Monday, December 19, 2005

Relative value of O and D

Here’s a paradox:
  • Offense and defense are equally important in ultimate.
  • Most of the important players are important because of their offense.
  • If you add up the individual values of all the players, the sum of the offensive guys will be more than that of the defensive guys. But see #1.

Is one of these assumptions in error? Which one(s)?

I’m going to go with the first assumption, and here’s why. The advanced view of “value” is “contribution above replacement level.” However, a lot of defense is simply showing up and not screwing up so badly that you hand away goals. A "replacement level" defense is still going to get turns, while a replacement level offense (especially in women's ultimate) is going to do really badly.

Let's just guess that in a decent game between decent teams, offenses score 50% of the time (and defenses get turnovers 50% of the time). In a blowout, say 15-5, the offense will still probably have maybe 10 turnovers, yielding a 60% efficiency against a replacement defense, meaning the other's team's (replacement) offense scores on only about 20% of their possessions. So, the average offense is (50% - 20%) better than a replacement offense, but an average defense is only (60% - 50%) better than a replacement defense.

Maybe this is what people are saying when they say defensive strategy is practically non-existent. Most of the value in playing defense is just being in position.

Part I of an ongoing thread on analysis of ultimate. (I don't really want to call it statisticial analysis because the numbers aren't the important thing, it's the concepts behind the numbers.)


Anonymous said...

Somewhere 'he who shall not be linked to' is rereading his post about how he cost his college team a visit to nationals by challenging the dump and giving up the GOAL...

and squirming....

a harvard fan.

Anonymous said...

< I’m going to go with the first assumption, and here’s why. The advanced view of “value” is “contribution above replacement level.” However, a lot of defense is simply showing up and not screwing up so badly that you hand away goals. >

I have always thought that it was the offense who was under pressure not to screw up and the defense had the luxury of the gamble. A high risk play on defense may result in a goal against, (which even against a replacement offense is likely to happen anyway) but may also get a turn and an opportunity for the valued and carefully counted break. High risk play on offense may result in a gaol in favor, but those risks are often weighed against the returns. A single goal isn't worth a whole lot if you're giving a fourth of them back in turns when your high risks aren't falling in your favor.

An excellent offense can keep a team in the game and put a lot of pressure on the opposing offense by scoring easily every time. An excellent defense can win a game outright simply by staying on the field (OK, it's not that simple). I'm not arguing that defense if more valuable than offense, only that there is more equality than your originally post implies.

I think the flaw is in one or both of the last two assumptions. What about the old adage "Offense sells tickets, Defense wins games?" When you mention "important" players, we are all likely thinking of those who sell tickets, not necessarily those who win games.


eric said...

I always believed that offensive players are more important than defensive players simply because a single O player has the ability to dominate a game, unlike a single D player. I believe it takes the whole team defense to control a game. However, there are always some stupid offenses that allow 1 defensive player to dominate. Yes, O does sell tickets. I cannot stand watching Bears' games, don't they frequently resemble a high school football team?

Anonymous said...

Jim could you give us statically inept a clearer description of what is meant by "replacement level".


oh and this is incredibly off topic, but are you going to add a link to Bob Loblaw's Law Blog?

parinella said...

Here's a definition of replacement level from the world of baseball: A commodity which is easily available to all teams at no or low cost confers no competitive advantage, and therefore is of minimal value. (Source: Introduction to VORP: Value Over Replacement Player. Also of note in this piece is the idea that average players have value since talent is scarce. This means that you do not use average as your baseline, but a level well below average. A guy with a lot of touches performing at team average (or even slightly below) efficiency is much more valuable than someone who is above average efficiency but with few touches.

In baseball, it's something like a .235 hitter or a pitcher a run above league average.

It's a little tricky in ultimate because everyone from the "major leagues" down to rookie ball is in the same league. But for a team, I would set the replacement level as either "the 15th best player on the team" (or "the 8th best player on the O (or D)") or as "the best local player not on the team". I suspect that the latter is too low, though. That article suggests that a MLB team of replacement players would still win about 1/4 of their games, which might translate to an RRI difference of about 100 points.

So, in summary, the replacement level depends on the "league" that you're in. I'll say it's about the level of one of the better players on the best team that you would never expect to lose to in a real game (an average score of, say, 15-9).

Tarr said...

Let's just guess that in a decent game between decent teams, offenses score 50% of the time (and defenses get turnovers 50% of the time). In a blowout, say 15-5, the offense will still probably have maybe 10 turnovers, yielding a 60% efficiency against a replacement defense, meaning the other's team's (replacement) offense scores on only about 20% of their possessions. So, the average offense is (50% - 20%) better than a replacement offense, but an average defense is only (60% - 50%) better than a replacement defense.

