Thursday, November 26, 2009

Thoughts on NFL Overtime

It is apparent to many observers of the NFL that the current overtime system (coin toss to determine which team kicks off, first points thereafter decide the game) is flawed. In a large number of cases, the team who receives the opening kick scores on this first possession, ending the game before the other team has had a chance at an offensive possession. Overall, teams winning the toss won 60% of all OT games between 2000 and 2007 (http://www.advancednflstats.com/2008/10/how-important-is-coin-flip-in-ot.html) and 59% of all OT games from 1994-2003 (http://www.footballcommentary.com/otauctions.htm). This means that a team will gain or lose 10% of win probability depending on a completely random event, clearly an unpalatable state of affairs. But it's worth examining the issue in more detail, as it is not as easy a case to resolve decisively as it may appear at first, and it gives rise to some interesting considerations along the way.

1) Proponents of the current system often attempt to entirely dismiss the primary objection - that the game can be decided without both teams having possession - by saying that the losing team in this scenario should have "played some defense." This is line of reasoning is obviously inadequate. It rests on the fallacy - still all too common in sports discussions - of treating game events as arising deterministically, rather than probabilistically, from the actions of the players. The fact that a team allows a score on a given possession does not necessarily imply that their performance was in any way sub-par; it is perfectly possible to perform at an average level - or even above this - and still suffer a reversal due to the random breaks of the game. (Note that these are not random in the strict quantum mechanical sense - but are determined by margins that are too fine to be precisely correlated with physical and/or mental actions of the players.) A given level of performance implies a probabilistic distribution of game outcomes, and vice versa. In the absence of further information, the end result of one possession is much too small a sample to infer anything about how well either team played. In general, NFL teams score on around 30% of their possessions. This does not mean that teams "played some defense" 70% of the time, and failed to do so on the other 30%. A good defensive performance on a possession may reduce the average probability of a score to 25% or 20%, but it does not reduce it to anywhere near 0% - that's just not how the world works. So even if the defensive team does all that can be asked of them on the first overtime possession, they have still been exposed to a substantial risk of losing immediately, while their opponents have faced only the comparatively trivial risk of losing on a turnover retured for a score.

2) Opponents of the current system often introduce a red herring into the discussion by calling it "unfair." As those who support the system tend to gleefully point out in response, this is not correct - both teams have an equal shot at the advantage resulting from the coin toss, so no fairness criteria are violated. A more precise way to state the objection is that the result of the game is highly influenced by an exogenous factor. After all, a system that determined the result of a game that was tied at the end regulation entirely by a coin toss (winner of the toss wins the game, no OT play at all) would be fair to both teams - but it would also be pretty stupid. One of the most important goals in constructing rules for a game should be to ensure that the greatest predictor of success is performance across a set of related skills. Some element of physical randomness is unavoidable (see #1 above) and even desirable. But introducing external random factors - such as coin tosses - into situations where they have a large impact on the outcome unnecessarily weakens the correspondence between performance and result.* If one were to graph the win probability of both teams over the course of the game, one of the largest single-event changes would result from the OT coin toss - it would rank alongside the game's biggest plays, and those in the "clutchiest" of situations, as one of the most significant events in determining a winner. When considered in these terms, the objection to the coin-toss/sudden death system should be obvious.

3) Even with the validity of the objection established, commonly-suggested alternatives often introduce flaws of their own. The most obvious possibility - stipulating an equal number of possessions for each team - risks making the game last substantially longer, exposing the players to greater risk of injury and (silly as this consideration sounds) interfering with TV scheduling. It also increases the possibility of the game ending in a tie, which many NFL fans seem to find an insufferable proposition. On the other hand, resorting to alternating possessions from the 25-yard line, as in NCAA football, offends football purists who deplore such gimmickry.

4) As a result, it may seem that we are trapped in a "de gustabus non disputandum est" situation, where every possible solution has its own strengths and weaknesses, and it is a matter of taste whether one prefers the current system or one of the alternatives. However, we could circumvent this problem if we were able to state the major objectives of an optimal overtime system, and present solutions that dominate the current system by performing equal or better in all categories. It seems to me that the main criteria are:

1) Minimize the probability of a tie
2) Minimize the amount of time it takes to reach a result
3) Minimize the effect of exogenous factors on the determination of the result
4) Maximize the similarity between OT and regulation play (i.e. avoid gimmicks)
5) Maximize "excitement" (the subjectivity of this criterion means that it can probably serve as a catch-all for all other specific criteria that one might think of)

Clearly, the current system does pretty well at 1, 2, 4 and 5. Solutions involving equal possessions or a fixed-time OT period improve on 3, but at the cost of a decline in 1 and 2. So whether one prefers these alternatives to the current system depends on how much weight one assigns to 1-3 on the list above. This makes it hard for supporters of the respective solutions to make any progress in persuading the other.

