# The mathematics of offside

I will start by as­sum­ing the fol­low­ing:

1. Ev­ery­one un­der­­s­tands the of­f­­side rule.

2. Ev­ery­one saw the first Cos­­ta Ri­­ca goal in to­­day's Cos­­ta Ri­­ca - Ger­­many match

One ba­sic rule of eco­nom­ics is that peo­ple, all things be­ing equal, will ra­tio­nal­ly choose the course of ac­tion that gives the great­est re­ward.

Know­ing that, why do team­s, even teams in the high­est lev­els of com­pe­ti­tion, in­sist on such plays as Ger­many at­tempt­ed?

The idea, ob­vi­ous­ly, is that the de­fend­ers play in a line, and move for­ward a frac­tion of a sec­ond be­fore the at­tack­ing for­ward starts the pass, thus leav­ing the re­ceiv­er of the pass in off­side. You do that, you get the bal­l. Sim­ple.

The bad news are, of course, that such plays work about 50% of the time. If that.

It re­quires the de­fend­ers to move for­ward in the ex­act same frac­tion of a sec­ond. If one stays late: it does­n't work.

It re­quires them to syn­chro­nize that way by an au­di­ble cal­l, be­cause it's very hard for them to see their whole line: they are stad­ing side­ways al­most ev­ery time.

If the pass­er is smart, he will sim­ply avoid the pass and run a di­ag­o­nal.

It the re­ceiv­er is smart, he will fall back, avoid­ing off­side, and re­ly on a team­mate to sprint for the pass.

And all these prob­lems can hap­pen ev­ery time the play is at­tempt­ed.

The risk is huge. In fac­t, nowa­days, in or­der to lure the at­tack­ing team in­to this trap, you need to play it with all your 4 de­fend­er­s! Each ex­tra de­fend­er prob­a­bly dou­bles the chance of er­ror.

And what do you avoid? ...a low prob­a­bil­i­ty long pass. Re­mem­ber, in foot­bal­l, ev­ery at­tack is low prob­a­bil­i­ty. A penal­ty is on­ly about 80%!

So, the ger­man coach is in­com­pe­ten­t. He may do some things well, but Ger­many's de­fense is atro­cious. They will not win the cup.

/ 2006-06-09 19:49:

thats why the german coach said after the game, that he didn't wanted his team to play on one line in the defense :-)
But the aim is just to score more goals then the oppenent (if you saw last years confed-cup you would know)

/ 2006-06-09 19:53:

After this match, I would stand on the sideline with an air rifle and shoot one of the guys whenever they look like they are lining up for this kind of thing :-)

About scoring more than the other... it's easier if you don't give away two goals :-)

As for the confed-cup... I didn't see Germany in the final ;-)

/ 2006-06-09 22:43:

no the defence is just bad - good defences can pull off the offside trap pretty much every time. watch italy play or a really good defence play...

/ 2006-06-09 22:55:

Italy has been doing offside traps? I must admit I haven't watched them much in the last 5 years, since my eyes started bleeding of boredom at their play.

On the other hand, the greatest offside-trapping team in history was Argentina 78, which did it on about half of the plays.

Offside traps ("achique") was the great tenet of Menotti's football ideology, and even he stopped doing it much in the late 80s.

/ 2006-06-10 15:42:

> The idea, obviously, is that the
> defenders play in a line, and move
> forward a fraction of a second
> before the attacking forward
> starts the pass, thus leaving the
> receiver of the pass in offside.
> You do that, you get the ball.
> Simple.

Simple. Simple, but wrong.

You're an excellent commentator, Roberto, but you would make an awfully bad football coach. :-)

Thing is, to successfully play the "offside trap", the recipe is *not* that "the defenders" (all 4 of them) play in a line. (That would mean they'd have to move in sync to gain the offside decision by the referee, which is very difficult to achieve, as you correctly note.)

> The bad news are, of course, that
> such plays work about 50% of the
> time. If that.

The recipe is that *all but one* defenders (3 in the cases of the Costa Rican goals) play on a line, and the last one (usually one of the 2 center defenders) is half a step behind, and it is solely *his* decision to play the offside trap card, by moving forward at the exactly correct time. That makes your "offside probability mathematics" turn out a bit different :-)

In both of the Costa Rican goals this did not work. In both cases it was the same defender who now is accused of having failed: Arne Friedrich. (As one standup comedian in German TV noted, "We'll have big chances to make it into the final, if Arne Friedrich gets heavily hurt before the next match..."). The first one of these goals was in fact *not* offside (as could be seen in German TV replays), but the second one very likely was offside (and thusly, a wrong referee call) by guessing from various TV dissections. Doesn't matter, however: referees decide; and we have to live with all their decisions, wrong or right. :-)

Good defender teams have defense players who can play the offside trap nearly perfectly (which often times includes a decision to *not* play it during this attack).

> So, the german coach is incompetent. He
> may do some things well, but Germany's
> defense is atrocious.

As far as I am concerned. the German defenders can go on playing for offside as long as they want, and it may go wrong as often as it goes; I don't care. I only care about this: that our forwards score two more goals than the other team... :-P ;-P

> They will not win the cup.

Heh... Let's see. Let's wait until the first week of July is over, OK? "The ball is round." - "Each match lasts (at least) 90 minutes." - "A world championship tournament is not decided by one match." - Andsoon, andsoforth....

:-)

/ 2006-06-10 16:00:

Kurt:

I would be an **atrocious** coach.

If the last defender is more than two steps behind the other three, he doesn't have time to set the attacker offside, so it is *practically* playing in line, within the margin of error ;-)

/ 2006-06-11 12:01:

don't think it's fair to blame the coach. germany's defense was atrocious under the one before him, too :-)

they probably won't win the cup, but at least it's fun to watch.

/ 2006-06-12 08:37:

Roberto, some more matches have been played since. The opening game was one of the better ones IMO. What about Sweden, England, Portugal? Where is their glory? Those matches have been boring.

As long as Germany wins his matches, it doesn't matter how good/bad the defense is. BTW, the second goal of Costa Rica had two of it's players offside. What about the referee? They weren't any better than the German defenders, were they?

Anyway, let's hope for a lot of goals and more matches ending 4:2 than 1:0 (or ven 0:0).

/ 2006-06-12 10:59:

Andreas: I wrote about some more yesterday.

The Costa Rica offside was by about 20cm. That is yet another problem with the offside trap: the recommended action for the referee is that when in doubt they must let the play continue.

Asking for perfet precision from the referees is like asking for forwards that score on every shot :-(