Taking shots

Chicks dig the long ball, but if we’re trying to score should we take it?  Zubair thinks you should always take the huck, and he mentioned that he worked out the math behind it.

I independently took a stab at the math behind going for the long ball v. grinding away underneath.  The starting base assumptions here are that teams have a different completion rate on smaller passes than on hucks.  These numbers will be different based on the team’s personnel and the opponent you’re up against.

Chance of completing a short pass:	90%	Chance of completing a short pass:	90%
Number of Shorts to Score:	8	Number of Shorts before Huck:	4
		Chance of Completing Huck:	75%
Odds of score:	43%	Odds of score:	49%

Alright where am I getting these numbers from?  A field is 70 yards, if we manage to gain on average about 10 yards each throw then that’s something like 8 passes (factoring the pull making it to the endzone).

Matt “Goose” Pasienski said good offense takes 45 seconds to score and I think you should throw around stall 4; that yields about 12 passes to score.

Chance of completing a short pass:	90%	Chance of completing a short pass:	90%
Number of Shorts to Score:	12	Number of Shorts before Huck:	4
		Chance of Completing Huck:	75%
Odds of score:	28%	Odds of score:	49%

I think that expecting your oline to score a clean point 28% is not that crazy of an expectation.  I also think that a 90% completion rate is a rough guess; screwing up 1 in ten passes feels about right.  But, I think a far more conservative guess is we screw up 1/7.

Chance of completing a short pass:	86%	Chance of completing a short pass:	86%
Number of Shorts to Score:	12	Number of Shorts before Huck:	4
		Chance of Completing Huck:	75%
Odds of score:	16%	Odds of score:	41%

Alright at this point it is overwhelming that we should go for the huck every time we can.  75% is massively high though, I am trying to remember the best hucking percentage I can, and I am thinking Kennedy was able to complete 2 in 3 to Dane back in the hay day, certainly I’ve never been on or around a team with a better completion than 66%.

Chance of completing a short pass:	86%	Chance of completing a short pass:	86%
Number of Shorts to Score:	12	Number of Shorts before Huck:	4
		Chance of Completing Huck:	66%
Odds of score:	16%	Odds of score:	36%

Alright so this drops pretty quickly.  What if you’re NUT 2015 and your completion percentage is 20% at best?

Chance of completing a short pass:	86%	Chance of completing a short pass:	86%
Number of Shorts to Score:	12	Number of Shorts before Huck:	4
		Chance of Completing Huck:	20%
Odds of score:	16%	Odds of score:	11%

Suddenly this is looking like we should definitely not take shots.  We should probably take this out of the vacuum and consider how taking a shot can affect your next possession.  First I will need to make another big assumption.  How many passes does it take to score based on field position:

Yards away:	Passes needed to score:
70	12
60	12
50	11
40	10
30	8
20	6
10	4

This is just a decay function, where the redzone has the highest weight of passes needed to score.  To me this is intuitive since the defense has the smallest amount of space needed to score, it should take relatively more passes to cover that smaller space.

So if we take a shot and miss, then we have to get a d.  Another massive assumption here: What is our chance of getting a D at different distances from the goal?

Yards to defend:	Chance of getting a D:
70	2%
60	5%
50	10%
40	15%
30	20%
20	30%
10	45%

Again these are all very rough numbers that will depend on how good your team is.  How do I justify these numbers?  Using the inverse!  The chance we don’t get a D is just 1 minus column 2.

Yards to defend:	Chance of getting a D:	Chance they don't turn it from here:	Chance they eventually score:
60	5%	95%	22%
50	10%	90%	24%
40	15%	85%	26%
30	20%	80%	31%
20	30%	70%	39%
10	45%	55%	55%

To me these numbers feel right.  I think teams score on NUT about 22% of the time they have to go the length of the field.  I think I am overvaluing NUT’s redzone defense, but I don’t feel like measuring this at all.  Anyway, I take comfort in my estimates by seeing the chances the other team will eventually score.

Alright so if we can get a d with 60 yards to defend, then we will have 10 yards to score and only need 4 passes.  That looks like the chart below.

Yards to defend:	Passes needed to score if we get the D:
60	6
50	8
40	10
30	11
20	12
10	12

Let’s start stacking these numbers:

Yards to defend:	Chance of getting a D:	Passes needed to score if we get the D:	Chance of scoring off the D:	Total Chance of scoring:
60	5%	6	40%	2%
50	10%	8	29%	3%
40	15%	10	21%	3%
30	20%	11	18%	4%
20	30%	12	16%	5%
10	45%	12	16%	7%

Suddenly this doesn’t look so good, and it feels like we should just grind underneath and try to maintain possession and score.  I believe the boost in odds of scoring by getting better field position is offset by the odds that we don’t get that D.

The art lies in understanding that these odds are constantly changing.  The factors of the game, your personnel against the other team, put these in constant flux and having some kind of unconscious gauge over them can help you take shots that are beneficial to them team.  If your teams completions on small passes is dipping below 2/3 you should probably start launching it and hoping for the best, if your connecting anywhere over ½ of your hucks again I think you should let it fly.

This is pretty clearly a case of confirmation bias out of me.  The way I want to play ultimate is to hold onto the disc and maintain possession, I think we should pour our effort points into improving the “Chance of completing a short pass:” category.  I don’t think the value of getting field position is worth it to take a bad huck.  Ultimate in my mind is a game of possession, the team that can complete more passes has the better chance of winning.