Monday, July 24, 2006

Value of a puller (warning: numbers)

What is the value of a good puller? George said he thought one of his teammates was worth 4-5 goals a game based on his pulls, but I think that a player worth 4-5 goals on defense would be the best defensive player on the planet.

So how do you go about estimating this? One way is to start by looking at breaks. Elite Open teams probably average only about 4 breaks a game against other elite teams. Splitting the credit among the 7 guys who play defense, this means each guy is only worth maybe 0.5 goal a game over an inflatable dummy. If a team averages 7-8 breaks a game (which would mean that they are more likely to score than the receiving team), then either that team is phenomenal or else (more likely) the playing environment (either bad weather or poor disc skills) means that even bad defense will get 3-4 breaks a game.

Or look at it on a point-by-point basis. Suppose that the odds of the O scoring the point (not the possession are 80% on a brick, 70% on an average/decent pull (lands in end zone, one free pass), and 60% on a terrific pull (lands in end zone and hangs long enough for D to contest first pass). 80% scoring rate would translate to 3 breaks in 15 opportunities (game to 15), 70% = 4.5 breaks, 60% = 6 breaks. A perfect puller would only be worth 3 breaks over the worst puller, and just 1.5 breaks over someone who just threw line drives into the end zone. Factor in that the perfect puller doesn’t exist (although the little guy on Bravo came awfully close when we played them at the Colorado Cup) and you are probably looking at about a 1 goal per game difference between a great puller and the average puller. (Keep in mind that the “average puller” is still better than “how the average player would pull.” Any defensive squad probably has 2-3 “average pullers”.) Now, this is quite valuable, as we showed above that a good defensive player might be worth only 0.5 goals a game over a field cone, but it’s not 4-5 goals a game.

Or consider a less efficient environment, where the O holds serve 60%, 50%, and 40% of the time on the three pulls. The team with the perfect puller would now get 9 breaks a game, but the team with the bad puller would get 6, leaving the same “value over replacement”.

You could probably do a similar exercise with O players and come up with the statement that a good O player is only worth a goal a game over a replacement. Let’s do it for fun. We’ll put the D team out there on O receiving the pull. They’ll still score, say, 60% of the time (6 breaks a game). Our great O team of great O players scores 95% of the time (0.75 breaks a game). That’s 5.25 breaks/7 players = 0.75 breaks/game/player. Maybe the best player is worth 2 and the others are worth 1.25, .75, .5, .5, and 0.25.

And going back to the kid’s observation in George’s blog, not to pick on him, but the official UPA writeup tells a different story. Wisconsin got only two breaks, at 8-6 and 9-8 (the writer makes an error by saying the break at 9-8 was their second straight), and their D forced turnovers throughout the game but were unable to convert.

23 comments:

Anonymous said...

Value of a player measured as goals is interesting. It makes me wonder if there are players whose value is actually negative? I.e. having them on the O line actually decreases scoring chances, compared to a dummy. A guy with high turnovers/touches (or turnovers/yards gained) ratio has to have negative value for the team, unless he also gets lot of D's (or gains huge yardage).

It seems to me that it is not always easy to identify such players and coaches can easily hurt the team by letting these people to play.

blw said...

Good stuff here.

The arbitrary assessment of 10% incremental differences probably isn't a terrible estimate, but you are drawing fairly exacting conclusions from them, so I think it is probably worth it to go into those numbers a bit more.

I think that, among high-level teams, the worst pullers are typically giving the offense (in an 'average weather' game) the disc at the brickmark consistently. Either the pull goes out, or the pull lands quickly enough that the O plays without defense until the brick mark.

Again among high level teams, it seems to me that the average pull from average pullers comes in at somewhere in the range from the goalline to the goalline+5. In thinking about pulls I have caught (and maybe more importantly, pulls that have been caught and thrownto me) I usually say to myself that it was a weak pull if it is caught at the 10, and a good one if it is caught 5 yards deep.

I'm assuming (wrongly) that the pull distance is roughly concordant with the time aloft...so longer pulls are always better. Maybe a better way to treat this is the place at which the offense starts working against a defense:

Worst of the very good teams' pullers: O starts against D at the Brick.

Average: Pull caught at 0-5, play started with D around the 10-15 yard mark.

Very Good: Pull caught around the -5, play starts at the 5 (ish).

The BEST pullers are consistently putting the disc into the field more than 5 yards into the endzone, with good hang (Cram of Sockeye/MG of Furious/Taylor of BayArea/Parker&Rouisse from Bravo) from fall into this category, I think). Not many people can do this, but then again, a team really only needs one.

Best pullers: Disc fielded at the -10 or better, play starts with D around the -5.

