Last week, Brian offered analysis on the new overtime format, particularly on fourth down decisions. The new OT format is inherently state based, as he mentions, and therefore can be modeled adequately by a Markov chain (thanks to some of the commenters for the idea). The Markov property, which essentially states that we only need the most recent event to predict future events, holds true. If we are in a sudden death state, we don't need to know whether both teams kicked field goals or who even received the opening kick in order to make a prediction about who will win the game.
The Set Up
In Brian's post, he discusses three distinct states: Opening of Overtime, The "Matching Field Goal" Drive (where teams get a chance to match or beat after a field goal), and Sudden Death. These will be referred to as Opening, Mid OT, and Sudden Death (SD) respectively from here on. In this Markov model, there will be 10 total states:
1. Pre-Coin Flip
2. Receive Opening Kick
3. Defend Opening Kick
4. Mid OT Offense
5. Mid OT Defense
6. Sudden Death Offense
7. Sudden Death Defense
State 1 is where the model always starts (but you cannot get there any other way) and states 8-10 are absorbing states (meaning once the model gets there, the process is complete and we cannot move to any other states).
Visually, the Markov chain looks like this once you have received the kick (the probabilities are opposite if you start on defense):
I ran my own numbers for the Mid OT states and keep in mind that they are just estimates based on similar historical situations -- down 3 points nearing the end of regulation with enough time left to make an actual drive. We will not know exactly how accurate these estimates are until there is a fairly large sample size of new overtime format games in which the Mid OT state occurs (that could be 5-10 years from now). Also, one assumption for the opening drive numbers is that coaches will not act differently in overtime than they would in regular. This is a large assumption, but it should be true if coaches are making decisions optimally.
We can then do some matrix manipulation to determine the probability of winning, losing and tying for all seven of the transient states (non-absorbing).
Notice that receiving the opening kickoff still has an advantage in the new format. If you kick a field goal on the opening drive, based on our Mid OT estimates, that equates to a 2/3 chance of winning the game. So why is this helpful? Using these probabilities, and especially the transition probabilities, will provide a baseline for overtime decision-making. There are tons of interesting and unexplored questions since the format is so new. Should you kickoff onside to open overtime or Mid OT (debated in the comments of Brian's article)? When should you go for it on fourth down in each state (see Brian's analysis for a good starting point)?
Incorporating time left into the analysis is extremely difficult, but the new format definitely means there is a greater likelihood of tying. In fact, the above tie numbers are only based on the historical sudden death numbers. We can adjust this by looking at the average time left in the new overtime when teams reach sudden death and comparing that to the percentage of historical sudden death games that lasted at least that long. Again, we'll need enough data to accurately calculate expected time left at the start of new sudden death.