What do we mean by win probability?

We talk 'win probability' on this site, so it's about time we say a little about what we mean when we use this term. What we don't mean is betting odds, although we understand that is what it sounds like.

Our aim has been to create a statistic which estimates the probability that a generic, 'average' team would win lose or draw from a given match situation (e.g. 173/3 after 45 overs on day 1, or 61/5 in the second innings having carried over a hundred run lead from the first), against another generic team in a particular run environment (climate, country or even ground). This means that prior to a match between Bangladesh and South Africa at Durban, both teams have the same 'win probability'.
Bet on the basis of WPA at your peril!
[a side note- in terms of draw probability, the model also assumes that all overs that can be played will be played; so rain delays cause changes in WPA as they happen, and overs are permanently lost. The model doesn't care for weather forecasts. See more discussion here].

So, we're not trying to replicate or beat the betting odds; we're trying to provide a measure of who contributes to winning.
What would happen if we did use the betting odds? If South Africa were 4/1 on at the start of their match against Bangladesh, they are estimated to start with an 80 percent chance of winning. This means that if they do go on to win, the players can only stand to share (in aggregate) 20% of a win. Surely that's not fair- after all it's because the Proteas are so good that they carried such short odds in the first place! Moreover, if the betting odds were indeed perfectly representative of win probability, over time the aggregate win probability added for each team would be zero. Team WPA would only be a testament to how accurate the odds were, and not how well a team has performed in absolute terms!

In our system, teams are measured against 'generic' sides and so, over time, good teams will earn positive WPA in aggregate, and bad teams will accrue negative WPA in aggregate.
But that's not the real point (we already know which team ends up winning!). The real point is to identify which player or players earned the wins. How much of a win does Hashim Amla contribute relative to a batsman from a 'generic' team in a South African run environment? How much of a win does Dale Steyn's second innings five-for contribute, compared to a 'generic' bowler? Maybe it swung the match, or maybe the game was already won?