Tuesday, December 22, 2009

Giants: Playoff hopes

What follows is a lesson in conditional probability and when to discard theory in favor of practical reality. The Giants are one game behind the Packers and Cowboys for the last wildcard spot and own the tiebreaker against both of them. Therefore, they need to win one more game than one of these two teams in order to make the playoffs. Put another way, both the Cowboys and the Packers need to win both of their games in order to shut the Giants out. In the abstract, suppose each game were a coin flip with a 50% chance of each team winning. Then the probability of all four games going against the Giants, i.e.both Packers and Cowboys going 2-0, would be 1/2 raised to the 4th power, or 1/16, which equals 6.25%. Those are pretty good odds for the Giants to have a window open to the playoffs. However, these games are clearly not coin flips, with each team having an equal chance of winning. Packers will be heavy favorites in both games and Cowboys will be heavily favored in one of their games. For arguments sake, let's install the Packers and Cowboys as prohibitive favorites in all 4 games and give them a 75% chance of winning each of the 4 games. In that case, the overall probability of both teams winning both of their games, is only 31.6%. If we were to lower the probability a little bit and assign the favorites a 60% chance of winning each game, then the probability of both teams winning out goes way down to 12.9%. From a purely mathematical point of view, then, if the Giants win their last two games, they would have a good chance of getting in.

However, you have to look a little closer at the matchups in each of these games and decide what the chances are for the opponents to win one of those games. Here are the relevant games on the schedule:

Vikings Schedule
Vikings @ Bears Monday night
Giants @ Vikings

Cowboys Schedule
Cowboys @ Redskins Sunday night
Eagles @ Cowboys

Packers Schedule
Seahawks @ Packers
Packers @ Cardinals

Giants Schedule
Panthers @ Giants
Giants @ Vikings

Eagles Schedule
Broncos @ Eagles
Eagles @ Cowboys

Let's look at the Packers first. Their first game is against the awful Seahawks, who are 5-9, have absolutely nothing to play for and got crushed at home last week by the 1-12 Buccaneers. Even though I assigned a nominal probability of them to beat the Packers of 25%, it is realistically quite a bit lower than that. The Packers last game of the season is on the road against the Cardinals. If this game were in the middle of the season, I would give the Cardinals a good chance to win. But Arizona has 9 wins and, unless the Vikings lose to the Bears this week, they are locked into the 4th seed in the NFC. They will surely rest Warner, Fitzgerald and some of their other starters who may be a little nicked up. This is especially true, because if the Packers make the playoffs, it is extremely likely that the Cardinals and Packers will meet in the first round, which means that they would play each other two consecutive weeks. Why then, would the Cardinals play their starters against the Packers in the last week of the season and let the Packers players get a read on how to play them. The Cardinals will probably mail it in on that last week of the season against the Packers.

Next, let's look at the Cowboys remaining games. They play the Redskins on the road next Sunday night and considering how awful the Redskins looked against the Giants Monday night, it's hard to imagine that they will put up much of a fight, no matter what happened the first time these two teams met. Cowboys are playing much better now after beating the Saints last week. Even if you assert that the Saints level of play has declined somewhat the last few weeks, the Cowboys played well and confidently and have surely broken the doldrums of their December curse. That means the best chance for the Cowboys to lose and the best chance for the Giants to make the playoffs is for the Cowboys to lose the last week of the season to the Eagles in Dallas. The Eagles will have some motivation to win that game and will probably not lay down. If the Eagles were to lose to the Cowboys, it would mean that the Cowboys would win the division and the Eagles would be only a wildcard. Consequently, the Eagles would not host a home playoff game and would have to go on the road in the first round. In fact, a likely matchup for the Eagles would be the Cowboys, if both teams make the playoffs. This means that, as with the Packers-Cardinals, the teams would play each other two weeks in a row, in week 17 and in the first round of the playoffs. Eagles, then have a lot to play for: if they lose to the Cowboys, they would have to play the Cowboys again in Dallas. On the other hand, if they beat the Cowboys, they would get to play the Giants in Philadelphia, a team they have handled 4 times in a row. Their motivation would be high, since the playoff matchups would be much better for them if they win.

All of this is predicated on the fact that the Giants will win their last two games, far from a certainty. In the remote circumstance that the Bears beat the Vikings this Monday night, then (assuming the Cardinals beat the Rams in week 16) the Vikings and the Cardinals would be only 1 game apart going into the last week. If the Giants beat the Vikings, then the Cardinals would have great motivation to beat the Packers. In this scenario, the Cardinals and Vikings would then be tied at 11-5 and since the Cardinals own the head-to-head tiebreaker having beaten them in week 13, they would be elevated into the 2 seed, which would give them a bye in the first round and a home game in the second round. Root for the Bears agains the ikings this weekend.

Returning to the probability model above, let's assign the following probabilities to the Cowboys and Packers winning their last two games.

Cowboys vs. Redskins: Probablity of Cowboys winning = 75%
Cowboys vs. Eagles: Probability of Cowboys winning = 55%
Packers vs. Seahawks: Probability of Packers winning = 90%
Packers vs. Cardnials: Probability of Packers winning = 90%

If you accept the above probabilites for each individual game, then the cumulative probability of both Packers and Cowboys going 2-0 and closing the window on the Giants playoff hopes is 30.375%. In other words, if the Giants win both their games, they have a nearly 70% chance of making the playoffs.

My head hurts from all these mathematical calculations. Giants have to win out and hope something good happens for them. The weirdest possible result of this NFC playoff race would be if both wildcard games would be repeats of week 17 matchups: Cardinals-Packers and Eagles-Cowboys.

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