In a team competition, you have to set up your team lineup in advance. How do you do this? It depends on your priorities. If your priority is strictly winning, then there are guidelines on how to do this, which I'll go over below. If your priority is to let the players play roughly equally, then you place them in any order you want, perhaps setting up a rotation. Or you might focus on the most important team matches and play your best lineup in those, while playing the "weaker" players more often in less important team matches, such as against teams that are much weaker. (You can also do this against teams that are much stronger, but your stronger players might want to play in those ones. It can be a tricky balance.) Or you might have players who want to play more, and others who want to play less.
The one thing I strongly advise is that the team decide in advance if they are playing strictly to win (i.e. best order in key team matches), playing so they play roughly equally (and so set up a rotation), or something in between. If your team is roughly equal, then perhaps drop all the calculations, set up a rotation (which you may make some adjustments as you go along), and then just let them play!
Swaythling Cup Format
There are many Teams tournaments that use the Swaythling Cup format, which is three players on each team, with all three players scheduled to play the other three in a best of nine, all singles. As soon as a team wins five, the team match normally ends, so not all nine matches are played.
How would you want to set up your team in such a format? There are several factors. Here is the normal rotation for such a team match:
At the start, the two teams flip a coin to see who gets to choose whether they are ABC or XYZ. Should you choose ABC or XYZ? If you are the ABC team, then you generally put your strongest player in the B position/seventh match, second strongest in the C position/eighth match, and the weakest in the A position/ninth match. (More on this below.) In this case, your weakest player, in the A position, plays two of the first five matches, which lowers your chance of an easy 5-0 win. If you are the XYZ team, then your Z player (generally your strongest player) doesn't play until the third match, but then plays the fifth and seventh match - so he gets less rest than the others, and so you might wear him out. For this reason, I usually go for ABC - but I don't consider it a huge issue. Here are the matches each player would play:
The order you set your lineup makes a difference. In the case of a tie between three or more teams, they go to the individual match record to break up the tie. (If it is still tied, then it goes to individual game record, and then point record.)
Suppose you are Team Loop. Suppose you beat Team Smash, 5-4, with your strongest player winning all three, including winning the ninth match. Team Smash then beats Team Chop, 5-3. Then Team Chop beats Team Loop, 5-3. The three teams are now tied, and so we go to the individual match record. Team Loop is 8-9 (5-4, 3-5); Team Smash is 9-8 (4-5, 5-3); Team Chop is 8-8 (3-5, 5-3). Result? Team Loop comes in third.
Now suppose Team Loop had instead played their strongest player in the seventh position against Team Smash and won that team match 5-2 instead of 5-4. Then Team Loop is now 8-7 (5-2, 3-5); Team Smash is 7-8 (2-5, 5-3); Team Chop is 8-8 (3-5, 5-3). Team Loop comes in first!!! Order matters.
So you'd normally want to set up your lineup to allow you win by as much as possible or lose by as little as possible. (But note that under Swaythling Cup the order has no direct effect on who wins that team match; it only matters in the case of a tie.) Assuming that, this usually means playing your strongest player in the #7 position, to maximize his number of matches. You'd want your next strongest player to play in the #8 position. Then you'd play your weakest player in the #9 position, minimizing the number of matches he'd play. The ranking of your players could also change, depending on who your opponents are - there are style advantages and past records to take into account. (As well as egos, but we won't get into that!)
On the other hand, whoever plays that #9 match is under a lot of pressure. So sometimes you may want to adjust the order and put your best "pressure" player in that position. Or you might have a team with an older player and two younger ones, where you might put the older player in the #9 position in most matches, so he plays less and gets more rest.
Many years ago, at the U.S. Open Teams (then played in Detroit), I was in exactly this last situation. I was player/coach with two up-and-coming junior players. I told them in advance that I'd play the #9 match in every team match. We ended up in the B Division (average rating 2250) - and we won it. I went in with the highest rating on the team, but the two juniors both passed me in that tournament - but I was 5-0 playing the ninth match!!!
There is another big exception to this rule. If you are pretty sure the opposing team is going to set their order in the conventional way, with their strongest player in the #7 position and so on, then you know in advance who would play who. In this case, you might set your lineup to set up the best matchups to maximize your chances of winning by as much as possible, keeping it close if you lose. For example, if one of your players has trouble against choppers and the other team has a chopper, you might set the lineup to avoid that. Or if you have a player who is great against choppers, you'd set the lineup to make sure they play. And so on. But beware - if the other team sees you doing all these calculations, they may realize what you are doing and cross you up. Or they may simply use a different order for their own reasons, and you end up with a weaker order from over-thinking.
There are other exceptions. Late in a tournament you might be in a position where you know you have to win 5-0 to advance. In that case, you'd look at the order of play and make sure your two strongest players play two matches in the first five matches.
Olympic Team Format
In this three-person team format, you have the following order:
Note the first match is doubles. (This might not be true in all tournaments.) Also note that one player plays two singles matches, while his teammates play doubles together plus one singles match each. In this format, most often you play your strongest player in the two singles matches. However, this gets tricky if the other two players aren't a good doubles team, or if the strongest singles player is even better at doubles. In this case, if you play the #1 player in singles, you get two wins but perhaps give up the doubles match, and so you have only two other matches to get the third needed win. But if your #1 player can team up with one of your other players and lock up that match and a singles match, that gives you three other matches to get that third win. So in this case you might play your #1 in the doubles.
In this format, the order has a direct affect on who wins. The team with the better order gets the matchups they want and avoids the ones they don't want.
In this format, it is generally an advantage to be the ABC team. This allows you to put your #1 player in the A position, playing two singles matches, with the second one in the fourth match. If you are the XYZ team and put your #1 player in the X position, where he plays two singles, he won't play his second singles match until the fifth match. So the ABC team has a better chance of winning 3-1 instead of 3-2, or losing 2-3 instead of 1-3. This helps if teams are tied - see example given above under Swaythling Cup.
Since you want to maximize your chances of winning by as much as possible, the ABC team, assuming their #1 player is the A player (with two singles matches), would normally want to play their second strongest player in the C position (third match), with their weakest player in the B position (fifth match). The XYZ team, assuming their #1 player is the X player (with two singles matches), would normally want to play their second strongest player in the Z position (also third match).
However, the biggest consideration under this format is trying to set up the matchups you want so as to actually win the team match. For example, you might be able to guess who the other team will play in the two singles matches and adjust your order accordingly. Or if both teams put their #2 player to play in the third match, and the opposing team's #2 has a style advantage or strong head-to-head record against your #2, you might want to rethink your order. In general, if you can guess the other team's lineup, you can set up your lineup accordingly. But beware - the other team may anticipate this and so cross you up! In a big match, it might be worth it for a team meeting to go over the possibilities and see if you can match up the players.
This is the simplest format. You can play with two players, where each plays the other two players, plus doubles (usually the third match), so it's best of five. You can have a third or fourth player, who only plays doubles. But the strategy here is simple: 1) play your best doubles team; 2) play your best player in the fourth position to maximize the chances he gets two matches, so you win by as much as possible or keep it closer if you lose. One key issue - you don't have to fill in your doubles team until after the first two matches are played (assuming the doubles is the third match). So unless you are playing with just two players, you should wait until those two matches are done, in case one of your doubles players gets injured playing in those singles matches. Once you fill in the doubles players, you can't change it, so why take the chance?