Friday, March 25, 2011

Value of a top player

I got a comment on the previous thread and posted a response but wanted to make a new post about it:
I would like to hear your statistically informed opinion on the following thought experiment: assume that there are thirteen players of roughly average (on the scale of all ultimate players) and equal ability (compared to each other). The fourteenth is a player of outstanding ability--someone widely thought to be one of the best players in the game.

They play a pickup game in which everyone is trying their best to win. What is the probability that the team with the elite player wins?

Hey, good question. I did some simulations about 15 years ago for a UPA Newsletter article. I will use the chart in there to make estimates.

(First, what is an "average" ultimate player? What is the average income between a homeless guy, Joe the Plumber, and Bill Gates? When you have such a range between high and low, "average" becomes a funny concept. I'll assume "average" is someone who would fit in nicely on a low-level regionals team.)

Two teams that score at equal rates will of course win an equal amount of the time (with a slight advantage to the team that receives in the first half, but we'll ignore that). A team that has a 5 percentage point advantage (e.g., 40% vs 35% of the time they touch the disc, they score) will win 65-75% of the time (with the bigger advantage when the percentages are at the lower end). A 10 point advantage goes from 76-87.

With the average groups, I'll assume that teams score about 30% of the time. Top Open teams playing against top Open teams in moderate wind might be around 50%. What effect does this awesome player have?

First, I think the effect on defense will be less than on offense. He will get some poach blocks but since there is no star on the other team he won't be able to thwart their offense. Let's assume he gets 3 additional blocks but otherwise has no effect on their offensive efficiency (such a player at the elite Open level would be possibly the best player in history). Previously they were 15/50 in a game to 15, change that to 15/53, that's a drop to only 28.3%. To lower their % to 25%, he'd need to get 10 blocks a game.

Let's pause for a minute and consider what a superstar team would do against this team. I'd guess 15-1 or 15-2 is a fairly typical score for a game like this, though there is a question of whether they are trying their best to win, if for no other reason than they have 4 games that day (but so does the other team, and I'll guess they aren't in as good shape so would be further from peak efficiency). If they had 5 turnovers, that'd only be 75%. So, adding 7 elite players to an average team would take you from 30% up to 75%. I suspect that most of the benefits come from the first one or two, and almost nothing from 5-7. (Dennis suggested 20 years ago that the highest marginal value is provided by the second player, because that gives the first player someone to throw to). So, to get those 45 percentage points, I'll say it's 14, 14, 9, 4, 2, 1, 1 for each added player.

That puts the O efficiency at 44%, D efficiency at 28%. That means the O will score 15/34 times instead of 15/50. The other team will score 28.3% of 33 times or 9.3 goals. Set the point spread at 5.5.

Using a Pythagorean exponent of somewhere between 4 and 6, which my earlier research has suggested, that gives an expected winning percentage of 87-95%. Interpolating my table would give an estimate of about 93%.

Also, IIRC, a 40 point difference in RRI translated to a 1 point difference in expected score.

Tuesday, March 08, 2011

Dorkapalooza, baby, Dorkapalooza!

I attended the Sloan Sports Analytics Conference (SSAC) last week. I really wanted to go last year but wasn't sure when my surgery was going to be (it's a year ago tomorrow), and by the time I tried to sign up, it was sold out. This year I got in early.

For those of you who have been under a rock these last five years, the SSAC, termed "Dorkapalooza" by ESPN's Bill Simmons, brings together bigwigs from across professional sports and focuses on what the data can and cannot tell you. Somewhat surprisingly, it seems that much of the focus is turning toward the squishier side of things. One talk suggested that they could predict achievement and likelihood of arrest for NFL players based solely on what they said during pre-draft interviews. (I missed most of this one, but they had one dimension that was Distrust and two that dealt with how players handled nuance.)