Well, first, we're not talking about two "decent" teams here. We're talking about two of the better teams in open ultimate, both playing at least moderately posession-oriented ultimate. That's the only time both teams tend to score 50% of their posessions.

And your examples can be easily used to support the opposite conclusion. Just start with two repacement teams playing one another, and then compare THAT to the blowout. Now it is the superior defense of the top team that effects the change. Say the replacement teams would score at a 45% clip against one another. (Because hey, we're in fantasy land where average teams score 50% of the time anyway.) "Average" defense turned 45% to 20%, while "average" offense turns 45% to 60%. Ergo, defense is more important.

When I look at Purdue's stats against Machine, I don't see a team that can't get the disc back. I see a team that can't score.

I'm not convinced you're wrong, but I'm not sure this line of argument really supports your point.

parinella said...

Tarr, thanks for the comments, even if a little hostile.

You're correct that we need to know how the replacement teams would do against each other in the 50% fantasy world. You suggested 45%, but I'd guess something closer to 30% was more realistic.

Could you do me a favor and look up your O and D %ages for Purdue in blowout wins and losses and compare that to their average?

parinella said...

Earth, fall 1991 (record 10-12, came in 4th at Regionals):
Overall: O 43%, D 39%
5 blowout wins, avg 15-4: O 52%, D 18%
2 blowout losses, 19-11: O 36%, D 63%

Commies, spring 1992 (record 32-6), 2nd at Nats that fall:
Overall: O 54%, D 36%
Blowout wins (19 of them): O 61%, D 24%
Other games: O 49%, D 45%

None of this answers how a replacement level team would do against a similar one, but there is a hint. Earth 1991 was a lot better than a replacement team compared to Commies 1992, but showed a drop in average efficiency from 47% to 41% playing teams equal in ability, suggesting a replacement team would be lower still.

Ok, I just lost the last 4 people who were tuned in.

parinella said...

When I look at Purdue's stats against Machine, I don't see a team that can't get the disc back. I see a team that can't score.

This suggests that your replacement level defense is a lot closer in ability to an average defense than your replacement level offense is to the average offense.

parinella said...

Or try these thought exercises:
1. Take your team's top 7 O guys and grant them average (for your team) D skills. Take your team's top 7 D guys and give them average O skills. Who would win the game? My money is on the O.
2. Rank everyone on your team according to both their O and D skills. Then rank them according to their overall value to the team. (There is the confounder that these two lists might be incredibly similar at the top.) Then compare the lists.

Mark said...

Where does the best overall player usually play? Our best overall player plays on the D team, but will also play on the O team occasionally.

Kid A said...

I don't think the first assumption is true. If it were, your 7 best defensive players, regardless of their offensive prowess would be on the line when you're pulling on Universe point. I don't think that is the case...

Many times, teams will put a decent (but not great) defensive player out on the D line, because they can handle better than most.

The game, in general suffers from an offensive bias (not that this is a bad thing, its good, in my opinion - time capped games at 5-3 would be horrible).

parinella said...

Mark's question is almost irrelevant here, since I'm talking about the player's offensive skills, not just his contribution to the O team.

It's interesting to look at a player and estimate how much of his value is offensive and how much is defensive. You can also break down into throwing vs catching, or routine plays vs spectacular. Some guys earn reputations by making occasional mind-boggling blocks or catches, but if that represents 75% of their value, they're overrated.

Tarr said...

Yeah, sorry if I was a tad hostile, I had just gotten off the phone with my health insurance. You're quite right that a lower percentage by our "replacement" folks would lead to O looking better. Of course, in reality, both "average" and "replacement" should go down more than a bit.

For the record, I think your latter thought experiments work better. But to some degre they simply reflect the fact that good athletes who play enough eventually mature into good O players, and that individial D skills are less taught/developed/understood than individual O skills. But that is just a long way of saying that at present, O is more important, or at least there is a greater gap between good and bad O than between good and bad D.

Anyway, some stats. Unfortunately our stat-guy left/stopped taking stats at some point in our blowout loss to Machine at '04 sectionals, as well as leaving early on the last game each day, so I don't have complete stats. Also, more critically, I can only find the stats which I use to derive my adjusted plus/minus stats, so I can only infer turnover percentages from overall O and D efficiency. These are not "per-posession" numbers, they are "per-point" numbers. Some other time I might go look at some of the other stats I have, where I have actual turnover numbers. I figured I'd start with the tournament where we played Machine since I mentioned them.