So, numbers for Total Distance of Offense w/ D Played:

Bad puller: 50 yards
Average: 55-60
Good: 65
Best puller: 75

If we make the assumption that offensive efficiency is proportional to distance, then we might conclude that the best puller gives the other team 1.5 times the difficulty to score (or 1.5 greater the risk of the initial turnover). This also should give the D, after a turn, a typically shorter field to work with. I think this might bump the difference between worst and best pullers up to something like 35%, but it's late and that translation I just estimated is a bit out of my depth.

In reality, the distance in the first half of the field is somewhat easier in one respect, because the defense has more ground to defend. It also increases the fear of a quick turn, though, increasing the gain of a punt. Maybe these cancel out? There's also the pressure of playing with a backwards restriction....

I guess my conclusion is that I think the best pullers put more pressure on the offense than your 10-20% figure indicates. Should probably also point out that a puller hitting a great pull for every brick is probably no better than average, and might give his team some great chances... But a puller hitting a great pull for every good pull and for every brick is below average.

My guess is that good Oteams in good weather against great pullers are probably more like 30% less efficient, instead of 20. Maybe only a half point a game worth...but many top level games are won 15-13.

The hoards out there more savvy than me should start the dissection now...I'm sure half of this is poorly reasoned...I just don't know which half.

Anonymous said...

Elite Open teams probably average only about 4 breaks a game against other elite teams. Splitting the credit among the 7 guys who play defense, this means each guy is only worth maybe 0.5 goal a game over an inflatable dummy.

Here's where I think you're wrong, Jim. To consistantly force turnovers in elite ultimate, you need all 7 guys on the field to be working hard and applying pressure. In other words, insert your inflatable dummy in your above scenario for any of the 7 players, and you may see the number of breaks fall from, say, 4 to 2.

Why do you assume that you have to split up the pie in terms of who gets credit for goals (on O or D, for that matter)? Why can't the entire D line get some credit for breaks?

On the flip side, I can much easier see an inflatable dummy hide in the stack on offense and let the powerhouse cutters dominate the game.

gcooke said...

Well, it is nice to ask for and then receive a discussion.

I wasn't clear enough in my post. While my father was a mathematician, I honestly did not get that gene. In 04, our primary puller consistently pulled -10 or better (to use Ben's nomenclature) with very good hang time. Combined with the speed of our team, it was frequent that the catcher of the disc would catch the disc 10 yards or more in their end zone and hear "stall 1". In 05, with our best puller injured, it was not uncommon that our opponents O was set up at +10-20 before the stall was initiated.

So perhaps a better way of saying what I was trying to say is: our pulls in 04 put a lot more pressure on their O than our pulls in 05.

My point with the other subject was not to say the camper in my discussion offered the correct analysis. It was to say that he offered some thoughts that were more insightful than "It was a good game. They threw well". I also think that whether or not there wer Florida turns is not the point. The point was that, from a fitness perspective, Wisconsin's pulls gave Florida an extra 30-35 yards per reception, and let them start at essentially the brick without marking pressure.

I do think, though, that this post is an interesting take on game analysis. Many times I think commentators offering analysis offer highly subjective perspectives. This post, which attempts to quantify an issue, is offered with a disclaimer in its title. While I find the numbers interesting, perhaps the general public wants subjective analysis that interprets the action, but creates a sense that it is backed up by statistics.

-George

parinella said...

The concept of "replacement level player" does get a little squishy when applied to such a team sport. It is most useful in baseball, which is much more linear, and where a replacement gets more or less the same opportunities as the regular. In ultimate, you can hide them on offense a bit, but they might get picked on on defense.

For ultimate, I earlier defined a replacement as something like the 8th best player on the D team (or O team). A "replacement player" is much better than an "inflatable dummy" (I used the term only because it's fun and to represent the absolute worst replacement). A team of replacements would still probably get 2 breaks against an opponent that would get broken 4 times by the starting team. You can have players who are below replacement value (see "inflatable dummy" or "turnover machine").

If the break comes as a result of good team pressure, I don't see the problem with splitting the credit among the 7 out there. Earlier, I estimated that turnovers were split roughly equally between good team defense, outstanding individual effort, and acceptable (replacement level) team defense accompanied by offensive error.

Ben, it looks like you're on the right track. My current mental model is that yards are twice as easy to come by before midfield because the D has to respect the huck. The "typical elite team" scores 90% at the goal line, subtracting 10% per 10 yards up to midfield, then 5% per 10 yards the rest of the way. This leads to 55% at midfield, 40% at the brick, 30% at the goal line, and 25% at -10. (Unfortunately, these %s are for scoring the possession, whereas we've been using "scoring the point.") I've done simulations before and could do another one, letting one team start at the brick every time and an otherwise equal team start at -10 and see how they end up. I'll take that as an action item.

