# Playoff Matchup Specific Win Probabilities

Apr 1, 2015; Milwaukee, WI, USA; Chicago Bulls guard Jimmy Butler (21) drives for the basket as Milwaukee Bucks forward Giannis Antetokounmpo (34) defends during the first quarter at BMO Harris Bradley Center. Mandatory Credit: Jeff Hanisch-USA TODAY Sports

As the regular season is coming to an end, a lot of pairings are still not decided. While there is still a complete mess in the Western Conference, the dust in the Eastern Conference seems to have at least partially settled.

One open question are the matchups between Chicago, Toronto, Washington and Milwaukee, where both Chicago and Toronto are still playing for the 3-seed and the honor to play Milwaukee. Most of the Milwaukee fans that I follow on Twitter are very vocal about preferring to play Toronto over Chicago[1. Okay, it’s only one guy. But @tpcourier is VEEEERY vocal about it.]. The reason is mostly subjective. Toronto is observed as a bit of a train wreck at the moment and the Bulls are perceived as harder opponent.

If you would look at a very simple model[2. Using the methods described here] that basically uses the offensive and defensive efficiencies of Chicago, Toronto and Milwaukee, this arguments would not hold. In this model, Milwaukee would have a 45.3% probability to win a game against Chicago and only a 42.4% probability to win against Toronto (both on a neutral field). But if we were to adjust those probabilities by the team’s tendencies and strengths we might see a different picture.

The following is a very crude method and you should not be gambled upon, but using NBA.com information about team play types (both defensive and offensive), we can calculate match-up specific win percentages. My very crude method would estimate that Milwaukee wins only 41.0% of games against Chicago, but 43.8% of games against Toronto. So the roles are basically inversed, the biggest difference being a 4.3% decrease of winning probability against Chicago.

To visually explain the method[3. The play-type data has defined 11 different play types (transition, cuts, PnR ball handler, PnR roller, spot ups,…). For each team information, about the offensive and defensive frequency and points per possession are available. Using this information, we can calculate the play-type adjusted offensive efficiency of team A vs team B as

You can now calculate formulas for each team which can then be plugged into other formulas that spit out a win percentage.

I am not very proud of this formula and it should not be used for serious things. For example, you can in theory get negative values for PPT and frequency. I basically used it because the numbers add up relatively well, meaning that in the end the frequencies of all 11 play types for a matchup sum up to 100%. Plus, if a defense allows a play with an average frequency or allows an average amount of points per possession, you would expect the offense to get to their own average.], let’s look at few of the play types and specifically how many points teams score or allow per 100 possessions. Let us start with an example where Milwaukee could get an advantage over Toronto: scoring on and defending against isolation plays:

The main information here is basically: Toronto is the team that scores the second most points per 100 possessions out of isolations of anyone in the league. Chicago barely scores out of isolations. Milwaukee (aka “the Kraken”) is the team that allows the 4th fewest points out of isolations – therefore Milwaukee probably has the possibility to limit one of Toronto’s strengths. But the biggest influence can probably be seen in how many points per 100 possessions are allowed to pick-and-roll ball-handlers, one of the three play types where most teams score more than 10 points per 100 possessions (the other two being transition and spot up shooting):

We see several things here. First of all, Milwaukee does not allow the pick-and-roll ball handler to score. Second, Toronto’s ball-handlers likes to score (increasing Milwaukee’s estimated winning percentage against Toronto). Chicago, on the other hand, allows a lot of points by the ball-handler (because they stay at home against rollers, cutters and spot-up shooters). Unfortunately for Milwaukee, this is not at all their strength.

From a qualitative standpoint one could summarize the situation as follows. Milwaukee is good at containing the direct threat (isolation player and pick-and-roll ball-handlers) – something that you would expect from a young athletic team with Pterodactyl arms. Chicago on the other hand is one of the prime examples of teams that do not over-help, but instead shuts down cutters and spot-up shooters – and Milwaukee might not be the team that makes them pay for it.

So in this example, the eye test and my crude analysis works perfectly. I am pretty sure that his is not always the case. I’ll post more once the Playoffs start, but once again: handle with care!