But what I have does tell an interesting tale, maybe. The wins at each tier were fairly consistent, but the three losses were so different in character that I think I should list them seperately.

Two blowout wins:

O: 6/8 (75%)
D: 16/20 (80%)

Two reasonably close games that we won:

O: 17/22 (77%)
D: 12/28 (43%)

Getting our tails handed to us by an utterly superior Machine team:

O: 2/10 (20%)
D: 1/4 (25%)

(The first 18 points of) losing a nailbiter to Illinois on the first day:

O: 4/9 (44%)
D: 5/9 (55%)

(The first 12 points of) a depleted squad getting blown out by Illinois in the game to go:

O: 4/8 (50%)
D: 0/4 (0%)

Conclusions? Well, the last game is noise for our purposes, I think. It does perhaps demonstrate that when you have no legs, your D suffers more than your O. No surprise there.

The fact that in the two other games against superior opponents, we did better on D than on O, suggests that field position is sufficiently important to render a lot of analysis of "% of posessions scored" useless. It's not that our D line played dramatically better O than our O line against Illinois in game 1, it's that they had short fields on a lot more of their posessions.

Field position - misunderstood by most players, and the bugaboo of statistical analysis to boot.

aj said...


Was your team divided along O/D lines?

When I get home I’ll dig up some college women stats and throw them up here for comparison.

parinella said...

I was actually more interested in the per-possession stats than in the per-point stats. I didn't want to mix in how teams construct their O or D lines. I mean, if you put a handler on the D team because of his O ability, that doesn't address how important his defensive ability is.

Bigger bugaboos are randomness and "other things being equal." These might be harder to overcome with traditional analysis.

Pink Daddy said...

How much can a defense bring down another team's offensive efficiency? For example, if team A scores 60% of the time on average, and team B scores 50% of the time on average, then one might expect team A to win most games between the 2 teams.

But what if team B had a strong defense that reduced their opponent's efficiency by 10% on average? And team A played a weak defense that increased their opponent's efficiency by 5% on average. Then, you might expect the results to be reversed, with team A operating effectively at 50% efficiency vs. team B's 55%.

In this particular case, defense becomes the determining factor. The general case is probably different depending on what level of ultimate you're talking about. I've played (and some might say continue to play) scrub-level ultimate where some teams would struggle to score with *no* defense on the field at all. In this case, having any kind of decent offense is enough to win games.

But I would imagine at the elite level, most teams operate at similar offensive efficiency levels. And a team's defensive ability to impact their opponent's efficiency becomes a bigger factor. But, having never played or even seen elite level ultimate, what do I know?

luke said...

i have an affinity for stats. but i have some unfounded feeling that simple stats are most important.

win vs loss.

you win, you take care of the disc. well, this seems to support jim's view that offense wins. therefore, i believe offense wins.

when we (sockeye) (although, 2 years out, and, not the good 2 years) beat jam at worlds, running off a bunch... down13-6 and 14-11 (or something), well, yes, the defense won the game... but our offensive efficiency was good. or more to the point, jam's was bad. that is, they tried to meet our low percentage d-trans game head on w/ athleticism, and got stoneyed.

where is mark stone in talks of awesome players.

anyway... i think kd said, game comes down to one call and flip of disc... that's a close game. in a not close game, if you just score, you win.

what needs statistical analysis. no turnovers wins. my unofficial analysis of furious, when their 'd' was led by jg was that they were actually less successful at getting d's than sockeye's d. but they were much more possession oriented. their long game was jg to serrags (sorry about spelling), and other than that they would grind it out when they got it.

my recollection of boston, at their best was that WHEN THEY GOT IT, they would keep it. scoring was all that mattered.

NYNY, I only saw them in Plano (didn't play them, we played boston)... they went bigger... but they might've had more of a GET THE BALL mentality than others...

enough. off to my site.

Justin R said...

I think whether D is more valuable than O depends on whether it is more difficult to (a) increase offensive efficiency at scoring points; or (b) increase defensive efficiency at scoring points.

Say hypothetically, a good offensive player has ten percent fewer turnovers. That means using those players increases your score by ten percent PLUS a percentage of the times that the defense loses possession. i.e. likely more than a ten percent increase in your team score.

Now say hypothetically a good defensive player has a ten percent greater chance of getting a turnover against another team. Problem is -- once you get that turnover, there is a chance your D squad loses the disc and gets scored on. i.e. 10 percent more turnovers results in LESS than 10 percent more points.