And my point wasn't to say that pullers aren't valuable, but to say it's likely that in elite ultimate that no one is worth 4 or 5 goals a game, and that someone who is truly worth 1.0 goals a game above another is extremely valuable.

parinella said...

George, I think your last paragraph summarizes the last 30 years of baseball statistical analysis. Geeks with access to mounds of data have studied situations so that the analysis doesn't have to be as subjective. People tend to latch onto one facet as a key to the game and use that to explain what happened, and the analysis provides a sanity check. A superstar going on the disabled list for 3 weeks will likely cost his team only 1 game and thus could not explain a 9-11 swoon.

Anonymous said...

If the break comes as a result of good team pressure, I don't see the problem with splitting the credit among the 7 out there.

Imagine a situation in which 7 great defenders work well together, deny their offensive counterparts the disc, and force turnovers. Let's make the assumption--albeit an extreme one--that adding a replacement player to this mix destroys the defense. His guy gets disc after disc on stall 9 bailouts, and the O only turns the disc over due to their own incompetences.

In this extreme situation, why wouldn't each of the 7 starters be worth closer to 1 point per break as opposed to 1/7 of a point? In other words, I am challenging your assumption that the sum of the players' credit has to be equal than or less to the total points scored by their team. You seem to imply otherwise. Or am I missing something in your analysis?

parinella said...

In this extreme situation, I would assign 1/6 to the 6 and -1 to the 1. If you add another replacement player, I'd give 1/5 to the good 5 and -0.5 to the 2 replacements. I think the paradox (normally "replacement" means 0.0 value) arises because the "replacements" would actually become "inflatable dummies" (i.e., much worse than "replacement") in this context. "Value" depends highly on the context. You also point out a limitation in the concept, that it's difficult to value extreme players. One reason is that you'll get a different answer if you're looking at a team of 7 of those players (and dividing by 7 to get the value of each player) versus putting that extreme player into a "normal" environment and seeing the difference.

Anonymous said...

My team did it's best at nationals so everybody had weird stats like the same guy scored all the double game points. But one statistic, that made alot of sense was our best puller averaged over 90% of pulls landing in the endzone which I don't remember him doing at any other tournament.

parinella said...

best puller averaged over 90% of pulls landing in the endzone
And do you have a breakdown on how the team did on those points compared to when the pull landed on the field proper or out of bounds? At a minimum, you'd need to adjust for upwind/downwind, and preferably also for quality of opponent. If all of his bricks came against the top opponent, that would skew the results.

Anonymous said...

Jim,

I think we are talking past each other. Either that or you are just talking past me.

I'll try to rephrase myself. It is my belief solid defense depends so much on all 7 guys on the field playing well together. Start putting in dummies or replacement players, and you get fewer turns as a D-line. The "extreme" players' value may actually go down with more of these duds on the field. He plays shutdown D, and his guy never sees the disc. He gets no opportunities to showcase his "extremities."

I think that good D players' values in a game may add up to more than the total number of points the D-line scores. In my extreme example above, when you add one dummy, the D-line goes from getting a break to not getting the D (and getting scored on). Wouldn't that make the value of each the 7 dominant D players closer to 1/1?

What I don't understand is why you seem to imply that the total sum of the values of the players in the game needs to add up to the number of goals that the team scored.

parinella said...

The "extreme" players' value may actually go down with more of these duds on the field.
That is a correct statement. His value goes down, even if his ability stays the same. I think this is where our crosstalk comes from, the definition of "value".

The reason for this decrease in value is that he shoulders less of the burden. His offensive counterpart would become more valuable (but not any "better"; in fact, his efficiency would probably decrease) in a similar situation because he would handle more of the burden. This makes the study of ultimate more complicated than that of baseball.

What I don't understand is why you seem to imply that the total sum of the values of the players in the game needs to add up to the number of goals that the team scored.
Because that's how I'm defining value, to be the contribution toward goals. But as we're both saying, it becomes a little fuzzy when you factor in the synergistic effects.

Sideline Engineer said...

And going back to the kid’s observation in George’s blog, not to pick on him, but the official UPA writeup tells a different story. Wisconsin got only two breaks, at 8-6 and 9-8 (the writer makes an error by saying the break at 9-8 was their second straight), and their D forced turnovers throughout the game but were unable to convert.

What the kid said makes sense in light of what happened. Wisconsion got turns but was not able to convert. If they had been pulling into the endzone, they would have had a more tired O to work against when they did get turn and less yards to go to score. That sounds like a recipe for more conversions to me.

Anonymous said...

is a good puller more valuable in calm conditions, or windy conditions? any thoughts....

Anonymous said...

defense = inflatable dummies...
offense = inflated dummies...

yes, it's easier to move the disc close to your own goal line... but turnovers in your own half of the field are much more likely to lead to scores...

luke

James Scott said...