But there seem to be good candidates for solutions that dominate across all five criteria:

1) Simply extend the fourth quarter. When time runs out in the fourth quarter with the game still tied, add 15 minutes to the clock, and continue play as before, with the next points deciding the game. This still gives one team the advantage of having the first opportunity to score, but the difference here is that there is no exogenous factor - the advantage is built-in to the game state at the end of the fourth quarter, such that both teams have ample time with which to factor it into their plans earlier in the game. Not only is a coin flip not responsible for a sudden spike in win probability - there is no spike in probability at all. (To confirm this, consider that the last moments of regulation are de facto sudden death, as there will be no time left for a score in response. So if a team keeps possession across the nominal end of the fourth quarter and into overtime, their win probability will not change, except to increase as their distance to field goal range decreases.)

So this possibility obviously does at least as well as the current system in categories 1, 2, and 3. In my opinion, it gets a particular added boost from its performance in category 5. Under the current system, a team driving down the field with little time left, trailing by 3 or 7 points, will often play for a tie, taking their 50% chance of winning in overtime minus whatever chance there is that their opponent scores in regulation. Under the extended fourth quarter overtime scenario, teams in this situation would know that the opponent would in effect be guaranteed to win the overtime coin toss, giving them greater incentive to play for an outright win in normal time. Teams trailing by 3 with a minute remaining might forego a 30-yard field goal on 4th and 2, and play for a touchdown instead, and teams who score a late touchdown when trailing by 7 may choose to attempt a two-point conversion. The decisions made by coaches in such situations are often excessively conservative, failing to maximize win probability (as well as being relatively boring.) It is therefore a beneficial secondary consequence of this overtime system that it would give them a nudge in the right direction. Besides being more exciting and representing less frustratingly bad decision-making, this incentive to play for a win also feeds back into the second criterion, making it more likely that the game will end sooner, without any extra time played at all.

Several people have objected that this system would take away the two-minute drill at the end of a game, as teams now know that with the ability to continue a possession beyond the end of the quarter, they now have no reason to hurry. But this only applies to situations where the game is tied - teams trailing by anywhere from one to eight points would still have to run their two-minute offense. And when the game is tied, the two-minute offense only has to reach the opposing team's 30-yard line in order to have a decent shot at a winning field goal. Is this really the most exciting thing in the world? (Perhaps Patriots fans have reason to be a little biased on this question, recalling SB XXXVI). In any case, this consideration is also counterbalanced by the fact that it avoids a situation where a team is pinned deep in their own territory late in the game decides to run out the clock and play for overtime rather than attempt to do anything with the final possession of regulation (what John Madden thought that the Patriots should have done.)

2) The key feature of the extended fourth quarter system is that both teams know which team will have the first chance to score in the sudden death period, before this period starts. This allows them to spread the win probability deficit out throughout many game events throughout regulation, and allows them to increase their chance of overcoming it entirely through the decisions they make. Therefore, overtime systems that make use of this principle allow us to keep the sudden death feature (which cuts down on time and on ties) without the ugly spike in win probability that occurs when one team suddenly finds out that they are the first to have their heads on the chop block (no pun.) There are other ways to accomplish this: giving the first overtime possession to the home/road team, performing the OT coin flip at half-time, and having the opening coin flip count as the OT coin flip are the most obvious. In both cases, the team who will be at a sudden-death disadvantage may have slight incentive throughout the game (or the second half in the case of the half-time flip) to unbalance the score by attempting two-point conversions in situations where they otherwise would not. This could be kind of cool, though I still prefer to give the incentive to unbalance the game to the team who trails last. Retaining the coin flip, either at the outset of the game or at halftime, allows the overtime period to begin with a kickoff, which might be construed as superior performance in the fourth criterion, and takes care of the two-minute drill problem (though it allows teams in some cases to sit on the ball and force overtime, as in the current system.) Personally, the extended fourth quarter remains my favorite of these possibilities.

3) Another solution entirely is to keep the sudden death element of overtime, but to determine possession by bidding on field position. For a full discussion of this, see http://www.footballcommentary.com/otauctions.htm. It could be maintained that this is subpar according to the fourth criterion, as it involves a coaching decision the like of which never appears at any other point in a football game. But it fulfills the basic requirement of dominating across the first three categories without resorting to anything excessively foolish, and therefore would be a better choice than the current system.

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