Crisp-Vogt-Semien-Fuld-Butler | 0.146 |
| 19 | Reddick-Crisp-Davis-Zobrist-Lawrie-Vogt-Semien-Fuld-Butler | 0.152 |
| 20 | Fuld-Crisp-Butler-Davis-Semien-Reddick-Lawrie-Vogt-Zobrist | 0.156 |
| 21 | Zobrist-Fuld-Lawrie-Davis-Crisp-Vogt-Semien-Butler-Reddick | 0.156 |
| 22 | Reddick-Zobrist-Davis-Lawrie-Crisp-Vogt-Semien-Fuld-Butler | 0.159 |
| 23 | Crisp-Butler-Reddick-Lawrie-Davis-Semien-Vogt-Zobrist-Fuld | 0.175 |
| 24 | Reddick-Crisp-Davis-Lawrie-Zobrist-Vogt-Semien-Fuld-Butler | 0.181 |
| 25 | Fuld-Crisp-Lawrie-Davis-Zobrist-Reddick-Semien-Vogt-Butler | 0.191 |
| 26 | Reddick-Zobrist-Lawrie-Davis-Semien-Fuld-Crisp-Vogt-Butler | 0.192 |
| 27 | Crisp-Zobrist-Reddick-Lawrie-Davis-Semien-Fuld-Butler-Vogt | 0.192 |
| 28 | Crisp-Davis-Lawrie-Reddick-Zobrist-Vogt-Semien-Butler-Fuld | 0.195 |
| 29 | Crisp-Fuld-Lawrie-Reddick-Zobrist-Semien-Vogt-Butler-Davis | 0.204 |
| 30 | Crisp-Semien-Davis-Lawrie-Reddick-Zobrist-Fuld-Butler-Vogt | 0.209 |
| 31 | Crisp-Fuld-Lawrie-Davis-Zobrist-Reddick-Butler-Semien-Vogt | 0.210 |
| 32 | Crisp-Zobrist-Davis-Lawrie-Fuld-Semien-Vogt-Butler-Reddick | 0.213 |
| 33 | Semien-Fuld-Lawrie-Reddick-Zobrist-Crisp-Vogt-Butler-Davis | 0.214 |
| 34 | Reddick-Crisp-Davis-Zobrist-Vogt-Lawrie-Semien-Fuld-Butler | 0.218 |
| 35 | Crisp-Zobrist-Reddick-Butler-Davis-Lawrie-Vogt-Semien-Fuld | 0.221 |
| 36 | Reddick-Zobrist-Davis-Lawrie-Fuld-Semien-Crisp-Vogt-Butler | 0.222 |
| 37 | Crisp-Davis-Butler-Reddick-Zobrist-Lawrie-Vogt-Semien-Fuld | 0.236 |
| 38 | Semien-Davis-Zobrist-Reddick-Crisp-Vogt-Lawrie-Fuld-Butler | 0.238 |
| 39 | Crisp-Vogt-Lawrie-Davis-Semien-Butler-Reddick-Zobrist-Fuld | 0.242 |
| 40 | Crisp-Zobrist-Reddick-Lawrie-Vogt-Semien-Fuld-Butler-Davis | 0.244 |
| 41 | Zobrist-Reddick-Lawrie-Davis-Crisp-Fuld-Butler-Semien-Vogt | 0.248 |
| 42 | Crisp-Butler-Reddick-Lawrie-Davis-Zobrist-Vogt-Semien-Fuld | 0.257 |
| 43 | Lawrie-Fuld-Butler-Davis-Crisp-Zobrist-Vogt-Semien-Reddick | 0.258 |
| 44 | Crisp-Reddick-Lawrie-Davis-Semien-Fuld-Butler-Zobrist-Vogt | 0.260 |
| 45 | Davis-Zobrist-Reddick-Lawrie-Fuld-Crisp-Vogt-Semien-Butler | 0.263 |
| 46 | Crisp-Fuld-Butler-Davis-Lawrie-Reddick-Semien-Vogt-Zobrist | 0.267 |
| 47 | Crisp-Reddick-Butler-Davis-Semien-Zobrist-Fuld-Lawrie-Vogt | 0.283 |
| 48 | Fuld-Semien-Lawrie-Davis-Crisp-Reddick-Zobrist-Vogt-Butler | 0.284 |
| 49 | Crisp-Vogt-Zobrist-Davis-Lawrie-Reddick-Semien-Butler-Fuld | 0.294 |
| 50 | Crisp-Reddick-Butler-Davis-Zobrist-Lawrie-Vogt-Semien-Fuld | 0.294 |
| BAD | Vogt-Butler-Fuld-Crisp-Semien-Davis-Zobrist-Reddick-Lawrie | 1.419 |
.