There are all sorts of assumptions and problems with that analysis (for example, good D players are generally good receivers, thus they increase aspects of offense and defense). But I think you can see that v a l u e of reducing your own turnovers by a fixed percentage is greater than the value increasing your opponents turnovers by the same fixed percentage.

Does that answer the question? I am not smart enough to know.

Justin R said...

Second para. "defense loses possession" should read "opponents offense loses possession".

Pink Daddy said...

Ok, so I think I remember enough math to be dangerous. And there's probably flaws in my argument. But let me attempt to take a scientific approach to all this:

* Let's assume team A operates at x% offensive efficiency, and team B operates at y%, where offensive efficiency is the probability of your team scoring on a given possession.

* The probability that team scores given that they start with the disc is:
* the probability that they score
* plus the probability that team B forces the turn-over, team A forces another turnover, then team A scores
* plus the probability that team B forces the turn, team A forces a turn, team B forces a turn, then team A forces a turn, then scores (this is what Justin is referring to up above)
* plus... ad infinitum. Mathematically, this is an infinite series which sums up to:
x + (1-x)(1-y)x + (((1-x)(1-y))^2)x + ...
= x/1-((1-x)(1-y))
= x/(x+y-xy)

* The probability that team A will score if they don't start with the disc is simply 100% less the probability that team B doesn't score if they start with the disc:
1 - (y/(x+y-xy))
= x(1-y)/(x+y-xy)

* So, assuming team A starts with the disc half the time, and team B starts with the disc the other half of the time (imagine a game to 1, with a toss to determine who gets initial possession), then the probability of team A winning becomes:
0.5 * (x/(x+y-xy) + x(1-y)/(x+y-xy))
= x*(2 - y)/2*(x+y-xy)

I think this formula is right. If A and B operate at the same efficiency (say 70% or 0.7), then the formula gives an answer of 50% (0.5), which is what you'd expect. If team A operates at 100% efficiency, and team B at 0%, then the formula gives team A a 100% chance of winning, which is also what you'd expect. Reverse it, with team A at 0% and team B at 100%, and you get a 0% chance of team A winning.

So, I plugged this into a 3d graphing tool (Calc 3D) and into Excel, and played around with the numbers asking the fundamental question:

Are you better off increasing your offensive efficiency by R%, or decreasing your opponent's offensive efficiency by R%?

And the answer I keep getting back is that it pays to focus on defense in the general case. However, there are scenarios where you should work on your O, depending on where you and your opponents lie in the offensive efficiency spectrum.

I really don't have time to get into the specifics of it, but I will follow up this post soon. Meantime, I would be happy to share the data with you, just email me at rob at mobius dot ph.

PS. Yes, yes, I know I'm oversimplifying things (for instance, an hour spent practicing O could result in bigger gains than an hour focussing on D, etc). But, whatever, I'm having fun doing math for the first time since, well, forever...

Alex said...

This is an often debated question it seems, but does it refer to the relative values of the Offensive Team vs the Defensive Team, or offensive skills vs defensive skills. Also if a person were the top defender on your team, but also the 4th best offensive player, where should they play?

Tarr said...

Pink Daddy,

Your analysis is useful for some things. For example, I have used efficiency percentages to calculate the cost of a turn and value of a goal, and to thereby compute weighted fantasy stats. So in a game between two teams that rarely turn the disc, a goal thrown or caught is not worth much, while a turnover is very costly and a block is gold. In a swillfest, the opposite is true. And all numbers are magnified in close games and diminished in blowouts (regardless of which side of the blowout you are on).

But beyond simple adjustments like that (which don't really need to be precise anyway since we're not trying to draw any deep conclusions), you're making way too many assumptions. The two most glaring IMO are:

1) There's no way to know that a given amount of practice will improve your defensive or offensive efficiency by more.

2) Due to several factors, most notably the vagaries of field position and the differences between D and O personnel on some teams, the assumption of equal likelihood of scoring on all posessions is inaccurate.


At that tournament, we had somewhat divided O and D lines. There was definitely an effort to put some people in more on O and some people in more on D, but there was not a clean split.


Getting back to something you mentioned earlier, about how much of a player's value is O vs. D. It seems to me that a great athlete who can dominate as a receiver and as a deep defender might be more useful to a great team on D than on O. After all, a good O team shouldn't need a bail-out receiver as much as the D team, and having that athlete back there forces the other team to go away from the quick bomb if they want to avoid your stud. This is sort of like what Furious has done with Grant, and what Sockeye does by splitting up Nord and Chase. I could see Danny Clark playing D for DoG next year for the same reason.