For you math nerds...is it better for a superior team to have a single home game, or 180 minutes...

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

It was my understanding there would be no math....

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

What data should I use to compare the two? There are plenty of two leg series, but other than MLS, which is one league and a small sample, where else should I look for individual knockout games among clubs? There are cup competitions, but if I use the FA Cup during the EPL season it's possible that club A was ahead of club B when they met in the FA Cup but club B was better in the final table after every club had played every other club twice. Even in MLS if you go back to when each club played the rest of the clubs in their conference four times and the clubs in the other conference twice then club A finishing with more points than club B could only be because if the difference in strength of schedule.

Looking at the 2010-2011 UEFA Champions League Second Qualifying Round, which had 17 two leg series, most of the time the seeded club scored more goals both in its home leg and in both legs combined. The only time where which club hosted the second leg may have mattered was when Inter Baku of Azerbaijan hosted the first leg against seeded club Lech Poznan of Poland. Both clubs won 1-0 on the road and Lech Poznan advanced on penalty kicks in the second leg which they hosted.

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

The answer really depends on the two teams involved. As EvanJ said above, it's hard to get a real data sample on actual results. However I have a system of predicting games that I got from Wayne Winston's book Mathletics. Essentially you can take all results that have happened in a league and use a least squares system to determine an offensive and defensive rating for each team as well as computing how playing at home or away affects the number of goals scored by a team (This is a league-wide number, not team specific). I won't go into the math, but this can all be done in Excel. It is a pretty accurate system, though obviously nothing can be perfect (It treats goals scored by home and away teams as independent, which has been proven inaccurate by scientific study).

In any case, this can be used to determine decent theoretical probabilities of how teams would fare against each other in a one-leg playoff at the better team, or a two-legged playoff.

A couple good examples are possible playoff scenarios: Let's say Real Salt Lake v FC Dallas and Los Angeles v Colorado.

In a one-off game between RSL and FC Dallas at RSL, Real Salt Lake has a 58.62% chance of winning, there is a 26.26% chance of a draw, and FC Dallas has a 15.12% chance of winning. Assuming a PK shootout is 50-50 (this may not be valid but for simplicity it will do), this gives:
% Chance that Real Salt Lake Advances: 71.75%
% Chance that FC Dallas Advances: 28.25%

After doing all of the possible permutations of first and second leg results, here are the probabilities for a two-legged playoff:
% Chance that Real Salt Lake Advances: 66.89%
% Chance that FC Dallas Advances: 33.11%

Here, it's shown that giving up home field advantage has a noticeable effect on the possible result of the fixture. This is because in the extra time that Real Salt Lake theoretically has to prove their dominance, they're actually not that dominant; the result of the second leg is close to a toss-up due to home field advantage.

Los Angeles v Colorado:
One-legged fixture:
% Chance for Los Angeles to Advance: 80.44%
% Chance for Colorado to Advance: 19.56%

Two-legged fixture:
% Chance for Los Angeles to Advance: 82.18%
% Chance for Colorado to Advance: 17.82%

Here we get the opposite result from the first scenario. This is because even on the road, Los Angeles is still much better than Colorado.

In conclusion, it all depends on the difference in quality between the two teams. If one team is clearly better, a two-legged fixture gives them a better chance of advancing, though it is not a huge difference. If the teams are a bit more evenly-matched, then the better team is better off keeping home field advantage and a one-legged fixture.

This is just one way to do it, and it takes a trusting of the numbers to give accurate probabilities of results. Any thoughts?

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

didn't the swedish league have play-offs for the league title in the 80's?

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

That suggests that the two-legged fixture more accurately reproduces the actual difference in quality between the teams, which seems like a reasonable goal for the playoffs.

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

If I understood the post correctly (and perhaps I didn't), there were two one- vs. two-legged comparisons, although I think both were theoretical. In the first case, one of the teams had a modest edge over the other. The theoretical series split was closer in the two-legged playoff than the one-legged playoff. In the second case, one of the teams had a pronounced edge over the other. The theoretical series split was farther apart in the two-legged playoff than the one-legged playoff.

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

You understood correctly--At the time of the post these would have been two first-round match-ups. Real Salt Lake vs. FC Dallas is the 2-3 match-up, while Los Angeles vs. Colorado is the 1-4 match-up.

Real Salt Lake is only slightly better than FC Dallas, and Real Salt Lake has a better (theoretical) chance of advancing in a one-legged playoff.

The second case of Los Angeles v. Colorado was to illustrate what happens when one team is much better than the other. Los Angeles has a better (theoretical) chance of advancing in a two-legged playoff.

I liked your interpretation in an earlier post that the MLS is better off with a two-legged playoff. As you said, this more accurately represents the actual gap in quality between the two teams, which should be the goal of any playoffs.

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

The equations would assume PKs at 90 minutes by default. Making them at 120 would give the home team about a 5-9% boost in their win probability (depending entirely on the match-up that could vary quite a bit), which is not insignificant.

Whether or not this is desirable is up for debate. It would certainly increase the value of home field advantage rather than accurately representing the true difference in quality between the teams, but it would still give the better team a better chance of winning.

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

www.wix.com/bigbet/soccer-big-bet

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

Since the issue is a lack of one legged "series", as a work-around solution can we not just take two-legged series that have no away-goals rule in which the higher-seed hosts the second leg and the first leg finished tied? In those situations we are left with the higher seed having 90/120 minutes to prove their superiority. Also we wouldn't have to assume that the penalties are 50/50. We would have real data.

Possible sample of data to look at are:
- 1989 to 2004 Copa Libertadores (before 1989 there was no knockout stage until the final, which was a best of 3. Away-goals rule kicked-in after 2004.)
- FMF playoffs (I don't think they use away-goals, do they?)

My hypothesis is that, at least in South America, it is better to have just one leg at home (ie. if you tied the first-leg away, you are in a better position than when you started).

 

Re: For you math nerds...is it better for a superior team to have a single home game, or 180 minutes

The tiebreaker is regular season points.