Troy Polamalu is one of my favorite players in the league. As a Ravens fan whose heart despises everything that is black and gold, I'm compelled to say that he is truly spectacular. (The picture to the left is his interception return for a touchdown that saved the AFC Championship game for Pittsburgh last year.) He's also a classy and selfless player who never showboats, a breath of fresh air in today's NFL. Unfortunately for Steelers fans, his injury this season has revealed just how great a player he is.
Polamalu has played in five games this season and has missed nine. Using the Win Probability (WP) model, we can calculate the Win Probability Added for any play (WPA). We can also sum WPA for any team, squad, or player to estimate the context-dependent contribution of that player to his team's chances of winning.
WPA for defensive players is particularly problematic. If a running back evades all ten other defenders but is tracked down 60 yards later at the 5-yard line by the eleventh, it's the tackler that will show up in the play-by-play and be charged with the loss in WP. That doesn't make sense.
But Polamalu's 2009 season provides us with a special opportunity. We can measure the WPA of the entire Steelers defense when Polamalu is playing and compare it to the WPA of the Steelers defense when he's not.
Essentially, this is a synthesis of two different concepts in advanced sports statistics: WPA and Plus/Minus. Win Probability Added may be familiar to readers here or to baseball sabermetric fans, but Plus/Minus may only be familiar to basketball and hockey fans. For example, in hockey, when a goal is scored, every player on the ice for the scoring team is credited with a plus, while every player on the ice for the team scored against gets a minus. This kind of stat is particularly useful for a player like a safety, who can deter a play by his very presence without actually defending a pass or making a tackle. He makes it easier for a teammate to make a play. This is also sometimes called a 'WOWY' stat--'With Or Without You.'
Combining these two concepts gives us WPA+/-, defined as the sum of the increases and decreases in WP for a player's team while he's on the field. For the vast majority of NFL players, this concept has very limited application. But when an undisputed difference-maker like Polamalu is suddenly sidelined, we can get a good idea of just how valuable he is.
For the five games in which Polamalu has played, the Steelers defense posted a -2.39 WPA, an average of -0.49 WPA/game. (Negative values are good for defenses.) To put that in perspective, a team starts with a 0.50 WP, so a net of another 0.50 WPA can add up to a win. You could say the Steelers defense, all by itself, could have won those five games with only a modest contribution from their offense.
In the nine games Polamalu has missed, the Steelers defense posted a +1.05 WPA, an average of +0.12 WPA/game. Losing Polamalu takes the Steelers defense from close-to-unbeatable to below-average.
You could say Polamalu has been worth a 0.61 WPA/game for Pittsburgh. Certainly part of that difference could be due to random variation or opponent strength, but it's very hard to discount the contribution of such a dynamic player. I bet if you polled the Steelers coaching staff, or their opponents' coaching staffs, they'd agree with this analysis.
The game-by-game breakdown of the Steelers defense WPA is provided in the table below. Games in which Polamalu participated are denoted by the asterisk.