The biggest problem was in trying to figure out what to attend. Except for the opening and closing panels, there were always five sessions going on at once. (Some or all of these will eventually appear on the web site; all were filmed.) The big ones were all panels with a moderator and four speakers. My favorite panel was the Referee Analytics hosted by the Sports Guy and featuring noted bad-ref-hater and Dallas Mavericks' owner Mark Cuban, longtime NFL ref Mike Carey, controversial author Jon Werstheim (who claims that most of home field advantage is due to referee bias), and sabermetrician Phil Birnbaum (who has rebutted (and confirmed) many of Werstheim and co-author's claims on his blog). Cuban muzzled himself a bit for fear of being fined yet again by the NBA (this was a frequent source of joking during the panel) but still managed to let his opinions be known. One of his pet peeves is that he feels (and Werstheim's book "Scorecasting" asserts as well) that NBA games are not called consistently over the course of the game. Carey couldn't stress strongly enough that in the NFL, a foul is a foul is a foul (though he did differentiate between grasping a jersey at the point of attack and doing so away from the play). Another interesting point brought up was whether refs profiled based on past history and whether it's more fair to do so or not.

The opening session was moderated by Malcolm Gladwell, author of the book "Outliers" which focused on talent and how people become experts. His book cited the "10 000 hour rule", that a person (who is talented above some threshold level) still has to do focused practice for 10 000 hours to truly become an expert. I calculated that I have only about 6000 or so hours of ultimate (counting games as 1 hour and practices as 2 hours, figuring that much of the time I'm at the field is down time). So does this mean that there are no experts at ultimate or other amateur sports? I've often wondered (not that it's even a meaningful question) how the best ultimate players rate compared to other sports, each within their sport. Obviously ultimate players aren't as good at ultimate as Tiger Woods is at golf, but where would they fall? My gut feel now is that it's somewhere around scratch golfers or low single-digit handicap (pros are 5-10 better than scratch), which is to say pretty damn good, but with inconsistencies and weaknesses and probably no aspect of their game truly world-class. (There are something like 25 million golfers in the US.)

Anyway, good discussion at this panel, which included Houston Rockets GM Daryl Morey (one of the founders of the conference), NYG DE Justin Tuck, former NBA coach and current announcer Jeff Van Gundy, and training scientist/CEO Mark Verstegen. It was pointed out that talent can be a curse if the talent possessor relies too much on the talent during their development and doesn't hone the other skills that will be necessary when he gets to a high enough level. (In some cases, like with Tracy McGrady, talent alone might be enough to be a perennial All-Star but still be considered an underachiever, and that if he had had "a desire to practice", he could have been one of the best ever.) I really liked a quote from Van Gundy: "Soft, stupid, or selfish. You can be ONE of these, but not TWO." The most amazing statement I heard was that the panel thought that intelligence was more necessary for defense than for offense, the reason being that stupid players will make mistakes that are easily exploited and if this is on defense, the whole D will fall apart. This contrasts with my image of ultimate, where the guys who can run but don't know the game or aren't skilled get put on D, while the O players have to recognize patterns and feel the flow of the game and identify the open field space. I felt that intelligence is more useful on offense to do these things and to be able to recognize those defensive mistakes as soon as they happen and punish them. Perhaps this again speaks to the immaturity of ultimate, that "punishing mistakes" is not a given for elite players.

