This is a trial post for what will be a weekly series on Field Gulls this season. I’m doing a test run with a game from last year to see how it’s received. In anticipation of the season starting, I chose last year’s opener when the Seahawks hosted the Dolphins and won 10-12.

## Let’s talk about game theory

Actually, this isn’t game theory, but it’s still a bit math-heavy. I promise we’ll get to the football soon, but first, a math lesson (from Wikipedia):

The expected value of a discrete random variable is the probability-weighted average of all possible values. In other words, each possible value the random variable can assume is multiplied by its probability of occurring, and the resulting products are summed to produce the expected value

We’re going to be talking about *expected *points, where the *expected* is the same *expected *as in *expected* value (I bet this isn’t what you expected). We’ll get to the “probability-weighted” part soon.

**#10. Q4 1-10 SEA 31: (4:28) (Shotgun) R.Tannehill pass short left to D.Williams pushed ob at SEA 2 for 29 yards (B.Wagner).**

Miami has the ball 1st and 10 from the Seattle 31. At this position, using past seasons of data to compute the probability of each event being the next scoring play given down, distance, and field position:

- There’s a 33% chance the next score is a Dolphins FG
- 41% Miami TD
- 3% Seahawks FG
- 5% Seattle TD

Obviously, these probabilities are favorable for the Dolphins because they have the ball 1st and 10 on Seattle’s side of the field, so it is extremely likely that they will be the next team that scores. For simplicity, let’s assume that the only possible ways to score are touchdowns and field goals (this omits things like safeties and 2 point conversion returns). So the *expected points *from the perspective of the team with the ball is the sum of [point value * probability] across all the types of scoring plays. Assuming 7 points for TDs for simplicity, with p(event) denoting the probability that an event happens:

Expected points =

p(MIA FG) * 3 + p(MIA TD) * 7 + p(SEA FG) * (-3) * p(SEA TD) * (-7) =

0.33*3 + 0.41*7 + 0.03*(-3) + 0.05*(-7) =

3.42 (expected points for Miami)

The negative signs on the probabilities of the Seahawks scoring are because them scoring is bad from the perspective of the team with the ball (Miami). Going back to the actual play at hand, this play moves the ball from the Seattle 31 to the Seattle 2 and increases Miami’s TD likelihood from 41% (prior to the play) to 80% (after the play) and expected points from 3.42 (prior to the play) to 5.88 (after the play), making the *expected points added *2.46 (the difference between 3.42 and 5.88).

**#9. Q3 2-7 MIA 44: (14:08) (Shotgun) R.Tannehill sacked at MIA 35 for -9 yards (M.****Bennett****).**

*EPA:2.48. WP before: 54. WP after: 62. TD prob before: 40. TD prob after: 26*

Throughout this series, win probability (“WP”) will refer to the likelihood that Seattle wins, with WP from before and after the given play shown. “TD prob” is the probability that the next score is in favor of the team that currently has the ball. In this play, we see that a drive-ending Michael Bennett sack reduces the probability that the next score is a Miami touchdown.

**#8. Q4 4-4 SEA 47: (2:08) (Shotgun) R.Wilson pass short left to D.Baldwin ran ob at MIA 31 for 22 yards (I.Abdul-Quddus).**

*EPA:2.74. WP before: 21. WP after: 42. TD prob before: 12. TD prob after: 36*

This 4th down conversion kept the Seahawks in the game, increasing their win probability from 21% to 42% in one play. It also illustrates why I’ve chosen to use EPA instead of WPA for this series: WPA is subject to wild swings at the end of games, so using EPA instead allows for a better range of plays throughout the game. This play ranks #8 in EPA but #2 in WPA.