Batting Order Frequency Table
| 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | |
|---|---|---|---|---|---|---|---|---|---|
| Crisp | 21 | 9 | 0 | 0 | 13 | 4 | 2 | 1 | 0 |
| Reddick | 8 | 10 | 7 | 9 | 2 | 9 | 1 | 0 | 4 |
| Lawrie | 2 | 0 | 25 | 11 | 3 | 4 | 4 | 1 | 0 |
| Davis | 2 | 5 | 8 | 26 | 5 | 0 | 0 | 0 | 4 |
| Zobrist | 8 | 9 | 2 | 3 | 15 | 5 | 3 | 3 | 2 |
| Vogt | 0 | 4 | 0 | 0 | 2 | 11 | 14 | 10 | 9 |
| Semien | 5 | 3 | 0 | 0 | 7 | 10 | 15 | 8 | 2 |
| Butler | 0 | 2 | 8 | 1 | 0 | 1 | 4 | 19 | 15 |
| Fuld | 4 | 8 | 0 | 0 | 3 | 6 | 7 | 8 | 14 |
.
Synergy
Back to Back Frequency Leaders
| Rank | Occurrences | Player 1 | Player 2 |
|---|---|---|---|
| 1 | 22 | Lawrie | Davis |
| 2 | 20 | Vogt | Semien |
| 3 | 20 | Semien | Fuld |
| 4 | 20 | Fuld | Butler |
| 5 | 18 | Reddick | Lawrie |
| 6 | 17 | Crisp | Vogt |
| 7 | 17 | Davis | Zobrist |
| 8 | 16 | Zobrist | Reddick |
| 9 | 15 | Butler | Reddick |
| 10 | 15 | Fuld | Crisp |
| 11 | 14 | Butler | Davis |
| 12 | 13 | Vogt | Butler |
| 13 | 12 | Reddick | Zobrist |
| 14 | 11 | Davis | Lawrie |
| 15 | 11 | Davis | Semien |
| 16 | 11 | Zobrist | Vogt |
| 17 | 10 | Reddick | Crisp |
| 18 | 10 | Lawrie | Reddick |
| 19 | 10 | Davis | Crisp |
| 20 | 10 | Butler | Fuld |
Back To Back to Back Frequency Leaders
| Rank | Occurrences | Player 1 | Player 2 | Player 3 |
|---|---|---|---|---|
| 1 | 13 | Vogt | Semien | Fuld |
| 2 | 13 | Semien | Fuld | Butler |
| 3 | 12 | Reddick | Lawrie | Davis |
| 4 | 10 | Zobrist | Reddick | Lawrie |
| 5 | 8 | Lawrie | Davis | Semien |
| 6 | 8 | Davis | Zobrist | Reddick |
| 7 | 7 | Crisp | Vogt | Semien |
| 8 | 7 | Lawrie | Davis | Crisp |
| 9 | 7 | Lawrie | Davis | Zobrist |
| 10 | 6 | Lawrie | Vogt | Semien |
| 11 | 6 | Davis | Lawrie | Reddick |
| 12 | 6 | Zobrist | Vogt | Semien |
| 13 | 6 | Vogt | Butler | Fuld |
| 14 | 6 | Semien | Fuld | Crisp |
| 15 | 6 | Butler | Reddick | Crisp |
| 16 | 6 | Butler | Reddick | Zobrist |
| 17 | 6 | Butler | Davis | Zobrist |
| 18 | 6 | Fuld | Butler | Reddick |
| 19 | 5 | Crisp | Vogt | Butler |
| 20 | 5 | Lawrie | Reddick | Zobrist |
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