There were a couple underlying themes throughout. One is that the pro teams aren't especially interested in ranking the players from top to bottom with a single metric but are more interested in the marginal production they will have on their team in a particular role. Mike Zarren of the Celtics maintained that the Kendrick Perkins trade actually made them more likely to win this year and was not a trade for future considerations (and that they felt really bad trading him since they all liked him so much, but hey, it's a business). Another theme was that you need not only play-by-play data but inside information (blocking schemes, pass coverage responsibilities) to make sense of what happens on a lot of plays, and that pro teams are hoarding this information (except for baseball, which is doing amazing things with Pitch F/X, Hit F/X and Field F/X). A final theme, mentioned above, is that teams are trying to get analytics on what might be better thought of as psychology. How can a team decide whether Player A or Player B is more likely to develop based on their personalities? They are trying to quantify this to improve their drafts and their development systems. This was a big topic in the opening panel. I felt that the panel seemed to place too much of the blame on the players when they fail to develop to their full potential and not enough on the coaches or on the specific player/coach/organization interaction. I'm not sure how they would measure this, but how much of an organization's success at "developing talent" is due to making smart personnel picks and how much is due to having a good organization? What if JaMarcus Russell had been picked by the Patriots instead of the Raiders?

One final theme is that all the panelists were gracious except for Aaron Schatz of Football Outsiders, who seemed irritated that all these idiots were preventing him from being known as the smartest man in football and that all these little people at the conference would deign to bother him. I talked to Mike Carey for several minutes one-on-one at the reception and discussed my own observing experiences and asked him how they deal with certain tough issues like profiling. (He said that they call everyone equally but did admit, I think, to focusing more on certain matchups where fouls were more likely to occur.) I chatted for several minutes with two of the golf panelists. (Mark Broadie, who developed the "strokes gained" formula, told me that all handicaps actually have about the same first putt distance on average but the pros will be hitting it to that distance with their five irons while the hackers are doing it with their chip shots.) I chatted for a couple minutes with basketball stat guru Dean Oliver about ultimate (he is friends with some West Coast ultimate players). I made acquaintance with one of the MIT Sloan students whose team won the AECOM business case contest and he was friendly.

Another favorite topic was on the "optical tracking" in the NBA. They put three cameras per half-court in a few arenas and captured 25 frames per second and so were able to track where everyone was all the time. Some interesting stats they came up:
A tip-in attempt is 22 percentage points lower in shooting average than a putback.
Every 1.5' in extra shot distance costs 1 percentage point.
A contested shot is 12 percentage points lower than an uncontested one from the same distance.
Defenders space themselves from the shooters close to optimally, so a shooter who steps back costs himself as much by having a longer shot as he gains by being more open.

I really enjoyed listening to Mark Cuban, who seemed to be on every panel. As befits a self-made billionnaire, he seemed quite sharp and tech-savvy and any fan should love to have him as his team's owner (though the Mavs do not use statistical process control on their metrics, he said). I do have to admit that I don't like the "game experience" that Cuban and other places offer these days, with the nonstop lights and loud noises that aren't part of the game-viewing experience. He seems to feel that it's about way more than just the game, that he needs to offer entertainment (in addition to a quality team playing basketball) in order to draw in fans and keep them. If you want to talk about the game, you can do it afterwards.

I was never quite sure from what perspective I was supposed to be listening during the conference, whether as an individual ultimate player, as an ultimate team leader, as a regular sports fan, as a wannabe sports stats nerd, or as an engineering metrics and stats guy. One of the presentations on some analytics software would have needed to have been modified only slightly to be presented at work, and they seemed even to have borrowed their "Analytics Maturity Model" from the Capability Maturity Model Integration (CMMI), which specifies best business practices for engineering organizations and with which I deal with frequently (we're undergoing a CMMI appraisal right now, in fact). I do occasional little studies with baseball or basketball stats (most recent one was to examine whether NBA players and coaches target round scoring numbers like 40 or 50 points (they do; there are about 50% more 50-52 point games than would be expected based on the number of all other high scoring games) but nothing too rigorous or involving too much database diving, though I keep telling myself I'll start one day (and could even justify the time as professional training).

All in all, it was a fun and worthwhile use of $275 and a vacation day. I brought home some insights, possibly some tips for work, and a heightened interest in sports. I did not bring home any ideas on the ultimate ultimate stat, and indeed have come to the conclusion that this stat is impossible to obtain due to sample size and context issues, but there is still hope for evaluating some strategic questions.