**#7. Q1 3-12 SEA 31: (10:04) (Shotgun) R.Wilson pass short right to C.Prosise to SEA 44 for 13 yards (K.Alonso; I.Abdul-Quddus).**

*EPA:2.92. WP before: 48. WP after: 57. TD prob before: 28. TD prob after: 44*

Converting on 3rd and long is relatively rare so the EPA model really likes this play even though it’s a relatively forgotten 1st quarter conversion. In the first NFL game, C.J. Prosise gave a taste of what he can provide as a 3rd down threat who can take a dump off for a 1st down.

**#6. Q1 4-1 SEA 17: (1:21) A.Foster up the middle to SEA 17 for no gain (K.Chancellor).**

*EPA:3.14. WP before: 53. WP after: 58. TD prob before: 19. TD prob after: 26*

The change in expected points here is close to the difference between the field goal Miami could have kicked and the zero points they ended up with.

**#5. Q2 3-5 SEA 23: (11:01) (Shotgun) R.Wilson pass deep right intended for L.Willson INTERCEPTED by I.Abdul-Quddus [J.Jones] at MIA 49. I.Abdul-Quddus to SEA 42 for 9 yards (L.Willson).**

*EPA:3.32. WP before: 56. WP after: 51. TD prob before: 25. TD prob after: 8*

A bad decision from Wilson here. And who could ever forget the outcry after this hit on Russell Wilson:

This looks not legal at all pic.twitter.com/3ip2y7ti0b

— Ben Baldwin (@guga31bb) September 12, 2016

*crickets*

**#4. Q4 4-9 SEA 9: (10:45) A.Franks 27 yard field goal is BLOCKED (C.Marsh), Center-J.Denney, Holder-M.Darr.**

*EPA:3.55. WP before: 53. WP after: 62. TD prob before: 1. TD prob after: 21*

I completely forgot about this play until I did this but now I remember all those “HAVE A GAME, CASSIUS MARSH” tweets.

**#3. Q3 4-1 MIA 31: (5:02) (Shotgun) R.Wilson pass incomplete short right to D.Baldwin (I.Abdul-Quddus).**

*EPA:3.64. WP before: 66. WP after: 57. TD prob before: 24. TD prob after: 21*

A failed 4th down conversion from field goal range. Seattle was up by 3 at the time, making this a bit of a weird decision. This was a disaster of a 4th down play, too: ~~Maybe they should have run the ball with Marshawn here.~~

**#2. Q1 3-6 MIA 24: (3:48) (Shotgun) R.Tannehill pass short left to A.Foster pushed ob at SEA 26 for 50 yards (K.Wright).**

*EPA:4.61. WP before: 62. WP after: 48. TD prob before: 28. TD prob after: 52*

I think Earl Thomas missed a tackle here. Well, I miss Earl.

**#1. Q4 2-9 SEA 44: (15:00) R.Wilson FUMBLES (Aborted) at SEA 37, RECOVERED by MIA-K.Alonso at SEA 38. K.Alonso to SEA 36 for 2 yards (G.Gilliam).**

*EPA:5.98. WP before: 67. WP after: 50. TD prob before: 39. TD prob after: 8*

And the most impactful play of the game in terms of expected points is created by Suh blowing up Mark Glowinski so that Wilson trips over him. For Week 1 2016, Jordan Phillips is “Ben’s Big Baller of the week.”

## Going forward

As you have probably figured out by now, this was a completely data-driven list of the 10 top plays as measured by EPA from the week 1 Dolphins-Seahawks game, with number one being the biggest play by EPA. There’s no discretion at all: I just press a button on my computer and out pops this list. If you think there’s a better way to do this, let me know in the comments or on twitter:

- Is 10 plays too many? Not enough?
- Should I split plays into offense and defense? Include a set number of each?
- Do you want to see both the positive and negative plays? How many people would want to read a list dominated by negative plays after a game the Seahawks lost?
- Should I include replays of every single play? Or just the ones I find most interesting?

As a final note, this is made possible by Ron Yurko’s work on the #nflscrapR project, so a big thanks to him and the others who have been working to make NFL statistics more accessible.