What Is The Value of a Break?

So what is the value of a break?  Every point in ultimate is worth one point in the game, so it seems like the answer to that question you be "one."  But in the elite game we all expect offensive holds and cherish breaks.

I wanted to get a better sense of breaks because I was looking at Draymond Green's plus minus rating from game four of the NBA finals and adjacent to the stat was his real plus minus.  While we can easily look at an ultimate players normal plus minus (stat heavy leagues like the AUDL have those values on their stats pages already), but how can we adjust those numbers?

I guess we could do some sort of heavy adjustment talking about when the break happens, but that seems a step too far right now.  Let's just set a simple bar and see if people tear it apart in the comments.

First, it is silly to think about most elite ultimate as single point endeavors.  I don't have the numbers in front of me (this is part of a different project for this summer) but if the Possessions Per Goal (PPG) metric for a team is greater than two it means they will need two possessions to score and that somewhat means that a single turnover is likely on any given point.  I ran the college numbers for ~12 games this season, and it seems like the most elite college teams can operate at sub 2.0 PPG, so let's assume that club teams can do similar or better. What that leaves us with is that a turnover in a possession is still unlikely (again, data unlikely) which holds with our expectation of club where offensive holds are expected.

With many elite club teams operating with an offensive line and a defensive line it makes more sense to think of a "round" of ultimate as being a two point exchange.  At any given time the actual "score" of the game should reflect that exchange, and one way to do that is to include half-point into the scoring system.  For example, if you receive the pull and throw a goal making the score 1-0, the score is actually +0.5 (where the plus indicates your team's value, it would be -0.5 for the opponent).  Upon the opponent scoring it would be driven back to +0.

Perhaps this comes from a mental game as a coach, where you tell your team that a lead isn't as big as it thinks it is.  Being up 4-3 but pulling means you aren't up at all.  But at the same time the half-score offers something that just pure breaks doesn't allow, an indication of who will win.  True, games are won by the number of breaks you get.  Sure, if you get more breaks than your opponent then you will win the game.  But if we just track breaks then who wins with a score of 0?  The team that wins the flip!  So there is good cause to think that is terms of game states the flip is worth +0.5.

Game state isn't the same as plus minus.  The point of looking at the value of the flip is that it shows you the value of the change of "serve" of the game: +0.5.  So if we treat an offensive hold as +1 (which seems like a good baseline) then we can argue that a break should be worth +1.5.

That is a simple formula.  A players plus minus is: (O-points scored+1.5*D-points scored)/points played.

I suppose we could go with a more mathematically complicated model where we scale the break multiplier based on the number of breaks in a game.  Something along the lines of

(O-points scores+(1.5-0.1*Game D-Breaks Scored)*D-points scored)/points played

This would reduce the value of your break based on the number of breaks in a game.  That kind of makes sense, and perhaps allows the statistic to be used on a wider level of play.  In games where offensive holds are difficult the value of a break would eventually get below 1, making it less valuable than an offensive hold.

So what are we trying to do with this statistic?  The number can only fluctuate between 0 and 1.5 and would seem to measure the value of a point with a person on the field.  Odds are your best offensive players are going to be just above 1.0 while a defender with a number greater than 1.0 is a godsend.

I've got some film to watch to look at PPG in the club division.  Maybe I'll go through some college games and track this or track it while I am following a few club games.