ZING!

Anonymous said...

...which i was actually wondering, does this in anyway justify the world of huck and hope (just don't i.e., don't give 'em an easy one) as kind of a corrollary to the whole zone thing (which i always think of as being 'less likely' to generate a turnover, but more likely to lead to a score, if a turnover happens... idle musings...

parinella said...

My issue with the Huck-n-Hope (TM) is not that teams throw deep too much but that it doesn't even look like they have a good cut where the receiver has more than a foot of separation.

Field position is part of the whole equation, yes, so H-n-H is related to good pulls is related to zone (actually, I would have said that the Clam is more this type of defense, an aggressive one designed to either get the d early or not at all). A full analysis considers the field position after a turnover in addition to the odds of scoring a possession. The better than an offense is, the less that distance from the goal line matters (but not necessarily distance from the sideline, so maybe a "good pull" is one that lands within 5 yards of the sideline with the defense already set up).

Anonymous said...

i think the huck and hope really earns it's paycheck on the 'underthrown disc'... where the receiver sees the throw much earlier...

do you think hnh reflects the increasing presence of hs players in the game? b/c, frankly, the long game can really dominate in the hs game, if you've got a couple throwers and a couple take down players.. and now, years later..

luke

gapoole said...

Luke, I disagree on principle with your comment about how HS players are pushing HnH in higher-level ultimate. My team worked hard to learn structured offense and, when I was captain, flow-based offense, and we always stayed away from HnH. All the competitive HS teams in NJ (Columbia, Princeton, Watchung, etc) play smart games, for the most part. We played a lot of teams this year, and not just in NJ--some of them play HnH, but they usually aren't the ones dominating. The sport is growing to the point where you need more than a couple throwers and a couple tall fast kids.

Julian said...

Luke made me think of this, so blame him.

I've been thinking about a way to write the underthrown disc into an offense. I think it might have a lot of value for teams where receivers and throwers are really on the same page. If a cutter is running deep and only marginally open, the "right" throw would be basically at his back. Once receivers are used to looking for this, they'll have the best shot at it every time.

Yup, it's risky. For sure. But might it have limited real value? I think so.

parinella said...

HnH (TM) seems to be more of a college phenomenon, because they're more likely to have athletes who can run and jump.

I would disagree that HnH (at least as I consider it) would be better for the underthrown disc. The stereotypical HnH huck is a flat pass straight down the field that flies really fast and then hovers for just long enough for the guy to chase it down if he's really fast. A "good" huck has some angle between the thrower and the cut. See pages 60-62 of UT&T regarding "Deep Cuts". http://books.google.com/books?vid=ISBN073605104X&id=Zvgbmv7OinAC&pg=PA62&lpg=PA62&dq=parinella+deep+cut&sig=MulbxoheIKDDXSSAC-qVTkDxVY4&hl=en (You can go to http://books.google.com/ and type in "parinella deep cut" and find page 62.)

The underthrown disc is most catchable on the S-cut (crossfield deep cut). For instance, disc on left side of the field forced forehand, cutter fakes to the line, D bites, cutter cuts long to the wide side of the field. A good throw will lead him to the endzone, but an (accidental) underthrow (think slightly quailing forehand; anyone who knows my game will immediately recognize this pass) will still get past the defender and be a completion, just not for a goal. (I'm not saying that I would deliberately throw this, but I know that a common "miss" for me on this throw is that exact pass which still has a high completion rate. In golf, it's smart to consider where your misses are likely to go when deciding on your shot.)

Julian, there definitely is a place for timing passes in ultimate (like the quick slant in football, receiver turns to see the ball already on top on him). However, neither O's nor D's are generally sophisticated enough to make it necessary. A lot of dump passes are timing passes, thrown exactly when the cutter makes his cut. Experienced teammates like Alex and I connect on a fair number of these downfield, but we've played together for 18 years and something like 1500 games plus a few hundred practices.

parinella said...

I think a good puller would be most valuable in moderately strong wind conditions. I would define the break point to be the amount of
wind that a team would barely prefer to be receiving upwind rather than pulling downwind. With more wind, teams would adopt a punt strategy and so it wouldn't matter how far the pull went.

I suppose a corollary of this is that against a HnH team, the distance of the pull matters a lot less than hang time. The worst pull is one that lets them get the play moving and gives the cutters a chance to run into their cuts from flow rather. A brick isn't great either, since the offense can set up at their leisure and time their cuts. A pull that floats and lands in bounds as the defense is arriving at the handlers is the best one (and not just against HnH, but against any offense) since the cutters have a more difficult time setting themselves up.

So, has anyone experimented with deliberate 60 yard pulls that let the D set up?